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VIEWS: 66 PAGES: 285


   Edited by:

  Musa Akrami
    Second Edition

    1384 / 2006
      Physics and Philosophy                                          Musa Akrami

   Table of Contents
   Preface to Second Edition
   Chapter1. A Brief history and philosophy of physics
   Introductory remarks
     1. 1. Earliest beginnings, and the Greeks
     1. 2. The Dark Ages, and the Translations
     1. 3. The Middle Ages
     1. 4. The Renaissance (1300-1700)
     1. 5. Development of the scientific method
     1. 6. The development of classical physics: Mechanics, Thermal physics,
          Optics, Electromagnetism, and Atoms
           1. 6. 1. Mechanics
           1. 6. 2. Thermal physics
           1. 6. 3. Light and Optics
           1. 6. 4. Electromagnetism
           1. 6. 5. Atoms
     1. 7. Modern physics: Relativity and Quantum physics
           1. 7. 1. Relativity
           1. 7. 2. Quantum physics
     1. 8. The unification of physical phenomena

   Chapter2. The Uncertainty Principle
    2. 1. Introduction
    2. 2. Heisenberg
           2. 2. 1 Matrix mechanis and wave mechanics
           2. 2. 2 Heisenberg's argument
           2. 2. 3. The interpretation of Heisenberg's relation
           2. 2. 4. Uncertainty relations or uncertainty principle?
    2. 3. Bohr
         Bohr's view on the uncertainty relations
    2. 4. The minimal interpretation
Chapter3. Copenhagen interpretation of Quantum mechanics
    3. 1. The background: Bohr’s model of hydrogen atom
    3. 2. The principles violated in classical physics
    3. 3. The Correspondence Rule

      Physics and Philosophy                                            Musa Akrami

     3. 4. Complementarity
          3.4. 1. From wave-particle duality to complementarity
          3.4. 2. Summary of Bohr's more mature view
          3.4. 3. Bohr’s philosophical tendencies

Chapter4. Philosophical and foundational issues in Quantum theories

Chapter5. The Einstein-Podolsky-Rosen argument in Quantum theory
    5. 1. Can quantum mechanical description of physical reality be
  considered complete?
         5. 1. 1 Setting and prehistory
         5. 1. 2. The argument in the text
         5. 1. 3. The key features of EPR
         5. 1.4 Einstein's versions of the argument
    5. 2. A popular form of the argument: Bohr's response
    5. 3. Development of EPR
         5. 3. 1 The Bohm version
         5. 3. 2 Bell and beyond
Chapter6. Bohmian mechanics
    6. 1.The completeness of the quantum mechanical description
    6. 2.The Impossibility of hidden variables ... or the inevitability of
    6. 3. History

   Chapter7. Early Philosophical Interpretations of General Relativity
    7.1. The Search for Philosophical Novelty
    7. 2. Machian Positivism
         7. 2. 1. In the Early Einstein
          7. 2. 2. A "Relativization of Inertia"?
           7. 2. 3. Positivism and the "Hole Argument"
           7. 2. 4. An Emerging Anti-Positivism
     7. 3. Kantian and Neo-Kantian Interpretations

   Physics and Philosophy                                         Musa Akrami

       7. 3. 1. Neo-Kantians on Special Relativity
       7. 3. 2. Immunizing Strategies
       7. 3. 3. Rejecting or Refurbishing the Transcendental Aesthetic
      7.3. 4. General Covariance: A Synthetic Principle of "Unity of
 7. 4. Logical Empiricism
       7.4. 1. Lessons of Methodology?
       7. 4. 2. From the "Relativized A priori to the "Relativity of Geometry"
       7. 4. 3. Critique of Reichenbachian Metric Conventionalism
 7. 5. "Geometrization of Physics": Realism and Transcendental Idealism
        7. 5. 1. Differing Motivations
        7.5. 2. "Geometrizing" Gravity: the Initial Step
       7.5.3. Extending "Geometrization"
       7. 5. 4. Eddington's "World Geometry"
       7.5. 5. Meyerson on "Pangeometrism"
       7. 5. 6. "Structural Realism"?
Chapter8. Cosmology: Methodological Debates in the 1930s and 1940s
 8. 1. Introduction
 8. 2. The Lead-up to the Debate
      8. 2. 1. Einstein's General Theory of Relativity
      8. 2. 2. Hubble's Expanding Universe
 8. 3. Cosmology and its philosophy
      8. 3. 1. Relativistic Cosmology: the majority philosophy
      8.3. 2. Milne's Philosophical Challenge
      8.3. 3. Kinematic Relativity—an alternative cosmology
 8. 4. The Great Cosmological Debate Begins: 1933-1934

  Physics and Philosophy                                        Musa Akrami

     8. 4. 1. Dingle's First Attacks
     8.4. 2. Two Ways to Disagree with Milne
     8.4. 3. Milne Makes Philosophical Improvements
     8.4. 4. A Major Philosophical Issue: What makes a scientific theory
     8. 4. 5. How to Choose Among Theories and Philosophies?
 8. 5. The Triumph of Milne's Methods 1935-36
      8. 5. 1. McCrea, Walker and Robertson Adopt Milne's Methods
     8. 5. 2. But Eddington Scoffd…
 8. 6. Dingle's Denoument
      8. 6. 1. Modern Aristotles?
      8.6. 2. Dingle as ‘True Believer’
     8. 6. 3. Wrong from the Very Start
     8. 6. 4. The Debate Goes Very Public
     8. 6. 5. The Counterattack
     8. 6. 6. The Coolest Voice
 8. 7. The Calm Between the Storms
      8. 7. 1. Two Equal Competitors
      8. 7. 2. The Origin and Evolution of Theories
     8. 7. 3. Milne's Ultimate Success
 8. 8. Steady-state Cosmology
     8. 8. 1. Bondi's Philosophical Origins
     8. 8. 2. Enter Popper
     8. 8. 3. But It's Milne In the End
     8. 8. 4. Return of the Cosmological Principle
     8. 8.5. A Popperian Conclusion

Chapter9. The Origin of the Universe and Contemporary Cosmology and
 9. 1. Introduction
 9. 2. Two Approaches in Cosmology
 9. 3. Dichotomy of Laws and Initial Conditions
 9. 4. In the Search of a New Type of Laws
 9. 5. World Without Borders

   Physics and Philosophy                                      Musa Akrami

 9. 6. Creative Conceptions of the Universe
 9.7. Creation from "Nothing"
 9. 8. Creation out of a "vacuum "
 9. 9. Conceptions of the Universe which is Infinite in Time
Chapter10. Cosmology and some Philosophical Questions
Chapter11. The Beginning of the Universe [Philosophical and Theological

   1. Scientific Cosmology
   2. Quantum Cosmology and Inflating Universes
   3. A Philosophical Evaluation of Quantum Cosmologies
   4. Philosophical Issues
   5. The Question of a Philosophical Cosmology or 6. [A Religious
      Cosmology: the Case of] A Christian Cosmology
   6. Something from Nothing
   7. Christian Spirituality and the New Cosmology


Chapter12. Philosophy of space and time
  1. Absolutism vs. Relationalism
  2. Conventionalism
  3. The structure of spacetime
     3.1. Invariance vs. Covariance
      3.2. Historical Frameworks
      3.3. Holes
  4. The direction of time
      4.1. The Causation solution
      4.2. The Thermodynamics solution
      4.3. The Laws Solution
  5. The flow of time
  6. Dualities
  7. Quantum gravity


Chapter13. [Philosophy of]Time


  Physics and Philosophy                                            Musa Akrami

   1. What should a philosophical theory of time do ?
   2. How is time related to mind ?
   3. What is time ?
   4.What does science require of time ?
   5. What sort of time travel is possible ?
   6. Is the relational theory of time preferable to the absolute theory ?
   7. Does time flow ?
   8. What gives time its direction or "arrow ?"
     a. What needs to be explained?
     b. Explanations or theories of the arrow
     c. Multiple arrows
     d. Reversing time
  9. Is only the present real ?
  11. Are there essentially tensed facts ?
  11. What is temporal logic, the symbolic logic of time ?

  12. Supplement of frequently asked questions

       References and Further Reading

Chapter14. Experiment in Physics

   1. Experimental Results

            A. The Case For Learning From Experiment

               An Epistemology of Experiment

               Galison's Elaboration

            B. The Case Against Learning From Experiment

               Collins and the Experimenters' Regress

               Pickering on Communal Opportunism and Plastic Resources

               Critical Responses to Pickering

Physics and Philosophy                                       Musa Akrami

             Pickering and the Dance of Agency

             Hacking's "Social Construction of What "?

2.The Roles of Experiment

          A. A Life of Its Own

          B. Confirmation and Refutation

             The Discovery of Parity Nonconservation: A Crucial

             The Discovery of CP Violation: A Persuasive Experiment

             The Discovery of Bose-Einstein Condensation: Confirmation
             After 70 Years

          C. Complications

             The Fall of the Fifth Force

             Right Experiment, Wrong Theory: the Stern Gerlach Experiment

             Sometimes Refutation Doesn't Work: The Double Scattering of

         D. Other Roles

             Evidence for a New Entity: J.J. Thomson and the Electron

             The Articulation of Theory: Weak Interactions

3. Conclusion


   Physics and Philosophy                                           Musa Akrami

Preface to Second Edition
Philosophy of Science has had two courses "Physics and Philosophy (1)" and
"Physics and Philosophy (2)" in its old M.Sc. programme in our "Department of
Philosophy of Science".
I had prepared the first edition of textbook Physics and Philosophy in two part
for those two courses. The first part had been edited to cover the course "Physics
and Philosophy (1)", while the second part had to be a supplement of my Az
Dam-e Sobh-e Azal tā Ākhar-e Shām-e Abad [=From the Beginning of the Dawn
of Pre-eternity to the End of the Night of Eternity] as the main text for the course
"Physics and Philosophy (2)".
According to the new programme, there is just one course as "Physics and
Philosophy". So, I decided to incorporate those two parts and make some
changes to satisfy new need for a relatively comprehensive textbook.
The present textbook, therefore, covers the most important topics and challenges
in regard with the history and philosophy of physics including philosophical
foundations and implications of quantum mechanics, theory of relativity,
cosmology, space and time as well as the place of experiment in physics.
Finally, the editor asks to be excused from obtaining written permission of the
authors (or any other real or legal person) for making use of their articles.

                                                                     Musa Akrami

                              Department of Philosophy of Science, IAU, Tehran

                                             Bahman 17th 1384/February 6th 2006

       Physics and Philosophy                                            Musa Akrami

Chapter1. A brief history and
philosophy of physics
Introductory remarks
1. 1. Earliest beginnings, and the Greeks
1. 2. The Dark Ages, and the Translations
1. 3. The Middle Ages
1. 4. The Renaissance (1300-1700)
1. 5. Development of the scientific method
1. 6. The development of classical physics: Mechanics, Thermal physics, Optics,
Electromagnetism, and Atoms
1. 6. 1. Mechanics
1. 6. 2. Thermal physics
1. 6. 3. Light and Optics
1. 6. 4. Electromagnetism
1. 6. 5. Atoms
1. 7. Modern physics: Relativity and Quantum physics
1. 7. 1. Relativity
1. 7. 2. Quantum physics
1. 8. The unification of physical phenomena

    By Alan J. Slavin, Dept. of Physics, Trent University, August 1994

Physics and Philosophy                                         Musa Akrami

     Introductory remaks
     This brief history and philosophy of physics has been written to
     give physics students some appreciation of where their
     discipline has come from, and of the philosophical principles
     underpinning it. It is hoped that this will provide students with
     a sense of physics as a living, evolving discipline, and of their
     place in its evolution. Physics, indeed all of science, is not a
     static agglomeration of proven facts and inviolable theories.
     While there are many theories which are so well tried that they
     are generally accepted as being correct, all scientific theories
     are still open to attack from some new, reproducible experiment
     which disagrees with them.
     This summary is designed to outline the general development
     of the main branches of physics as we know them today. It is
     presented here as occurring in a fairly linear fashion, and
     discusses only the principal figures in each area.

   Physics and Philosophy                                          Musa Akrami

1. 1. Earliest beginnings, and the Greeks
People have always been acutely aware of the regularities in nature: the sun
rises every day; the moon appears at the same place in the sky roughly every
twenty-seven days; the seasons always follow in the same order; the pattern of
the "fixed" stars (all the heavenly bodies except for the planets, sun, moon and
comets) repeats itself at the same time every year; a dropped stone always falls.
In fact, the very well-being of a family depended until recent times on knowing
when to plant, or when to move camp for the next season's game.
This obvious order begged for explanation, and the earliest people attributed it
to a range of gods and goddesses who controlled the world.
"Science" is the attempt to give a rational, rather than religious or magical,
explanation for the order in nature. People in different parts of the world began
to develop science at different times, with different emphases.
The first European attempts to provide a rational explanation for the workings of
nature began with the Greeks, about 600 B.C. For example, Pythagoras (582-500
B.C.) and his followers belonged to a religious fraternity dedicated to the study
of numbers. They believed that the world, like the whole number system, was
divided into finite elements, an early precursor to the idea of atoms ("atom"
means "indivisible"). Their discovery of irrational numbers, which could not be
expressed as a ratio of whole numbers, was a serious threat to this system.
The Greeks Leucippus (~440 B.C.), Democritus (~420 B.C.) and Epicurus (342-
270 B.C.) put forward the hypothesis that matter was composed of extremely
small atoms, with different materials being composed of different combinations
of these atoms. Aristarchus of Samos (310-230 B.C.) is the first person known to
have proposed that the earth rotates once per year around the sun, rather than the
intuitive explanation that the sun rotates around the earth. He also attempted to
calculate relative sizes for the earth, moon and sun. However, it was not
considered necessary by the Greeks to test such hypotheses experimentally; all
that most of them were looking for was a self-consistent explanation of the
world based on a small number of philosophical principles.
Aristotle is generally credited with providing the most comprehensive of such
He, following Anaxagoras and Plato, believed that there were four earthly
elements: earth, water, air and fire. Each had its natural place determined by its
weight. Earth, being the heaviest, "wanted" to be at the centre of the universe.
Water was above the earth, with air above water, and then fire. This order makes
intuitive sense. The farther a body was from the earth, the more perfect it
became. Hence the moon was the least perfect of the heavenly bodies, as could
be seen by its uneven appearance, while the fixed stars were the most perfect of
all, and were composed of a fifth element (the "quintessence") which had no
weight at all.

   Physics and Philosophy                                          Musa Akrami

In Aristotle's physics, a moving body of any mass had to be in contact with a
"mover", something which caused its motion, or it would stop. This mover could
either be internal or external. Aristotle said that a vacuum was impossible
("nature abhors a vacuum"). However, because the stars were without mass,
once they were put in motion by a "prime mover" they could continue to move
by themselves.
The Greeks spent much effort trying to explain the motion of the sun, moon,
planets and stars.
Eudoxus of Cnidus (409-356 B.C.) was apparently the first Greek to use
quantitative observation to develop a mathematical description. Noting that the
motion of the planets was periodic, he developed a system of spheres each of
which carried a planet, with each sphere centred on the earth but with its axis of
rotation fixed in a larger sphere. This explanation fitted with the Greek belief
that the circle was the most perfect geometrical form.
As the accuracy of the mathematical description increased, so did the need for
reliable observations. This was recognized by Hipparchus of Nicea (190-120
B.C.) who had studied the observational records of the earlier Greeks and
Babylonians, with the latter dating back to the seventh century B.C. To satisfy
the need for accurate data, Hipparchus catalogued the position and brightness of
1080 stars.
Of course, the Greeks did not restrict their science to physics. Aristotle's most
lasting contribution to science was in biology, where he classified about 540
animal species, and carried out careful dissections of at least 50 different
Archimedes (287-212 B.C.), scientist-engineer, has been described as one of the
three greatest geniuses of all time. He discovered the principle of buoyancy of a
body in a liquid.

1. 2. The Dark Ages, and the Translations
With the fall of the Roman empire about 400 A.D., most of the Greek learning
was lost to Europe as it entered the Dark Ages. Even the knowledge that the
Earth was round, known to the Greeks who had a good estimate for its diameter,
was replaced by the conception of a flat Earth. (This does not mean that all
learning stopped during the Dark Ages; important technological discoveries
were made during this period, such as the invention of the plough and the water
wheel.) The Greek knowledge itself, however, was not lost. It had migrated into
the Middle East and Egypt under the Greek and Roman empires, and was
translated into Arabic by the people who lived in these regions. The Muslims
(or, more generally, those speaking Arabic) not only kept Greek science alive,
but hey added to it considerably. For example, the Arabs had important medical
schools and first discovered the law of refraction, now known as Snell's law.

   Physics and Philosophy                                           Musa Akrami

They also translated major Indian scientific works into Arabic, and began to use
the numerals and algebra developed in India. Al-Battani (~858-929 A.D.)
measured a value for the precession of the equinoxes that was more accurate
than Ptolemy's. The Arabs also transported the art of paper-making from China
to the west.
When Christians recaptured Spain in the eleventh century, the bridge was
formed to carry this learning back into Europe. A major translation centre was
set up in Toledo after it was captured in 1085, with a lesser centre in Sicily after
it fell to the Christians in 1091. Translation was done primarily into Latin, the
language of learning in Europe at this time. However, most of the translators
focused on the Greek works, and some Arabic and Persian works remain
untranslated today.

1. 3. The Middle Ages
The scholarly work in Europe during the Dark Ages had been primarily
concerned with the copying of church manuscripts. As a result, it was natural
that as ancient learning began to reach Europe it should be studied first in the
cathedral schools. These schools evolved into the first universities, with colleges
in Cambridge and Oxford, for example, being founded in the 1200s. These were
followed by universities set up by both city (e.g. Bologna, Padua) or state (e.g.
Naples) governments. The scholars in these early universities laid much of the
groundwork for later scientific developments.
One of the most important schools for the development of physics was in
Oxford, where the impetus theorists, beginning with William of Ockham
(~1295-1349), investigated the cause of motion. They believed that a body in
motion did not need to be in contact with a "mover" to stay in motion as
Aristotle had claimed, but did so out of its own "impetus". This was a precursor
to our modern concept of momentum. Another major contribution has become
known as "Ockham's Razor". This principle states that the best scientific theory,
other things being equal, is the one which requires the fewest new starting
assumptions. It is still accepted today. It was important historically because it
provided an objective means for choosing between two theories and did not
attempt to answer the question of which was "true".
The flood of ancient, "pagan" knowledge into Europe through the translations
from Arabic produced a crisis for Christian theologians: How could one accept a
world philosophy that was not rooted in the Christian faith? This problem was
largely overcome, at least for the time being, by St. Thomas Aquinas (1225-74)
who integrated Aristotelian philosophy and Greek logic with Catholic theology.
One must ask why, when so many of the early scientific discoveries were made
in the east, the development of modern science was primarily in the west.

   Physics and Philosophy                                          Musa Akrami

1. 4. The Renaissance (1300-1700)
The rebirth ("Renaissance") of knowledge and learning in Europe, which
followed the rediscovery of Greek and Arab learning, affected all of society.
Awakened to the fact that there was so much "new" knowledge to be explored,
people became free to invent their own. The arts flourished. It saw the beginning
of the Protestant Reformation in 1517. This was the period of the great European
voyages of discovery, with Columbus arriving in America in 1492.
During the Renaissance Aquinas' integration of Greek, and particularly
Aristotelian, philosophy with Catholic theology eventually led to as many
problems for the church as it had solved. Copernicus' suggestion (about 1530)
that the Earth and the other planets moved around the sun, rather than the
reverse, was seen as heresy by the Church. Not only did it contradict Aristotle's
teaching and several Biblical assertions that the Earth was stationary, it also
challenged the authority of the Church by questioning the hierarchical structure
on which its entire existence was based. The idea of a moving Earth was so
revolutionary that Copernicus did not agree to have it published until he was on
his death bed (1543). It is no surprise that the two people most responsible for
the publishing of Copernicus' book were followers of Martin Luther, who had
dared to question the authority of the Catholic church on scriptural matters.
The Renaissance also saw the beginnings of modern science under Galileo
Galilei (1564-1642). One of Galileo's greatest contributions was to recognize
that the role of the scientist was not to explain "why" things happened as they do
in nature, but only to describe them. This new role greatly simplified the work of
the scientist, who no longer had to wonder why God would have caused a
particular phenomenon to occur. It sufficed to recognize that it did occur, and
allowed one to get on with the job of deciding how best to describe it.
This leads us to Galileo's second major contribution, the description of natural
phenomena using mathematics and the appeal to nature through
experimentation to see if the description is correct.
This was a major deviation from the qualitative science of Aristotle in which, for
the most part, all that was required of an explanation was that it agreed
qualitatively with reality. In Galileo's science one had to describe
mathematically how far an object fell in a given time, and then verify
experimentally that this description was correct. Moreover, he recognized that
the experimenter had to devise the experiment so as to isolate the phenomenon
being studied.
Galileo's most important applications of these ideas were in the mechanics of
falling bodies, building on the early ideas of the impetus theorists. He showed
that all compact bodies fell at the same rate, such that the distance covered was
proportional to the square of the elapsed time of fall.

   Physics and Philosophy                                            Musa Akrami

Galileo is probably best known for his conflict with the Catholic church over his
support for Copernicus' description of the solar system. When Galileo heard of
the invention of the telescope, he designed and built one for himself. This, the
first telescope usable for astronomical observations, quickly led Galileo to
realize that Copernicus' theory was more than just an alternative to the Ptolemaic
approach for calculating the positions of the planets. He saw that Jupiter had
moons, and so was a miniature model of the solar system in itself; that Venus
showed phases similar to those of the moon, as it must under the Copernican
system; and that the moon had mountains and so was similar to the Earth. No
wonder the church saw him as a threat! Galileo, aged sixty-eight, was tried by
the Inquisition and sentenced to house arrest for the remainder of his life for
daring to support Copernicus' theory

1. 5. Development of the scientific method
Francis Bacon (1561-1626) takes credit for providing much of the philosophical
basis for our modern scientific method. His major works were very influential in
directing the approach to science over the next two hundred years and remain
relevant today. Bacon had a vision that science could greatly improve the lot of
humanity.The right of man to dominate the rest of nature has been a guiding
principle of science and technology for most of the time since Bacon. It is only
now beginning to be challenged by the developing ecological awareness that
people, too, are part of nature, and that they ignore the inter-relationship at their
Bacon's approach was basically experimental, qualitative and inductive. He
rejected a priori assumptions such as the idea of the perfection of spherical
motion used by the Greeks. Rather, Bacon believed that if enough observations
could be made which involved a particular phenomenon, an observer could use
these to induce the fundamental principles involved.
The first step of this process, then, was the gathering of as many unbiased facts
as possible, drawing heavily on information already available in craft and
industrial processes.
The next was to correlate these so as to discern the fundamental truths within
René Descartes (1596-1650) proposed a different approach to the development
of science. Instead of starting with raw facts,Descartes believed that the basic
principles ruling nature could be obtained by a combination of pure reason and
mathematical logic. His approach was analytic. It involved breaking down a
problem into its parts and arranging them logically, a technique which is still
used constantly in science today. It is termed "reductionism", because its basic
assumption is that we can reduce a phenomenon to a collection of independent
components; if we can understand each of them taken independently, then we

   Physics and Philosophy                                           Musa Akrami

can understand the entire phenomenon, in a way similar to our understanding of
the operation of a machine. This approach has dominated scientific investigation
over the last three hundred years, and has proven very successful in areas in
which the parts really are largely independent.
Descartes' "mathematical-deductive" approach was diametrically opposed
to Bacon's "qualitative-inductive" method, whereas modern science uses a
combination of the two.
Given Bacon's emphasis on experimentation, and Descartes' emphasis on
deductive reasoning, it is not too surprising that in the next hundred years
English scientists stressed experimentation while French scientists stressed
mathematical theory.
Descartes really believed that the world and most of what was in it were
essentially machines. God had created and wound up the system at the
beginning, and it had been running ever since under the laws of nature without
further intervention. The one exception to a machine was the soul (or mind) of a
human, which was divine and separate from the mechanical body. This concept
of the world as a machine persisted for many years, and was strengthened by
Newton's mechanics.
In fact, in 1812 Laplace, a great mathematical physicist, made the following
statement "If an intelligence, for a given instant, recognizes all the forces which
animate Nature, and the respective positions of all things which compose it, and
if that intelligence is sufficiently vast to subject these data to analysis, it will
comprehend in one formula the movements of the largest bodies of the universe
as well as those of the minutest atom; nothing will be uncertain to it, and the
future as well as the past will be present to its vision.”

   Physics and Philosophy                                          Musa Akrami

1. 6. The development of classical chysics:
Mechanics, Thermal physics, Optics,
Electromagnetism, and Atoms

1. 6. 1. Mechanics
Sir Isaac Newton (1642-1727), born the year Galileo died, is the most important
figure in the development of mechanics. His three "laws" form the base on
which all of mechanics prior to 1900 was constructed. This model of building an
edifice of theory on the foundation of a few fundamental definitions and laws is
essentially that used by Euclid in his geometry. It became the ideal for all future
physical theories, including thermodynamics with three basic laws (zeroth, first
and second), optics (laws of reflection and refraction) and electromagnetism
(Maxwell's laws). Much of the physics of the hundred years after the death of
Newton was spent in applying his three laws to different phenomena.
Newton's crowning accomplishment was the application of his mechanics to
show that the entire universe obeyed the same laws of nature, as published in his
Mathematical Principles of Natural Philosophy. By assuming that two masses
attracted each other with a force inversely proportional to the square of the
distance between them, Newton proved that the mechanics which determined
how bodies fall on Earth also explained the periodic motions of the planets.
However, Newton did not restrict his work to mechanics

1. 6. 2. Thermal physics
The invention of a practical steam engine prompted great scientific interest in
the study of heat, and was a major contribution to the industrial revolution which
began in England in the mid 18th century. Sadi Carnot (1796-1832), a French
engineer, laid the basis for our understanding of heat engines. He compared the
operation of a heat engine with that of a waterwheel, with heat "falling" from a
higher to a lower temperature. Joseph Black (1728-99began to quantify heat by
the measurement of the specific heat capacities (the amount of heat required to
raise the temperature of a given mass by one degree) of different substances,
compared to that of water. Count Rumford (1753-1814) first showed that heat
could be produced in limitless quantities by friction, and so was not a material
substance (caloric) as had been believed previously.
James Prescott Joule (1818-89 established a numerical equivalence between
work and heat. He also showed that the heat produced by an electrical current I
in a wire of resistance R was given by I2R, a relationship now known as Joule's
law. Joule's quantitative work on the interconversion of energy laid the basis for

   Physics and Philosophy                                          Musa Akrami

the first law of thermodynamics, which says that the change in the energy of a
system is equal to the heat input to it plus the mechanical work done on it. This
law was first stated explicitly by the German Rudolph Clausius and Englishman
William Thomas Kelvin in 1851. Clausius also realized that a heat engine could
utilize only some of the available heat to do work, and from this developed the
concept of entropy, the quantity of heat transferred divided by the temperature.
Clausius showed that the entropy always increased in any spontaneous natural
process, and so established the second law of thermodynamics. As with
Newton's three laws, the laws of thermodynamics form the foundation for the
understanding of thermal physics.

1. 6. 3. Light and Optics
The Greeks had applied the methods of geometry to the study of optics, and
Ptolemy had a crude approximation to the law of refraction. This work was
extended by the Arab Al-Hazen (965-1038), who showed that Ptolemy's law was
just an approximation, valid at small angles. Al-Hazen also carried out
experiments which brought him close to the thin lens formula for convex lenses.
The telescope and compound microscope were invented in Holland near the
beginning of the seventeenth century, with the telescope used to advantage by
the early astronomers including Galileo. In 1621 Willebrod Snell rediscovered
the correct formula for the refraction of light, which now bears his name.
From the time of Descartes there was considerable debate as to whether light
consisted of small particles which were localized and travelled in straight lines,
or of waves which spread out in space. Descartes adhered to the former
explanation whereas in the late 1600s Christian Huygens argued for a wave
theory, with the waves travelling through an ether which permeated all space
and all objects. Newton used a combination of the two approaches: while light
itself consisted of "corpuscles", he believed that these particles could induce
vibrations in the ether through which they travelled, which in turn could affect
the transport of the particles. For a century after Newton, the majority of
scientists adhered to the corpuscular theory.
Thomas Young (1773-1829) revived the wave theory for light. It was generally
accepted that sound was transported by waves carried through the air, and
Young argued that light travelled in a similar way. He used the interference
pattern produced in his famous "two-slit experiment", still studied in
introductory physics courses today, as proof of this wave nature. From these
patterns he was able to measure the wavelength of light which he proved to be
very small. He went on to show that this led to light travelling in approximately
straight lines for the vast majority of common cases, although it did bend

   Physics and Philosophy                                           Musa Akrami

slightly around objects to produce patterns in their shadows, patterns which
could be explained by his wave theory.
Then, in 1817, the Frenchman Augustin Fresnel showed that all known optical
phenomena could be explained by the wave theory provided that, following a
suggestion of Young's, the vibrations were transverse (perpendicular to the
direction of light propagation) rather than parallel to it as for sound waves. This
firmly established the wave theory as dominant, although it did raise the
question of how a fluid such as the ether could support a transverse vibration,
since fluids usually have only longitudinal vibrations. This problem was a
harbinger of an upcoming debate over the very existence of the ether.

1. 6. 4. Electromagnetism
The study of electromagnetism began in experimental studies of such
effects as static electricity and magnetism. People had known from
ancient times that rubbing certain materials on dry hair would make
the two attract each other.
Systematic studies of electricity began in earnest once apparatus had been
invented for generating and storing electrical charge. The first electrostatic
generator was invented by Otto von Guerike (1602-86). The voltaic cell
(battery), invented by Volta in Italy in 1799, could provide a continuous flow of
Benjamin Franklin's main contribution to the theory of electricity was his
suggestion that charge came in two types, which he called positive and negative,
with like charges repelling each other and unlike charges attracting. By these
simple assumptions he could explain all known experimental facts about
electricity, whereas previous theories had required about 20 different
assumptions, including different shapes for particles of electricity in different
media. This is one example of the use of Ockham's Razor in deciding between
rival theories.
Franklin also showed that there was a connection between electricity and
magnetism, because iron needles could be magnetized by placing them near a
wire carrying an electrical current.
In 1750 John Mitchell had discovered the inverse-square repulsion of magnetic
In a period beginning in 1785, the Frenchman Charles Augustin Coulomb
showed that both magnetic and electric forces experienced an inverse-square
dependence on distance, now called "Coulomb's law" in the case of
In Germany there developed a separate school of thought, that of the "nature
philosophers". They believed that matter was not inert, as claimed by the

   Physics and Philosophy                                          Musa Akrami

mechanist school, but alive, with a universal world spirit that interconnected all
The study of both electricity and magnetism was popular with German scientists,
because the presence of opposite polarities in these phenomena fitted with their
philosophy. These ideas also led to the conviction that every effect in nature had
its inverse effect, since the vital forces were all connected.
The belief in the interconnectedness of all forces in nature led Hans Christian
Oersted, in Copenhagen, to announce in 1807 that he was looking for a
connection between magnetism and electricity. He found that a magnet would
move in a circle around a wire carrying a current, and that a wire carrying a
current would move around a magnet. This is the principle required for the
construction of an electric motor.
The next major contributions in electricity and magnetism came from the
theoretician André Marie Ampère in France, and the experimentalist Michael
Faraday in England. Ampère (1775-1836) developed a theory for the calculation
of magnetic forces caused by a given electrical current, and suggested that the
magnetic effects of some solids were caused by small circulating currents in the
particles making up these materials.
Faraday (1791-1867), on the other hand, had very little mathematics but was a
superb experimentalist. His most important experimental observation in
electromagnetism was that of induced currents, made in 1831: a wire loop would
have an electric current developed in it, if either the loop was moved near a
magnet, or the magnet was moved.
Even though mathematically unlearned, Faraday made a very important
contribution to the development of the theory of electromagnetism by
constructing a qualitative model of how electrical and magnetic forces acted. He
supposed that each "particle" of electricity or magnetism produced a "line of
force" which emanated from a positive pole of a particle and returned to a
negative pole. Moreover, Faraday believed that the lines of force would be
present even if only a single charged or magnetic object existed; that is, even if
there were no other body on which the first one could exert a force. Thus he
invented the concept of the "field", as a physical presence which had the ability
to produce a force -- magnetic, electric or gravitational -- if a second body
happened to come into its vicinity. The concept of the field has served as one of
the most powerful of all theoretical tools of modern physics.
James Clerk Maxwell (1831-79) set out to make Faraday's ideas quantitative.
The resulting set of only four equations ("Maxwell's equations") described all
known electric and magnetic phenomena exactly.
One of the unexpected results of Maxwell's work was that it predicted that
electromagnetic waves could be produced which would propagate at the speed

   Physics and Philosophy                                            Musa Akrami

of light. This showed that light was an electromagnetic phenomenon, and not a
separate subject.
Discoveries in electromagnetism were applied quite rapidly to the development
of useful devices.

1. 6. 5. Atoms
Until the twentieth century, the development of the atomic theory of matter was
pursued by scientists who are often more closely identified with chemistry than
with physics. In 1789 Antoine Lavoisier published his Elements of Chemistry. In
this work, he emphasized the need for quantitative methods in chemistry.
Then in 1802 John Dalton, an English schoolmaster, revived the theory of
atoms. It was known by this time that gases always combine in fixed ratios by
mass. For example one gram of hydrogen burns with eight grams of oxygen to
produce nine grams of water. Dalton proposed that these ratios of whole
numbers could be explained if the gases were formed of atoms whose masses
were, themselves, in the ratio of simple integers.
In 1869 Dimitri Mendeleev of Russia, combining Dalton's atomic description
with the fact that certain groups of elements had similar chemical properties,
constructed the first periodic table. He pointed out that the gaps in this table
should correspond to as-yet-undiscovered elements, and was able to predict their
properties and atomic masses. Armed with this knowledge, scientists very
quickly discovered most of the missing elements.

1. 7. Modern Physics: relativity and
quantum physics
1. 7. 1. Relativity
By the end of the nineteenth century, most physicists were feeling quite smug.
They seemed to have theories in place that would explain all physical
phenomena. There was clearly a lot of cleaning up to do, but it looked like a
fairly mechanical job: turn the crank on the calculator until the results come out.
Apart from a few niggling problems like those lines in the light emitted by gas
discharges, and the apparent dependence of the mass of high-speed electrons on
their velocity ....
Twenty-five years later, this complacency had been completely destroyed by the
invention of three entirely new theories: special relativity, general relativity, and
quantum mechanics. The outstanding figure of this period was Albert Einstein.
His name became a household word for his development, virtually single-
handedly, of the theory of relativity, and he made a major contribution to the

   Physics and Philosophy                                           Musa Akrami

development of quantum mechanics in his explanation of the photoelectric
Einstein was a clerk in a Swiss patent office when he published his special
theory of relativity in 1905. He claimed in later life that the need for this theory
emerged out of Maxwell's equations. Those equations changed their form when
one rewrote them from the conventional perspective of a person moving at
constant velocity. On the other hand, our experience tells us that we cannot tell if
we are moving as long as our velocity is constant: you can throw a ball back and
forth in a rapidly moving train car just as you can when the train is still. It is
only when it accelerates -- slows down or speeds up -- that one experiences a
change. Moreover, Maxwell's equations indicated that the speed of light did not
depend on the speed of the person measuring this speed, whereas if one throws a
stone while running, the speed of the runner contributes to the speed of the
stone. To overcome these apparent difficulties with Maxwell's theory, which
Einstein believed to describe reality correctly, he considered the effect of two
postulates. The first was that all physical phenomena must obey the same
equations for people moving at different constant velocities (the principle of
relativity), and the second was that the speed, c, measured for light does not
depend on the speed of the "observer" (the person carrying out the
These two postulates led directly to almost unbelievable results. They showed
that the measurement of space and time depended on each other (that the time
you measured for an occurrence depended on your position), and also depended
on the speed of the observer. One immediate result is that "simultaneity" is
relative to the observer. Two "events" that occur at the same time for one
observer occur at different times as seen by an observer in motion relative to the
first, provided that the events occur at different spatial locations; the concept of
absolute time and space which had underpinned mechanics for two centuries lay
in shatters. Einstein's theory also showed that the measured mass of an object
depended on its velocity, and that mass (m) could be converted to energy (E)
according to E=mc2, the principle behind the atomic bomb and nuclear power
One of the beauties of Einstein's theory was that, as you let a body's speed
become small compared to the speed of light, the equations would reduce to
those of Newtonian mechanics. This requirement of physics, that a more general
theory must reduce in some limit to more restrictive theories, is called the
"correspondence principle". Thus we see that the development of the special
theory of relativity in no way diminishes the stature of Newton. Although his
concept of absolute space and time were incorrect, his genius remains: Newton's
mechanics is still correct except for bodies whose speeds approach that of light.

   Physics and Philosophy                                            Musa Akrami

It is important to discuss the fact that the results of the special theory contradict
"common sense": we know that we do not have to correct our watches after we
have been in a car, and that people who are running do not appear thinner than
when at rest. The problem here is that our common sense is, by definition, the
sense of how the common world works. However, the effects predicted by the
special theory are significant only at a speed approaching that of light, and none
of us has ever moved at such a speed relative to another object with which we
can interact. Therefore, we must not assume that our low-speed common sense
also applies at very high speeds. Similarly, we will see that the mechanics
governing sub-microscopic bodies such as atoms is quite different to the
mechanics describing 60-kg human beings.
In 1887 the Americans Albert Michelson and Edward Morley had attempted to
measure the speed of the Earth through the ether by measuring the difference in
the speed of light travelling in two perpendicular directions. A difference was
expected, for the same reason that the speed of a water wave relative to you
depends on whether you are travelling in the same direction as the wave or
otherwise. They found no dependence on the direction of motion of the light,
and interpreted this null result by claiming that the Earth dragged the ether with
it. But if the ether interacted with matter in this way, why could it not be
detected directly? Moreover, the observation by James Bradley in 1725 of stellar
aberation rules out the hypothesis of ether drag. (Stellar aberation is the apparent
movement of the stars in a small ellipse over the course of a year, because the
Earth is moving and it takes some time for the light of the stars to reach Earth.)
In 1892, Hendrik Lorentz and G.F. Fitzgerald independently hypothesized that
the size of Michelson and Morley's measuring device must depend on its
velocity so as to contract in the direction of motion exactly enough to give the
null result.
Einstein's second postulate presented yet another possibility: the measured speed
of light was intrinsically independent of the speed of the observer. However, it
went much beyond interpreting the Michelson -Morley result and explained, for
example, the experimental observation that an electron's mass depended on its
velocity. In fact, Henri Poincaré, a renowned physicist, had suggested a year
before Einstein's publication that a whole new mechanics might be required, in
which mass depended on velocity. Einstein's theory cleared up so many
outstanding problems that it was quite quickly accepted by most physicists.
Before leaving special relativity it is important to discuss briefly Einstein's role
in the development of nuclear weapons. Nuclear fission had been discovered in
Germany in 1938, just after the invasion of Austria by Hitler's forces. In 1939,
faced with the threat that Germany would develop a nuclear bomb, Einstein was
convinced by physicist Leo Szilard to write to President Roosevelt, pointing out
the possibility and encouraging American research in this direction. In spite of

   Physics and Philosophy                                            Musa Akrami

this, Einstein actively opposed further development of nuclear weapons
following the Second World War. In fact, he and British
philosopher/mathematician Bertrand Russell founded the Pugwash organization,
named after its first meeting in Pugwash, Nova Scotia, in 1954. This
organization of leading scientists throughout the world, and its student wing, still
meet regularly to discuss issues concerning the impact of science on society, and
to prepare position papers for presentation to governments and the United
The General Theory of Relativity extended Einstein's ideas to bodies which are
accelerating, rather than moving at constant velocity. Einstein showed that
spacetime near masses could not be described by Euclidean geometry, but rather
that a geometry invented by Riemann must be used. In this way, gravitation was
shown to be a result of the curvature of spacetime in the vicinity of mass. The
general theory allowed Einstein to predict the amount of the deflection of light
in the eclipses of 1919 and 1921, a value which agreed with that measured.
However, Einstein's theory of general relativity was not the last word on the
subject. General relativity is still an active area of research today, partly because
it provides us with much evidence on the evolution of the universe including
such questions as, "Will the universe someday begin to collapse back upon itself
under its gravitational attraction?"

1. 7. 2. Quantum Physics
 Einstein's theories of relativity were developed in a way close to
Descartes' mathematical-deductive method. The special theory came from an
attempt to harmonize electromagnetic theory with the principle of relativity. The
general theory evolved from trying to reconcile the fact that inertial mass, the
"resistance" to the force in the equation F=ma, has the same value as
gravitational mass, even though the two are totally unrelated in Newtonian
Quantum physics, on the other hand, emerged from attempts to explain
experimental observations. In the late 1890s a major area of research centred
on the explanation of "blackbody" radiation: a black object such as a fireplace
poker, when heated until it begins to glow, emits light whose intensity depends
on wavelength in a way which depends largely on the temperature of the
body and little on its material of construction. Because of the universal nature
of this phenomenon, it was apparent that it must depend on fundamental
physical principles. In 1900 Max Planck used a "lucky guess" to obtain a
mathematical equation which fitted the experimental data accurately. Three
months later he derived the expression theoretically. To do this he assumed that
a blackbody contained many small oscillators which emitted the light, much the

   Physics and Philosophy                                          Musa Akrami

way the oscillations of electrons along a transmission antenna emit radio waves.
However, he had to allow these oscillators to emit energy only at certain
frequencies rather than with a continuous range of frequencies, as would be
expected from classical electromagnetism. Planck had no physical basis for this
assumption; it was just the only way that he could fit the data.
Einstein used Planck's idea in his explanation of the photoelectric effect, in
which electrons are ejected from a metal when it is exposed to light whose
frequency exceeds a certain value. Einstein extended Planck's ideas on the
emission of light from a blackbody to the general statement that light, itself,
came in packets of energy, or quanta (called "photons" from the Greek "photos"
meaning "light").
Each quantum has an energy E=hf, where f is the frequency of light and h is
"Planck's constant". This was a bold move, since the work of Young and Fresnel
had seemed to establish beyond all doubt that light acted as a wave, and
Maxwell's theory did not include any mention of a particle nature to light.
However, Einstein's assumption explained the fact that even an intense light
below a certain frequency could not cause the emission of electrons: if each
incoming light quantum gave all its energy to an electron in the metal, the
electron could not escape if this energy was less than the binding energy of the
electron. This explanation dismayed Planck, who never expected his suggestion
to be applied so broadly.
In 1911 Ernest Rutherford fired very small particles, emitted in radioactive
decay, at a thin film of gold. From the scattering pattern of the particles, he
determined that the atom consisted of a small, heavy, positively charged nucleus
surrounded by very light electrons. Niels Bohr used this model and the quantum
ideas of Planck and Einstein in 1913 to explain why the light from gas
discharges was emitted at only a few, discrete frequencies; this light formed
emission "lines" of different colours when the light was passed through a slit and
dispersed by a prism. Bohr suggested that the electrons in an atom were only
allowed to occupy certain orbits of definite radius r around the nucleus,
namely orbits whose angular momentum was given by mvr=n where m and v
are the mass and velocity of the electron, and n is an integer. When an electron
gained energy and was "excited" to a higher orbit during the gas discharge, it
could lose this energy only by falling back to one of the lower allowed orbits,
with its energy loss E being carried off by the emission of a quantum of light of
energy f=E/h. The predicted frequencies for hydrogen matched the
experimental values.
Beginning with the claim that mechanical models such as Bohr's were
inappropriate because they tried to use the mechanics which had been developed
for macroscopic bodies in situations where it might not apply, Werner
Heisenberg in 1925 derived a purely mathematical theory that incorporated

   Physics and Philosophy                                          Musa Akrami

directly the empirical data, such as the wavelengths of spectral lines. The same
year, Louis de Broglie argued that if light could act both as a wave and as a
particle (photon) with definite energy, then perhaps material particles such as
electrons could as well. He suggested that such a particle should have a
wavelength given by =h/mv, where m is the particle's mass and v is its
By the next year, de Broglie's hypothesis had been used by Erwin Schrödinger
to explain the quantization of Bohr's orbits. Moreover, Schrödinger showed that
his wave mechanics was equivalent to Heisenberg's theory. By 1927, C.J.
Davisson and L.H. Germer had confirmed de Broglie's hypothesis directly by
producing a diffraction pattern by scattering electrons from the ordered atoms on
the surface of a nickel sample, much like the two-slit interference pattern used
by Thomas Young to prove that light behaved as a wave. This result is
impossible if we consider the electron as a classical particle: it means that the
electron must scatter off more than one nickel atom simultaneously or, in the
two-slit analogy, go through both slits at the same time!
Rather than placing the electrons in the atom in definite orbits as envisioned by
Bohr, Schrödinger's wave mechanics, as interpreted by Max Born, treated the
square of the particle's wave amplitude as giving the probability that the electron
was at a particular place in space, with the most probable positions
corresponding to Bohr's orbits. From this discussion it is clear that we are
treating the electron both as a particle and a wave. Consider Young's two-slit
experiment again, but using electrons instead of light as the incident radiation.
Suppose we position a fluorescent screen behind the two holes, and decrease the
intensity of the electron beam until only one electron hits the screen at a time.
Experimentally we see that each electron produces a tiny flash on the screen, as
though it were struck by a particle rather than a wave. However, the number of
particles arriving in a given region of the screen is greater where the diffraction
pattern has its maxima. The electron acts like a particle when we demand a
particle-like response, but like a wave when we demand a wave-like response.
This is the conclusion come to by Bohr, in establishing his "principle of
complementarity": the wave and particle descriptions of matter (or
electromagnetic radiation) are complementary, in the sense that our experiments
can test for one or the other, but never for both properties at the same time.
In 1927 Heisenberg proved that it was impossible to determine both a particle's
position and momentum with arbitrary precision; if one is known very
accurately, then the uncertainty in the other becomes large. This "Uncertainty
Principle" showed that there are theoretical limits on a person's ability to
describe the world. The limits are not a serious consideration for large bodies,
but become very important for bodies the size of an atom or smaller. The
uncertainty principle also makes it clear that the presence of the experimenter

   Physics and Philosophy                                            Musa Akrami

always affects the results of an experiment at some level. For example, if we try
to determine the position of a small particle very accurately we must, in
principle, change its momentum by the very act of observing it.
Quantum mechanics has now been extended to explain a wide range of
phenomena at the sub-microscopic level, including the structure of the atomic
nucleus. Experimentally, this structure has been determined in a manner similar
in principle to Rutherford's scattering experiment, using accelerators which
produce incident particles of very high energy.
Philosophically, the developments of quantum mechanics were far-
reaching. Like relativity, they again showed that humans could not assume that
the physical laws which seem to govern a 60-kg person moving at speeds up to
several hundred kilometres per hour also applied to bodies far from this regime.
They also brought into question the assumption of the perfectly deterministic
world proposed by Laplace. Clearly it was impossible to predict the position and
velocity of every body for all future times if you could not even know these
coordinates accurately at a single instant in time. This conclusion has even been
used as the basis of the claim that humans have free will, that all is not
predetermined as would seem to be the case in a purely mechanistic,
deterministic world governed by the laws of physics. These ideas are still
heavily debated today, as in a recent article by Roger Penrose in the book
Quantum Implications.
Indeed, Einstein himself was never able to accept fully the uncertainty implied
in quantum mechanics, declaring that he did not believe that God played dice
(Clark, pp.414, 415). In an attempt to show that quantum theory was at variance
with the real world, he helped develop the Einstein-Podolsky-Rosen (EPR)
paradox, a "thought experiment" which shows that quantum mechanical
theory must lead to what seems like an impossible situation: what you do to one
particle can affect a second, even if they are sufficiently separated in space that a
light signal could not pass from the first to the second fast enough to cause the
observed effect. That is, either the knowledge of the event can travel between
the particles faster than the speed of light, or the two particles really are not
separate but remain interconnected in some fundamental sense. It was the latter
option which was under debate.
An experiment designed to test this hypothesis was carried out by D. Aspect
and coworkers in 1981 [Physical Review Letters 47,460 (1981) and 49, 91
(1982)] and was shown to confirm what was predicted: the two particles really
were connected over large distances by "non-local" forces acting
instantaneously. That is, the EPR paradox, rather than showing a basic
inconsistency in quantum theory, actually points to one more aspect of nature
that contravenes common sense.

   Physics and Philosophy                                          Musa Akrami

1. 8. The unification of physical phenomena
The work of Maxwell represents the first great theoretical unification of physical
phenomena, in this case the integration of magnetic, electrical and optical theory
into one all-encompassing framework. Again, this must be seen as desirable
under Ockham's Razor, which argues for economy of understanding. Such
economy is the strength of modern analytical science, which emphasizes the
logical description of a vast range of physical phenomena from a few basic
principles, rather than the memorization of a large number of isolated facts or
formulae. The former approach enables the user to predict effects not seen
previously, to invent, whereas the latter restricts one to what already is known.
Other great unifications that have taken place in physics include the integration
of classical mechanics, quantum physics and heat in the development of
statistical mechanics. This subject assumes that the properties of large systems,
such as gases or solids, can be calculated by working out the average of the
properties of all their constituent particles. For example, the relationship
between the temperature and pressure of a gas can be calculated by treating the
gas as being made up of a very large number of independent molecules, and
calculating the average force they produce as they collide with the container
walls, using Newtonian mechanics for the particles.
This approach was followed for gases by Maxwell and Ludwig Boltzmann
(1844-1906). Boltzmann also showed that Clausius' entropy could be interpreted
as a measure of the disorder of a system. In particular, he proved that the value
for entropy can be obtained from a knowledge of the total number of different
states in which a system can be found. That, in turn, depends on the number of
different potential configurations of all the particles which comprised the
system. This statistical approach has led to the development of "quantum
statistics", the application of statistical mechanics to quantum phenomena.
Perhaps the greatest such unification that has taken place in this century is the
integration of electromagnetism and quantum mechanics, in quantum
electrodynamics (QED). This feat earned Richard Feynman, Julian
Schwinger, and Sin-itiro Tomonaga the Nobel Prize for physics in 1965. It is
capable of predicting the spin g-factor of the electron with a numerical accuracy
of 1 part in 1010!
In 1979, Sheldon Glashow, Abdus Salam, and Stephen Weinberg were given
the Nobel Prize for their "electroweak theory" that unified the electromagnetic
and weak nuclear forces. Attempts have also been made to form a quantum
theory of the strong nuclear force. Because of its similarity to QED, it has been
called quantum chromodynamics (QCD). "Chromo" comes from the Greek
word for colour, and refers to the fact that the quarks that make up neutrons and
protons come in several varieties that have been given the names red, blue and
green, and their antiparticles. (These names have been chosen in analogy to

   Physics and Philosophy                                        Musa Akrami

light. These three colours can be combined to give white light; the three quarks
combine to give a "colourless" particle.) The combination of electroweak theory
and QCD comprises what is called the "Standard Model". Attempts are still
under way to integrate QCD and electroweak theory into a single "Grand
Unified Theory" (GUT).
Much effort has also gone into trying to unify electromagnetism and gravitation.
In fact, Einstein spent most of the latter part of his life trying to create a
quantum form of the general theory of relativity. As can be seen from these
few examples, the nineteenth-century belief that the main theoretical work of
physicists was over could not have been further from the truth!

Butterfield, H., The Origins of Modern Science, 1300-1800

(Clarke-Irwin, Toronto) 1977. A good discussion of the interplay between
science and society.

Capra, F., The Turning Point (Simon and Schuster, New York) 1982.
Reductionist vs. holistic science, from a physicist's perspective.

Clark, R.W., Einstein, The Life and Times (Avon, New York) 1971.

Cline, B.L., Men who Made a New Physics (previously entitled The
Questioners) (Signet, New York) 1965. A very readable account of the origins
of quantum physics and relativity.

Cole, M.D., The Maya, 3rd ed. (Thames and Hudson, London) 1984.

Dijksterhuis, E.J., The Mechanization of the World Picture (Oxford University)

Drake, S., Telescopes, Tides and Tactics: A Galilean Dialogue about the Starry
Messenger and Systems of the World (University of Chicago Press, Chicago)
1983. This book includes a translation of Galileo's description of his first
astronomical observations, and MUST be read. It contains copies of Galileo's
original sketches of the appearance of the Moon and of the moons of Jupiter.

Drake, S., The Role of Music in Galileo's Experiments Scientific American, p.
98, June 1975.

   Physics and Philosophy                                         Musa Akrami

Finocchiaro, M.A., The Galileo Affair, A Documentary History (University of
California Press, Berkeley) 1989. Gives the context for Galileo's trial, and a
translation of a number of the original documents.

French, M., Beyond Power (Ballantine, New York) 1985. A feminist perspective
on patriarchal society.

Hawking, S.W., A Brief History of Time (Bantam, 1988). A discussion of
modern cosmology for the layperson, from one of the world's experts.

Horgan, J., Quantum Philosophy, Scientific American, July 1992, p.94. A
discussion of recent investigations of the EPR paradox.

Hiley, B.J. and Peat, F.D. (editors), Quantum Implications - Essays in Honour of
David Bohm (Routledge, New York) 1987. An excellent but fairly mathematical
consideration of the implications of quantum theory.

Kramer, E., Nature and Growth of Modern Mathematics, (Princeton University
Press, New York) 1982.

Jammer, M., The Conceptual Development of Quantum Mechanics, (McGraw-
Hill, New York) 1966. This book is quite mathematical.

Mason, S.F., A History of the Sciences (Collier, New York), 1962. An excellent
general history, very complete.

Rossiter, M.W., Women Scientists in America: Struggles and Strategies to 1940,
(John Hopkins University Press, Baltimore) 1982.

Schneer, C.J., The Evolution of Physical Science (Grove Press, New York) 1960.
Greeks to modern physical science.

Tuana, N. (editor), Feminism and Science (Indiana University Press,
Bloomington) 1989. Addresses gender bias in science.

Whitehead, A.N., Science and the Modern World, (Cambridge University Press)

Williams, L.P., The Origins of Field Theory (Random House, Toronto) 1966.
(Not in Trent Library).

       Physics and Philosophy                                         Musa Akrami

   Chapter2. The Uncertainty Principle
2. 1. Introduction
2. 2. Heisenberg
2. 2. 1 Matrix mechanis and wave mechanics
2. 2. 2 Heisenberg's argument
2. 2. 3 The interpretation of Heisenberg's relation
2. 2. 4 Uncertainty relations or uncertainty principle?
2. 3. Bohr
Bohr's view on the uncertainty relations
2. 4. The Minimal Interpretation

              Introductory Remarks
              The transition from classical to quantum physics marks a
              genuine revolution in our understanding of the physical
              One striking aspect of the difference between classical and
              quantum physics is that whereas classical mechanics
              presupposes that one can assign exact simultaneous values to
              the position and momentum of a particle, quantum mechanics
              denies this possibility. Instead, according to quantum
              mechanics, the more precisely the position of a particle is
              given, the less precisely one can say what its momentum is.
              This is (a simplistic and preliminary formulation of) the
              quantum mechanical uncertainty principle. This principle
              played an important role in many discussions on the
              philosophical implications of quantum mechanics and on the
              consistency of the interpretation endorsed by the founding
              fathers Heisenberg and Bohr, the so-called Copenhagen
              This, of course, should not suggest that the uncertainty
              principle is the only aspect in which classical and quantum
              physics differ conceptually. In particular the implications of
              quantum mechanics for notions such as (non)-locality,
              entanglement and identity play no less havoc with classical

   By Jan Hilgevoord and Jos Uffink, University of Utrecht 

   Physics and Philosophy                                          Musa Akrami

2. 1. Introduction
The uncertainty principle is certainly one of the most famous and important
aspects of quantum mechanics. Often, it has even been regarded as the most
distinctive feature in which this theory differs from a classical conception of the
physical world. Roughly speaking, the uncertainty principle states that one
cannot assign exact simultaneous values to the position and momentum of a
quantum mechanical system. Rather, we can only determine such quantities with
some characteristic ‘uncertainties’, which cannot both become arbitrarily small
at the same time. But what exactly is the meaning of this uncertainty principle?
And indeed, is it really a principle of quantum mechanics? In particular, what
does it mean that a quantity is determined only up to some uncertainty? These
are the main questions we will explore in the following, focussing on the views
of Heisenberg and Bohr.
In many expositions of the subject, the ‘uncertainty’ may refer sometimes to a
lack of knowledge of a quantity by an observer, or to the experimental
inaccuracy with which a quantity is measured, or to some ambiguity in the
definition of a quantity, or to a statistical spread in some ensemble of
similarly prepared systems. Corresponding to this confusing multitude of
different meanings, there are many different names for these ‘uncertainties’. For
example, apart from those already mentioned (inaccuracy, spread) one finds
imprecision, indefiniteness, indeterminateness, indeterminacy, latitude, etc.
Even Heisenberg and Bohr did not decide on a single terminology. Forestalling a
discussion about which name is the most appropriate, we mention here that we
use the name ‘uncertainty principle’ simply because it seems the most common
one in the literature.

2. 2. Heisenberg
2. 2. 1 Matrix mechanics and wave mechanics
Heisenberg introduced his now famous relations in an article of 1927, entitled
"Ueber den anschaulichen Inhalt der quantentheoretischen Kinematik und
Mechanik". A (partial) translation of this title is: "On the anschaulich content of
quantum theoretical kinematics and mechanics". Here, the term anschaulich is
particularly notable. Apparently, it is one of those German words that defy an
unambiguous translation into other languages. Heisenberg's title is translated as
"On the physical content …" by Wheeler and Zurek (1983). His collected works
(Heisenberg, 1984) translate it as "On the perceptible content …", while
Cassidy's biography of Heisenberg (Cassidy, 1992), refers to the paper as "On

   Physics and Philosophy                                            Musa Akrami

the perceptual content …". Literally, the closest translation of the term
anschaulich is ‘visualizable’. But, as in most languages, words that make
reference to vision are not always intended literally. Seeing is widely used as a
metaphor for understanding, especially for immediate understanding. Hence,
anschaulich also means ‘intelligible’ or ‘intuitive’.[1]
Why was this issue of the Anschaulichkeit of quantum mechanics such a
prominent concern to Heisenberg? This question has already been considered by
a number of commentators. For the answer, it turns out, we must go back a little
in time. In 1925 Heisenberg had developed the first coherent mathematical
formalism for quantum theory. His leading idea was that only those quantities
that are in principle observable should play a role in the theory, and that all
attempts to form a picture of what goes on inside the atom should be avoided. In
atomic physics the observational data were obtained from spectroscopy and
associated with atomic transitions. Thus, Heisenberg was led to consider the
‘transition quantities’ as the basic ingredients of the theory. Max Born, later that
year, realized that the transition quantities obeyed the rules of matrix calculus. In
a famous series of papers Heisenberg, Born and Jordan developed this idea into
the matrix mechanics version of quantum theory.
Formally, matrix mechanics remains close to classical mechanics. The central
idea is that all physical quantities must be represented by infinite self-adjoint
matrices (later identified with operators on a Hilbert space). It is postulated that
the matrices q and p representing the canonical position and momentum
variables of a particle satisfy the so-called canonical commutation rule

qp − pq = i                                    (2-1)

Where = h/2π, h denotes Planck's constant, and boldface type is used to
represent matrices. The new theory scored spectacular empirical success by
encompassing nearly all spectroscopic data known at the time, especially after
the concept of the electron spin was included in the theoretical framework.
It came as a great surprise, therefore, when one year later, Erwin Schrödinger
presented an alternative theory, which became known as wave mechanics.
Schrödinger assumed that an electron could be represented as an oscillating
charge cloud, evolving continuously in space and time according to a wave
equation. The discrete frequencies in the atomic spectra were not due to
discontinuous transitions (quantum jumps) but to a resonance phenomenon.
Further, Schrödinger argued that the two theories were equivalent.
Even so, the two approaches differed greatly in interpretation and spirit.
Whereas Heisenberg eschewed the use of visualizable pictures, and accepted
discontinuous transitions as a primitive notion, Schrödinger claimed as an
advantage of his theory that it was anschaulich. In Schrödinger's vocabulary,

   Physics and Philosophy                                          Musa Akrami

this meant that the theory represented the observational data by means of
continuously evolving causal processes in space and time. He considered this
condition of Anschaulichkeit to be an essential requirement on any acceptable
physical theory. In fact, Schrödinger was not alone in appreciating this aspect of
his theory. Many other leading physicists were attracted to wave mechanics for
the same reason.
For a while in 1926, before it emerged that wave mechanics has serious
problems of its own, Schrödinger's approach seemed to gather more support in
the physics community than matrix mechanics.
Understandably, Heisenberg was unhappy about this development. In a letter of
8 June 1926 to Pauli he confessed that Schrödinger's approach disgusted him,
and in particular: "What Schrödinger writes about the Anschaulichkeit of his
theory, … I consider Mist (Pauli, 1979, p. 328)". Again, this last German term is
translated differently by various commentators: as "junk" (Miller, 1982)
"rubbish" (Beller 1999) "crap" (Cassidy, 1992), and perhaps more literally, as
"bullshit" (de Regt, 1997). Nevertheless, in published writings, Heisenberg
voiced a more balanced opinion. In a paper he summarized the peculiar situation
which the simultaneous development of two competing theories had brought
about. Although he argued that Schrödinger's interpretation was untenable, he
admitted that matrix mechanics did not provide the Anschaulichkeit which made
wave mechanics so attractive. He concluded: "to obtain a contradiction-free
anschaulich interpretation, we still lack some essential feature in our image of
the structure of matter". The purpose of his 1927 paper was to provide exactly
this lacking feature.

2. 2. 2 Heisenberg's argument
Let us now look at the argument that led Heisenberg to his uncertainty relations.
He started by redefining the notion of Anschaulichkeit. Whereas Schrödinger
associated this term with the provision of a causal space-time picture of the
phenomena, Heisenberg, by contrast, declared:
   We believe we have gained anschaulich understanding of a physical
   theory, if in all simple cases we can grasp the experimental consequences
   qualitatively and see that the theory does not lead to any contradictions.
   (Heisenberg, 1927, p. 172)
His goal was, of course, to show that, in this new sense of the word, matrix
mechanics could lay the same claim to Anschaulichkeit as wave mechanics.
To do this, he adopted an operational assumption: terms like ‘the position of a
particle’ have meaning only if one specifies a suitable experiment by which ‘the
position of a particle’ can be measured. In general, there is no lack of such

   Physics and Philosophy                                            Musa Akrami

experiments, even in the domain of atomic physics. However, experiments are
never completely accurate. We should be prepared to accept, therefore, that in
general the meaning of these quantities is also determined only up to some
characteristic inaccuracy.
As an example, he considered the measurement of the position of an electron by
a microscope. The accuracy of such a measurement is limited by the wave length
of the light illuminating the electron. Thus, it is possible, in principle, to make
such a position measurement as accurate as one wishes, but only by using light
of a very short wave length, e.g., γ-rays. But for γ-rays, the Compton effect
cannot be ignored: the interaction of the electron and the illuminating light
should then be considered as a collision of at least one photon with the electron.
In such a collision, the electron suffers a recoil which disturbs its momentum.
Moreover, the shorter the wave length, the larger is this change in momentum.
Thus, at the moment when the position of the particle is accurately known,
Heisenberg argued, its momentum cannot be accurately known.
   At the instant of time when the position is determined, that is, at the
   instant when the photon is scattered by the electron, the electron
   undergoes a discontinuous change in momentum. This change is the
   greater the smaller the wavelength of the light employed, i.e., the more
   exact the determination of the position. At the instant at which the
   position of the electron is known, its momentum therefore can be known
   only up to magnitudes which correspond to that discontinuous change;
   thus, the more precisely the position is determined, the less precisely the
   momentum is known, and conversely (Heisenberg, 1927, p. 174-5).
This is the first formulation of the uncertainty principle. In its present form it is
an epistemological principle, since it limits what we can know about the
electron. From "elementary formulae of the Compton effect" Heisenberg
estimated the ‘imprecisions’ to be of the order

δpδq  h                                       (2-2)

He continued: "In this circumstance we see the direct anschaulich content of the
relation qp − pq = i ".
He went on to consider other experiments, designed to measure other physical
quantities and obtained analogous relations for time and energy:

δt δE  h                                      (2-3)

and action J and angle w

   Physics and Philosophy                                          Musa Akrami

δw δJ  h                                    (2-4)

which he saw as corresponding to the "well-known" relations

tE − Et = i or wJ − Jw = i                   (2-5)

However, we must say that these generalisations did not turn out as
straightforward as Heisenberg suggested.
The first mathematically exact formulation of the uncertainty relations is due to
Kennard. He proved in 1927 the theorem that for all normalized state vectors |ψ>
the following inequality holds:

Δψp Δψq ≥    /2                               (2-6)

Here, Δψp and Δψq are standard deviations of position and momentum in the
state vector |ψ>, i.e.,

(Δψp)² = <p²>ψ − (<p>ψ)², (Δψq)² = <q²>ψ − (<q>ψ)².             (2-7)

where <·>ψ = <ψ|·|ψ> denotes the expectation value in state |ψ>. This inequality
(7) was generalized in 1929 by Robertson who proved the result that for all
observables (self-adjoint operators) A and B

ΔψA ΔψB ≥ ½|<[A,B]>ψ|                        (2-8)

where [A, B] = AB − BA denotes the commutator. This relation was in turn
strengthened by Schrödinger (1930), who obtained:

(ΔψA)² (ΔψB)² ≥ ¼|<[A,B]>ψ|² + ¼|<{A−<A>ψ, B−<B>ψ}>ψ|²                  (2-9)

where {A, B} = (AB + BA) denotes the anti-commutator.
Since the above inequalities have the virtue of being exact and general, in
contrast to Heisenberg's original semi-quantitative formulation, it is tempting to
regard them as the exact counterpart of Heisenberg's relations (2)-(4). Indeed,
such was Heisenberg's own view. In his Chicago Lectures (Heisenberg 1930, pp.
15-19), he presented Kennard's derivation of relation (6) and claimed that "this
proof does not differ at all in mathematical content" from the semi-quantitative
argument he had presented earlier, the only difference being that now "the proof
is carried through exactly".
But it may be useful to point out that both in status and intended role there is a
subtle difference between Kennard's inequality and Heisenberg's previous

   Physics and Philosophy                                           Musa Akrami

formulation (2). The inequalities discussed here are not statements of empirical
fact, but theorems of the formalism. As such, they presuppose the validity of this
formalism, and in particular the commutation relation (1), rather than elucidating
its intuitive content or to create ‘room’ or ‘freedom’ for the validity of this
relation. At best, one should see the above inequalities as showing that the
formalism is consistent with Heisenberg's empirical principle.
This situation is similar to that arising in other theories of principle where, as
would be noted, one often finds that, next to an empirical principle, the
formalism also provides a corresponding theorem. And similarly, this situation
should not, by itself, cast doubt on the question whether Heisenberg's relation
can be regarded as a principle of quantum mechanics.
There is a second notable difference between (2) and (6). Heisenberg did not
give a general definition for the ‘uncertainties’ δp and δq. The most definite
remark he made about them was that they could be taken as "something like the
mean error". In the discussions of thought experiments, he and Bohr would
always quantify uncertainties on a case-to-case basis by choosing some
parameters which happened to be relevant to the experiment at hand. By
contrast, the inequalities (6)-(9) employ a single specific expression as a
measure for ‘uncertainty’: the standard deviation. This choice is not unnatural,
given that this expression is well-known and widely used in error theory and the
description of statistical fluctuations.
Heisenberg summarized his findings in a general conclusion: all concepts used
in classical mechanics are also well-defined in the realm of atomic processes.
But, as a pure fact of experience experiments that serve to provide such a
definition for one quantity are subject to particular indeterminacies, obeying
relations (2)-(4) which prohibit them from providing a simultaneous definition
of two canonically conjugate quantities. Note that in this formulation the
emphasis has slightly shifted: he now speaks of a limit on the definition of
concepts, i.e. not merely on what we can know, but what we can meaningfully
say about a particle.

2. 2. 3 The interpretation of Heisenberg's
The relations Heisenberg had proposed were soon considered to be a cornerstone
of the Copenhagen interpretation of quantum mechanics. Just a few months
later, Kennard (1927) already called them the "essential core" of the new
theory. Taken together with Heisenberg's contention that they provided the
intuitive content of the theory and their prominent role in later discussions on the

   Physics and Philosophy                                          Musa Akrami

Copenhagen interpretation, a dominant view emerged in which they were
regarded as a fundamental principle of the theory.
The interpretation of these relations has often been debated.
Do Heisenberg's relations express restrictions on the experiments we can
perform on quantum systems, and, therefore, restrictions on the information we
can gather about such systems; or
Do they express restrictions on the meaning of the concepts we use to describe
quantum systems? Or else,
Are they restrictions of an ontological nature, i.e., do they assert that a quantum
system simply does not possess a definite value for its position and momentum
at the same time?
The difference between these interpretations is partly reflected in the various
names by which the relations are known, e.g. as ‘inaccuracy relations’, or:
‘uncertainty’, ‘indeterminacy’ or ‘unsharpness relations’, etc. The debate
between these different views has been addressed by many authors, but it has
never been settled completely. Let it suffice here to make only two general
First, it is clear that in Heisenberg's own view, all the above questions stand or
fall together. Indeed, we have seen that he adopted an operational
"measurement=meaning" principle according to which the meaningfulness of a
physical quantity was equivalent to the existence of an experiment purporting to
measure that quantity. Similarly, his "measurement=creation" principle
allowed him to attribute physical reality to such quantities. Hence, Heisenberg's
discussions moved rather freely and quickly from talk about experimental
inaccuracies to epistemological or ontological issues and back again.
However, ontological questions seemed to be of somewhat less interest to him.
For example, there is a passage (Heisenberg, 1927, p. 197), where he discusses
the idea that, behind our observational data, there might still exist a hidden
reality in which quantum systems have definite values for position and
momentum, unaffected by the uncertainty relations. He emphatically dismisses
this conception as an unfruitful and meaningless speculation, because, as he
says, the aim of physics is only to describe observable data. Similarly in the
Chicago Lectures (Heisenberg 1930, p. 11) he warns against the fact that the
human language permits the utterance of statements which have no empirical
content at all, but nevertheless produce a picture in our imagination. He notes,
"One should be especially careful in using the words ‘reality’, ‘actually’, etc.,
since these words very often lead to statements of the type just mentioned." So,
Heisenberg also endorsed an interpretation of his relations as rejecting a reality
in which particles have simultaneous definite values for position and

   Physics and Philosophy                                           Musa Akrami

The second observation is that although for Heisenberg experimental,
informational, epistemological and ontological formulations of his relations
were, so to say, just different sides of the same coin, this does not hold for those
who do not share his operational principles or his view on the task of physics.
Alternative points of view, in which e.g. the ontological reading of the
uncertainty relations is denied, are therefore still viable. The statement, often
found in the literature of the thirties, that Heisenberg had proved the
impossibility of associating a definite position and momentum to a particle is
certainly wrong. But the precise meaning one can coherently attach to
Heisenberg's relations depends rather heavily on the interpretation one favors for
quantum mechanics as a whole. And in view of the fact that no agreement has
been reached on this latter issue, one cannot expect agreement on the meaning of
the uncertainty relations either.

2. 2. 4. Uncertainty relations or uncertainty
Let us now move to another question about Heisenberg's relations: do they
express a principle of quantum theory? Probably the first influential author to
call these relations a ‘principle’ was Eddington, who referred to them as the
‘Principle of Indeterminacy’. In the English literature the name uncertainty
principle became most common. It is used both by Condon and Robertson in
1929, and also in the English version of Heisenberg's Chicago Lectures
(Heisenberg, 1930), although, remarkably, nowhere in the original German
version of the same book (see also Cassidy, 1998). Indeed, Heisenberg never
seems to have endorsed the name ‘principle’ for his relations. His favourite
terminology was ‘inaccuracy relations’ (Ungenauigkeitsrelationen) or
‘indeterminacy relations’ (Unbestimmtheitsrelationen). We know only one
passage (Heisenberg, 1958, p. 43), where he mentioned that his relations "are
usually called relations of uncertainty or principle of indeterminacy". But this
can well be read as his yielding to common practice rather than his own
But does the relation (2) qualify as a principle of quantum mechanics? Several
authors, foremost Karl Popper (1967), have contested this view. Popper argued
that the uncertainty relations cannot be granted the status of a principle, on the
grounds that they are derivable from the theory, whereas one cannot obtain the
theory from the uncertainty relations. (The argument being that one can never
derive any equation, say, the Schrödinger equation, or the commutation relation
(1), from an inequality.)

   Physics and Philosophy                                             Musa Akrami

Popper's argument is, of course, correct but we think it misses the point. There
are many statements in physical theories which are called principles even though
they are in fact derivable from other statements in the theory in question. A more
appropriate departing point for this issue is not the question of logical priority
but rather Einstein's distinction between ‘constructive theories’ and ‘principle
According to Einstein (Einstein, 1919), constructive theories are theories which
postulate the existence of simple entities behind the phenomena. They
endeavour to reconstruct the phenomena by framing hypotheses about these
entities. Principle theories, on the other hand, start from empirical principles, i.e.
general statements of empirical regularities, employing no or only a bare
minimum of theoretical terms. The purpose is to build up the theory from such
principles. That is, one aims to show how these empirical principles provide
sufficient conditions for the introduction of further theoretical concepts and
The prime example of a theory of principle is thermodynamics. Here the role of
the empirical principles is played by the statements of the impossibility of
various kinds of perpetual motion machines. These are regarded as expressions
of brute empirical fact, providing the appropriate conditions for the introduction
of the concepts of energy and entropy and their properties. (There is a lot to be
said about the tenability of this view, but that is not the topic of this entry.)
Now obviously, once the formal thermodynamic theory is built, one can also
derive the impossibility of the various kinds of perpetual motion. (They would
violate the laws of energy conservation and entropy increase.) But this
derivation should not misguide one into thinking that they were no principles of
the theory after all. The point is just that empirical principles are statements that
do not rely on the theoretical concepts (in this case entropy and energy) for their
meaning. They are interpretable independently of these concepts and, further,
their validity on the empirical level still provides the physical content of the
A similar example is provided by special relativity, another theory of principle,
which Einstein deliberately designed after the ideal of thermodynamics. Here,
the empirical principles are the light postulate and the relativity principle. Again,
once we have built up the modern theoretical formalism of the theory (the
Minkowski space-time) it is straightforward to prove the validity of these
principles. But again this does not count as an argument for claiming that they
were no principles after all. So the question whether the term ‘principle’ is
justified for Heisenberg's relations, should, in our view, be understood as the
question whether they are conceived of as empirical principles.
One can easily show that this idea was never far from Heisenberg's intentions.
We have already seen that Heisenberg presented them as the result of a "pure

   Physics and Philosophy                                           Musa Akrami

fact of experience". A few months after his 1927 paper, he wrote a popular paper
with the title "Ueber die Grundprincipien der Quantenmechanik" ("On the
fundamental principles of quantum mechanics") where he made the point even
more clearly. Here Heisenberg described his recent break-through in the
interpretation of the theory as follows: "It seems to be a general law of nature
that we cannot determine position and velocity simultaneously with arbitrary
accuracy". Now actually, and in spite of its title, the paper does not identify or
discuss any ‘fundamental principle’ of quantum mechanics. So, it must have
seemed obvious to his readers that he intended to claim that the uncertainty
relation was a fundamental principle, forced upon us as an empirical law of
nature, rather than a result derived from the formalism of this theory.
So, although Heisenberg did not originate the tradition of calling his relations a
principle, it is not implausible to attribute the view to him that the uncertainty
relations represent an empirical principle that could serve as a foundation of
quantum mechanics. In fact, his 1927 paper expressed this desire explicitly:
"Surely, one would like to be able to deduce the quantitative laws of quantum
mechanics directly from their anschaulich foundations, that is, essentially,
relation [(2)]" (ibid, p. 196). This is not to say that Heisenberg was successful in
reaching this goal, or that he did not express other opinions on other occasions.
Let us conclude this section with three remarks.
First, if the uncertainty relation is to serve as an empirical principle, one might
well ask what its direct empirical support is. In Heisenberg's analysis, no such
support is mentioned. His arguments concerned thought experiments in which
the validity of the theory, at least at a rudimentary level, is implicitly taken for
granted. Jammer (1974, p. 82) conducted a literature search for high precision
experiments that could seriously test the uncertainty relations and concluded
they were still scarce in 1974. Real experimental support for the uncertainty
relations in experiments in which the inaccuracies are close to the quantum limit
have come about only more recently.
A second point is the question whether the theoretical structure or the
quantitative laws of quantum theory can indeed be derived on the basis of the
uncertainty principle, as Heisenberg wished. Serious attempts to build up
quantum theory as a full-fledged Theory of Principle on the basis of the
uncertainty principle have never been carried out. Indeed, the most Heisenberg
could and did claim in this respect was that the uncertainty relations created
"room" (Heisenberg 1927, p. 180) or "freedom" (Heisenberg, 1931, p. 43) for
the introduction of some non-classical mode of description of experimental data,
not that they uniquely lead to the formalism of quantum mechanics. A serious
proposal to construe quantum mechanics as a theory of principle was provided
only recently by Bub (2000). But, remarkably, this proposal does not use the
uncertainty relation as one of its fundamental principles.

   Physics and Philosophy                                         Musa Akrami

Third,    it is remarkable that in his later years Heisenberg put a somewhat
different gloss on his relations. In his autobiography, he described how he had
found his relations inspired by a remark by Einstein that "it is the theory which
decides what one can observe" -- thus giving precedence to theory above
experience, rather than the other way around. Some years later he even admitted
that his famous discussions of thought experiments were actually trivial since
"… if the process of observation itself is subject to the laws of quantum theory,
it must be possible to represent its result in the mathematical scheme of this
theory" (Heisenberg, 1975, p. 6).

2. 3. Bohr
In spite of the fact that Heisenberg's and Bohr's views on quantum mechanics
are often lumped together as (part of) ‘the Copenhagen interpretation’, there is
considerable difference between their views on the uncertainty relations.
Bohr's view on the uncertainty relations
In his Como lecture, published in 1928, Bohr gave his own version of a
derivation of the uncertainty relations between position and momentum and
between time and energy. He started from the relations

E = hν and p = h/λ                    (2-10)

which connect the notions of energy E and momentum p from the particle
picture with those of frequency ν and wavelength λ from the wave picture. He
noticed that a wave packet of limited extension in space and time can only be
built up by the superposition of a number of elementary waves with a large
range of wave numbers and frequencies. Denoting the spatial and temporal
extensions of the wave packet by Δx and Δt, and the extensions in the wave
number σ = 1/λ and frequency by Δσ and Δν, it follows from Fourier analysis
that in the most favorable case Δx Δσ ≈ Δt Δν ≈ 1, and, using (10), one obtains
the relations

Δt ΔE ≈ Δx Δp ≈ h                     (2-11)

Note that Δx, Δσ, etc., are not standard deviations but unspecified measures of
the size of a wave packet. (The original text has equality signs instead of
approximate equality signs, but, since Bohr does not define the spreads exactly
the use of approximate equality signs seems more in line with his intentions.
Moreover, Bohr himself used approximate equality signs in later presentations.)

   Physics and Philosophy                                         Musa Akrami

These equations determine, according to Bohr: "the highest possible accuracy
in the definition of the energy and momentum of the individuals associated
with the wave field" (Bohr 1928, p. 571). He noted, "This circumstance may be
regarded as a simple symbolic expression of the complementary nature of the
space-time description and the claims of causality" (ibid).] We note a few points
about Bohr's view on the uncertainty relations.
   First of all,    Bohr does not refer to discontinuous changes in the
   relevant quantities during the measurement process. Rather, he
   emphasizes the possibility of defining these quantities. This view is
   markedly different from Heisenberg's.
Indeed, Bohr not only rejected Heisenberg's argument that these relations are
due to discontinuous disturbances implied by the act of measuring, but also his
view that the measurement process creates a definite result.
Nor did he approve of an epistemological formulation or one in terms of
experimental inaccuracies.
Instead, Bohr always stressed that in his point of view the uncertainty
relations are foremost an expression of complementarity. At first sight, this
might seem odd, since, after all, complementarity corresponds to a
dichotomic relation between two types of description. The uncertainty
relations "express" this dichotomy in the informal sense that if we take
energy and momentum to be perfectly well-defined, i.e., symbolically ΔE =
Δp = 0, the position and time variables are completely undefined, Δx = Δt =
∞, and vice versa. However, by focussing on these extremes only, we leave
out of consideration that the uncertainty relations also (and more properly)
allow for an intermediate situation in which the mentioned uncertainties are
all non-zero and finite.
However, Bohr never followed up on this suggestion that we might be able to
strike a compromise between the two mutually exclusive modes of description in
terms of unsharply defined quantities. Indeed, an attempt to do so, would take
the formalism of quantum theory more seriously than the concepts of classical
language, and this step Bohr refused to take. Instead, in his later writings he
would be content with stating that the uncertainty relations simply defy an
unambiguous interpretation in classical terms.
It must here be remembered that even in the indeterminacy relation [Δq Δp ≈
h] we are dealing with an implication of the formalism which defies
unambiguous expression in words suited to describe classical pictures. Thus a
sentence like "we cannot know both the momentum and the position of an
atomic object" raises at once questions as to the physical reality of two such
attributes of the object, which can be answered only by referring to the

   Physics and Philosophy                                           Musa Akrami

conditions for an unambiguous use of space-time concepts, on the one hand,
and dynamical conservation laws on the other hand. (Bohr, 1949, p. 211)
Finally, on a more formal level, we note that Bohr's derivation does not rely on
the commutation relations (1) and (5), but on Fourier analysis. To be sure, these
two approaches are equivalent as far as the relationship between position and
momentum is concerned. But this is not so for time and energy. This means that,
for a derivation based on the commutation relations, the position-momentum and
time-energy relations are not on an equal footing, which is contrary to Bohr's
approach in terms of Fourier analysis (Hilgevoord, 1996 and 1998).

2. 4. The minimal interpretation
In the previous two sections we have seen how both Heisenberg and Bohr
attributed a far-reaching status to the uncertainty relations. They both argued that
these relations place fundamental limits on the applicability of the usual classical
concepts. Moreover, they both believed that these limitations were inevitable
and forced upon us. However, we have also seen that they reached such
conclusions by starting from radical and controversial assumptions. This entails,
of course, that their radical conclusions remain unconvincing for those who
reject these, or other assumptions. Indeed, the operationalist-positivist viewpoint
adopted by these authors has long since lost its appeal among philosophers of
So the question may be asked what alternative views of the uncertainty relations
are still viable. Of course, this problem is intimately connected with that of the
interpretation of the wave function, and hence of quantum mechanics as a whole.
Since there is no consensus about the latter, one cannot expect consensus about
the interpretation of the uncertainty relations either. Here we only describe a
point of view, which we call the ‘minimal interpretation’, which seems to be
shared by both the adherents of the Copenhagen interpretation and of other
In quantum mechanics a system is supposed to be described by its quantum
state, also called its state vector. Given the state vector, one can derive
probability distributions for all the physical quantities pertaining to the system
such as its position, momentum, angular momentum, energy, etc. The
operational meaning of these probability distributions is that they correspond to
the distribution of the values obtained for these quantities in a long series of
repetitions of the measurement. More precisely, one imagines a great number of
copies of the system under consideration, all prepared in the same way. On each
copy the momentum, say, is measured. Generally, the outcomes of these
measurements differ and a distribution of outcomes is obtained. The theoretical

   Physics and Philosophy                                           Musa Akrami

momentum distribution derived from the quantum state is supposed to coincide
with the hypothetical distribution of outcomes obtained in an infinite series of
repetitions of the momentum measurement. The same holds, mutatis mutandis,
for all the other physical quantities pertaining to the system. Note that no
simultaneous measurements of two or more quantities are required in defining
the operational meaning of the probability distributions.
Uncertainty relations can be considered as statements about the spreads of the
probability distributions of the several physical quantities arising from the same
state. For example, the uncertainty relation between the position and momentum
of a system may be understood as the statement that the position and momentum
distributions cannot both be arbitrarily narrow -- in some sense of the word
"narrow" -- in any quantum state. Inequality (9) is an example of such a relation
in which the standard deviation is employed as a measure of spread. From this
characterization of uncertainty relations follows that a more detailed
interpretation of the quantum state than the one given in the previous paragraph
is not required to study uncertainty relations as such. In particular, a further
ontological or linguistic interpretation of the notion of uncertainty, as limits on
the applicability of our concepts given by Heisenberg or Bohr, need not be
Indeed, this minimal interpretation leaves open whether it makes sense to
attribute precise values of position and momentum to an individual system.
Some interpretations of quantum mechanics, e.g. Heisenberg and Bohr, deny
this; while others, e.g. the interpretation of de Broglie and Bohm insist that each
individual system has a definite position and momentum. The only requirement
is that, as an empirical fact, it is not possible to prepare pure ensembles in which
all systems have the same values for these quantities, or ensembles in which the
spreads are smaller than allowed by quantum theory. Although interpretations of
quantum mechanics, in which each system has a definite value for its position
and momentum are still viable, this is not to say that they are without problems
or, at least strange features, of their own. They do not imply a return to classical
We end with a few remarks on this minimal interpretation. First, it may be noted
that the minimal interpretation of the uncertainty relations is little more than
filling in the empirical meaning of inequality (9), or an inequality in terms of
other measures of width, as obtained from the standard formalism of quantum
mechanics. As such, this view shares many of the limitations we have noted
above about this inequality. Indeed, it is not straightforward to relate the spread
in a statistical distribution of measurement results with the inaccuracy of this
measurement, such as, e.g. the resolving power of a microscope. Moreover, the
minimal interpretation does not address the question whether one can make
simultaneous accurate measurements of position and momentum. As a matter of

   Physics and Philosophy                                       Musa Akrami

fact, one can show that the standard formalism of quantum mechanics does not
allow such simultaneous measurements. But this is not a consequence of relation
If one feels that statements about inaccuracy of measurement, or the
possibility of simultaneous measurements, belong to any satisfactory
formulation of the uncertainty principle, the minimal interpretation may
                                                         thus be too minimal.

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   Heisenberg, W )1969( .Der Teil und das Ganze (München : Piper) .
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    Unbestimmtheitsrelation ’Physikalische Blätter .196-193 11 English
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    Zeitschrift für Physik .25-1 44
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    the longitudinal coherence length of a thermal neutron beam ’Physical
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    Zeitschrift für Physik .352-326 44 ,
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   Pauli, W‘ )1933( .Die allgemeinen Prinzipien der Wellenmechanik’ in K.
    Geiger, and H. Scheel (eds) Handbuch der Physik2 nd edition, Vol. 245,
    (Berlin: Springer) .
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    V.F. Weiskopf (eds) (Berlin: Springer) .
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    Bunge (ed.) Quantum Theory and Reality( Berlin :Springer) .
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     .574-573Reprinted in Wheeler and Zurek (1983 )pp. 127-128 .
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   Schrödinger, E‘ )1931( .Zum Heisenbergschen Unschärfeprinzip ’Berliner
    Berichte .313-296
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    interferometry ’Physics Letters 153 A .62-59
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   Wheeler, J.A. and Zurek, W.H. ( eds) (1983) Quantum Theory and
    Measurement , Princeton NJ: Princeton University Press.

      Physics and Philosophy                                             Musa Akrami

  Chapter3. Copenhagen interpretation
  of quantum mechanics
3. 1. The background: Bohr’s model of hydrogen atom
3. 2. The principles violated in classical physics
3. 3. The Correspondence Rule
3. 4. Complementarity

             Introductory Remarks
             As the theory of the atom, quantum mechanics is perhaps the
             most successful theory in the history of science. It enables
             physicists, chemists, and technicians to calculate and predict
             the outcome of a vast number of experiments and to create new
             and advanced technology based on the insight into the behavior
             of atomic objects. But it is also a theory that challenges our
             imagination. It seems to violate some fundamental principles of
             classical physics, principles that eventually have become a part
             of western common sense since the rise of the modern
             worldview in the Renaissance. So the aim of any
             metaphysical interpretation of quantum mechanics is to
             account for these violations.
             The Copenhagen interpretation was the first general attempt to
             understand the world of atoms as this is represented by
             quantum mechanics. The founding father was mainly the
             Danish physicist Niels Bohr, but also Werner Heisenberg, Max
             Born and other physicists made important contributions to the
             overall understanding of the atomic world that is associated
             with the name of the capital of Denmark.
             In fact Bohr and Heisenberg never totally agreed on how to
             understand the mathematical formalism of quantum mechanics,
             and none of them ever used the term “the Copenhagen
             interpretation” as a joint name for their ideas. In fact, Bohr once
             distanced himself from what he considered to be Heisenberg's
             more subjective interpretation (APHK, p.51). The term is rather
             a label introduced by people opposing Bohr's idea of
             complementarity, to identify what they saw as the common
             features behind the Bohr-Heisenberg interpretation as it

   By Jan Faye

      Physics and Philosophy                                        Musa Akrami

           emerged in the late 1920s. Today the Copenhagen
           interpretation is mostly regarded as synonymous with
           indeterminism, Bohr's correspondence principle, Born's
           statistical interpretation of the wave function, and Bohr's
           complementarity interpretation of certain atomic

   3. 1. The background: Bohr’s model of
   hydrogen atom
   According to classical mechanics and electrodynamics one might expect that the
   electrons orbiting around a positively charged nucleus would continuously emit
   radiation so that the nucleus would quickly swallow the electrons.
   At this point Niels Bohr entered the scene and soon became the leading physicist
   on atoms. In 1913 Bohr, visiting Rutherford in Manchester, put forward a
   mathematical model of the atom which provided the first theoretical support for
   Rutherford's model and could explain the emission spectrum of the hydrogen
   atom (the Balmer series). The theory was based on two postulates:
1. An atomic system is only stable in a certain set of states, called stationary
   states, each state being associated with a discrete energy, and every
   change of energy corresponds to a complete transition from one state to
2. The possibility for the atom to absorb and emit radiation is determined by
   a law according to which the energy of the radiation is given by the
   energy difference between two stationary states being equal to hv.

   Some features of Bohr's semi-classical model were indeed very strange
   compared to the principles of classical physics. It introduced an element of
   discontinuity and indeterminism foreign to classical mechanics:
1. Apparently not every point in space was accessible to an electron moving
   around a hydrogen nucleus. An electron moved in classical orbits, but
   during its transition from one orbit to another it was at no definite place
   between these orbits. Thus, an electron could only be in its ground state
   (the orbit of lowest energy) or an excited state (if an impact of another
   particle had forced it to leave its ground state.)
2. It was impossible to predict when the transition would take place and how
   it would take place. Moreover, there were no external (or internal) causes

      Physics and Philosophy                                           Musa Akrami

   that determined the “jump” back again. Any excited electron might in
   principle move spontaneously to either a lower state or down to the
   ground state.
3. Rutherford pointed out that if, as Bohr did, one postulates that the
   frequency of light v, which an electron emits in a transition, depends on
   the difference between the initial energy level and the final energy level, it
   appears as if the electron must “know” to what final energy level it is
   heading in order to emit light with the right frequency.
4. Einstein made another strange observation. He was curious to know in
   which direction the photon decided to move off from the electron.
   Between 1913 and 1925 Bohr, Arnold Sommerfeld and others were able to
   improve Bohr's model, and together with the introduction of spin and Wolfgang
   Pauli's exclusion principle it gave a reasonably good description of the basic
   chemical elements. The model ran into problems, nonetheless, when one tried to
   apply it to spectra other than that of hydrogen. So there was a general feeling
   among all leading physicists that Bohr's model had to be replaced by a more
   radical theory. As we have told, in 1925 Werner Heisenberg, at that time Bohr's
   assistant in Copenhagen, laid down the basic principles of a complete quantum
   mechanics. In his new matrix theory he replaced classical commuting variables
   with non-commuting ones. The following year, Erwin Schrödinger gave a
   simpler formulation of the theory in which he introduced a second-order
   differential equation for a wave function. He himself attempted a largely
   classical interpretation of the wave function. However, already the same year
   Max Born proposed a consistent statistical interpretation in which the square of
   the absolute value of this wave function expresses a probability amplitude for
   the outcome of a measurement.

   3. 2. The principles violated in classical
   Bohr saw quantum mechanics as a generalization of classical physics although it
   violates some of the basic ontological principles on which classical physics rests.
   These principles are:
           The principle of space and time, i.e., physical objects (systems)
             exist separately in space and time in such a way that they are
             localizable and countable, and physical processes (the evolution
             of systems) take place in space and time;
           The principle of causality, i.e., every event has a cause;
           The principle of determination, i.e., every later state of a system
             is uniquely determined by any earlier state;

   Physics and Philosophy                                           Musa Akrami

        The principle of continuity, i.e., all processes exhibiting a
           difference between the initial and the final state have to go
           through every intervening state; and finally
        The principle of the conservation of energy, i.e., the energy of a
           closed system can be transformed into various forms but is never
           gained, lost or destroyed.
Due to these principles it is possible within, say, classical mechanics, to define a
state of a system at any later time with respect to a state at any earlier time. So
whenever we know the initial state consisting of the system's position and
momentum, and know all external forces acting on it, we also know what will be
its later states. The knowledge of the initial state is usually acquired by
observing the state properties of the system at the time selected as the initial
moment. Furthermore, the observation of a system does not affect its later
behavior or, if observation somehow should influence this behavior, it is always
possible to incorporate the effect into the prediction of the system's later state.
Thus, in classical physics we can always draw a sharp distinction between the
state of the measuring instrument being used on a system and the state of the
physical system itself. It means that the physical description of the system is
objective because the definition of any later state is not dependent on measuring
conditions or other observational conditions.
Much of Kant's philosophy can be seen as an attempt to provide satisfactory
philosophical grounds for the objective basis of Newton's mechanics against
Humean scepticism. Kant showed that classical mechanics is in accordance with
the transcendental conditions for objective knowledge. Kant's philosophy
undoubtedly influenced Bohr in various ways as many scholars in recent years
have noticed (Hooker 1972; Folse 1985; Honnor 1987; Faye 1991; Kaiser 1992;
and Chevalley 1994). Bohr was definitely neither a subjectivist nor a positivist
philosopher, as Karl Popper (1967) and Mario Bunge (1967) have claimed. He
explicitly rejected the idea that the experimental outcome is due to the observer.
As he said: “It is certainly not possible for the observer to influence the events
which may appear under the conditions he has arranged” (APHK, p.51). Not
unlike Kant, Bohr thought that we could have objective knowledge only in case
we can distinguish between the experiential subject and the experienced object.
It is a precondition for the knowledge of a phenomenon as being something
distinct from the sensorial subject, that we can refer to it as an object without
involving the subject's experience of the object. In order to separate the object
from the subject itself, the experiential subject must be able to distinguish
between the form and the content of his or her experiences. This is possible only
if the subject uses causal and spatial-temporal concepts for describing the
sensorial content, placing phenomena in causal connection in space and time,
since it is the causal space-time description of our perceptions that constitutes

   Physics and Philosophy                                          Musa Akrami

the criterion of reality for them. Bohr therefore believed that what gives us the
possibility of talking about an object and an objectively existing reality is the
application of those necessary concepts, and that the physical equivalents of
“space,” “time,” “causation,” and “continuity” were the concepts “position,”
“time,” “momentum,” and “energy,” which he referred to as the classical
concepts. He also believed that the above basic concepts exist already as
preconditions of unambiguous and meaningful communication, built in as rules
of our ordinary language. So, in Bohr's opinion the conditions for an objective
description of nature given by the concepts of classical physics were merely a
refinement of the preconditions of human knowledge.

3. 3. The Correspondence Rule
The guiding principle behind Bohr's and later Heisenberg's work in the
development of a consistent theory of atoms was the correspondence rule. Bohr
had realized that according to his theory of the hydrogen atom, the frequencies
of radiation due to the electron's transition between stationary states with large
quantum numbers, i.e. states far from the ground state, coincide approximately
with the results of classical electrodynamics. Hence in the search for a theory of
quantum mechanics it became a methodological requirement to Bohr that any
further theory of the atom should predict values in domains of large quantum
numbers that should be a close approximation to the values of classical physics.
The correspondence rule was a heuristic principle meant to make sure that in
areas where the influence of Planck's constant could be neglected the numerical
values predicted by such a theory should be the same as if they were predicted
by classical radiation theory.
The correspondence rule was an important methodological principle. In the
beginning it had a clear technical meaning for Bohr. It is obvious, however, that
it makes no sense to compare the numerical values of the theory of atoms with
those of classical physics unless the meaning of the physical terms in both
theories is commensurable. The correspondence rule was based on the
metaphysical idea that classical concepts were indispensable for our
understanding of physical reality, and it is only when classical phenomena and
quantum phenomena are described in terms of the same classical concepts that
we can compare different physical experiences. It was this broader sense of the
correspondence rule that Bohr often had in mind later on.
Bohr's practical methodology stands therefore in direct opposition to Thomas
Kuhn and Paul Feyerabend's historical view that succeeding theories, like
classical mechanics and quantum mechanics, are incommensurable. In contrast
to their philosophical claims of meaning gaps and partial lack of rationality in

   Physics and Philosophy                                          Musa Akrami

the choice between incommensurable theories, Bohr believed not just
retrospectively that quantum mechanics was a natural generalization of classical
physics, but he and Heisenberg followed in practice the requirements of the
correspondence rule. Thus, in the mind of Bohr, the meaning of the classical
concepts did not change but their application was restricted. This was the lesson
of complementarity.

3. 4. Complementarity
3. 4. 1. From wave-particle duality to
Long before the development of modern quantum mechanics, Bohr had been
particularly concerned with the problem of particle-wave duality, i.e. the
problem that experimental evidence on the behaviour of both light and matter
seemed to demand a wave picture in some cases, and a particle picture in others.
Yet these pictures are mutually exclusive. Whereas a particle is always
localized, the very definition of the notions of wavelength and frequency
requires an extension in space and in time. Moreover, the classical particle
picture is incompatible with the characteristic phenomenon of interference.

Bohr’s long struggle with wave-particle duality had prepared him for a radical
step when the dispute between matrix and wave mechanics broke out in 1926-
27. For the main contestants, Heisenberg and Schrödinger, the issue at stake was
which view could claim to provide a single coherent and universal framework
for the description of the observational data. The choice was, essentially
between a description in terms of continuously evolving waves, or else one of
particles undergoing discontinuous quantum jumps. By contrast, Bohr insisted
that elements from both views were equally valid and equally needed for an
exhaustive description of the data. His way out of the contradiction was to
renounce the idea that the pictures refer, in a literal one-to-one correspondence,
to physical reality. Instead, the applicability of these pictures was to become
dependent on the experimental context. This is the gist of the viewpoint he
called ‘complementarity’.
Bohr first conceived the general outline of his complementarity argument in
early 1927, during a skiing holiday in Norway, at the same time when
Heisenberg wrote his uncertainty paper. When he returned to Copenhagen and
found Heisenberg's manuscript, they got into an intense discussion. On the one
hand, Bohr was quite enthusiastic about Heisenberg's ideas which seemed to fit
wonderfully with his own thinking. Indeed, in his subsequent work, Bohr always

   Physics and Philosophy                                         Musa Akrami

presented the uncertainty relations as the symbolic expression of his
complementarity viewpoint. On the other hand, he criticized Heisenberg
severely for his suggestion that these relations were due to discontinuous
changes occurring during a measurement process. Rather, Bohr argued, their
proper derivation should start from the indispensability of both particle and
wave concepts. He pointed out that the uncertainties in the experiment did not
exclusively arise from the discontinuities but also from the fact that in the
experiment we need to take into account both the particle theory and the wave
theory. It is not so much the unknown disturbance which renders the momentum
of the electron uncertain but rather the fact that the position and the momentum
of the electron cannot be simultaneously defined in this experiment.
We shall not go too deeply into the matter of Bohr's interpretation of quantum
mechanics. It may be useful, however, to sketch some of the main points.
Central in Bohr's considerations is the language which we use in physics. No
matter how abstract and subtle the concepts of modern physics may be, they are
essentially an extension of our ordinary language and a means to communicate
the results of our experiments. These results, obtained under well-defined
experimental circumstances, are what Bohr calls the "phenomena". A
phenomenon is "the comprehension of the effects observed under given
experimental conditions" (Bohr 1939, p. 24), it is the resultant of a physical
object, a measuring apparatus and the interaction between them in a concrete
experimental situation. The essential difference between classical and quantum
physics is that in quantum physics the interaction between the object and the
apparatus cannot be made arbitrarily small; the interaction must at least
comprise one quantum. This is expressed by Bohr's quantum postulate:
    [… the] essence [of the formulation of the quantum theory] may be
    expressed in the so-called quantum postulate, which attributes to any
    atomic process an essential discontinuity or rather individuality,
    completely foreign to classical theories and symbolized by Planck's
    quantum of action. (Bohr, 1928, p. 580)
A phenomenon, therefore, is an indivisible whole and the result of a
measurement cannot be considered as an autonomous manifestation of the object
itself independently of the measurement context. The quantum postulate forces
upon us a new way of describing physical phenomena:
   In this situation, we are faced with the necessity of a radical revision of
   the foundation for the description and explanation of physical phenomena.
   Here, it must above all be recognized that, however far quantum effects
   transcend the scope of classical physical analysis, the account of the
   experimental arrangement and the record of the observations must always

   Physics and Philosophy                                           Musa Akrami

   be expressed in common language supplemented with the terminology of
   classical physics. (Bohr, 1948, p. 313)
This is what Scheibe (1973) has called the "buffer postulate" because it
prevents the quantum from penetrating into the classical description: A
phenomenon must always be described in classical terms; Planck's constant does
not occur in this description.
Together, the two postulates induce the following reasoning. In every
phenomenon the interaction between the object and the apparatus comprises at
least one quantum. But the description of the phenomenon must use classical
notions in which the quantum of action does not occur. Hence, the interaction
cannot be analysed in this description. On the other hand, the classical character
of the description allows to speak in terms of the object itself. Instead of saying:
‘the interaction between a particle and a photographic plate has resulted in a
black spot in a certain place on the plate’, we are allowed to forgo mentioning
the apparatus and say: ‘the particle has been found in this place’. The
experimental context, rather than changing or disturbing pre-existing properties
of the object, defines what can meaningfully be said about the object.
Because the interaction between object and apparatus is left out in our
description of the phenomenon, we do not get the whole picture. Yet, any
attempt to extend our description by performing the measurement of a different
observable quantity of the object, or indeed, on the measurement apparatus,
produces a new phenomenon and we are again confronted with the same
situation. Because of the unanalyzable interaction in both measurements, the two
descriptions cannot, generally, be united into a single picture. They are what
Bohr calls complementary descriptions:
    [the quantum of action]...forces us to adopt a new mode of description
    designated as complementary in the sense that any given application of
    classical concepts precludes the simultaneous use of other classical
    concepts which in a different connection are equally necessary for the
    elucidation of the phenomena. (Bohr, 1929, p. 10)
The most important example of complementary descriptions is provided by the
measurements of the position and momentum of an object. If one wants to
measure the position of the object relative to a given spatial frame of reference,
the measuring instrument must be rigidly fixed to the bodies which define the
frame of reference. But this implies the impossibility of investigating the
exchange of momentum between the object and the instrument and we are cut
off from obtaining any information about the momentum of the object. If, on the
other hand, one wants to measure the momentum of an object the measuring
instrument must be able to move relative to the spatial reference frame. Bohr
here assumes that a momentum measurement involves the registration of the

   Physics and Philosophy                                           Musa Akrami

recoil of some movable part of the instrument and the use of the law of
momentum conservation. The looseness of the part of the instrument with which
the object interacts entails that the instrument cannot serve to accurately
determine the position of the object. Since a measuring instrument cannot be
rigidly fixed to the spatial reference frame and, at the same time, be movable
relative to it, the experiments which serve to precisely determine the position
and the momentum of an object are mutually exclusive. Of course, in itself, this
is not at all typical for quantum mechanics. But, because the interaction between
object and instrument during the measurement can neither be neglected nor
determined the two measurements cannot be combined. This means that in the
description of the object one must choose between the assignment of a precise
position or of a precise momentum.
Similar considerations hold with respect to the measurement of time and energy.
Just as the spatial coordinate system must be fixed by means of solid bodies so
must the time coordinate be fixed by means of unperturbable, synchronised
clocks. But it is precisely this requirement which prevents one from taking into
account of the exchange of energy with the instrument if this is to serve its
purpose. Conversely, any conclusion about the object based on the conservation
of energy prevents following its development in time.
The conclusion is that in quantum mechanics we are confronted with a
complementarity between two descriptions which are united in the classical
mode of description: the space-time description (or coordination) of a process
and the description based on the applicability of the dynamical conservation
laws. The quantum forces us to give up the classical mode of description (also
called the ‘causal’ mode of description by Bohr): it is impossible to form a
classical picture of what is going on when radiation interacts with matter as, e.g.,
in the Compton effect.
A causal description of the process cannot be attained; we have to content
ourselves with complementary descriptions. "The viewpoint of complementarity
may be regarded", according to Bohr, "as a rational generalization of the very
ideal of causality".
In addition to complementary descriptions Bohr also talks about
complementary phenomena and complementary quantities. Position and
momentum, as well as time and energy, are complementary quantities.
We have seen that Bohr's approach to quantum theory puts heavy emphasis on
the language used to communicate experimental observations, which, in his
opinion, must always remain classical. By comparison, he seemed to put little
value on arguments starting from the mathematical formalism of quantum
theory. This informal approach is typical of all of Bohr's discussions on the
meaning of quantum mechanics. One might say that for Bohr the conceptual

   Physics and Philosophy                                           Musa Akrami

clarification of the situation has primary importance while the formalism is only
a symbolic representation of this situation.
This is remarkable since, finally, it is the formalism which needs to be
interpreted. This neglect of the formalism, certainly, is one of the reasons why it
is so difficult to get a clear understanding of Bohr's interpretation of quantum
mechanics and why it has aroused so much controversy.

3. 4. 2. Summary of Bohr's more mature view
Until the mid-1930s when Einstein, Podolsky and Rosen published their famous
thought-experiment with the intention of showing that quantum mechanics was
incomplete, Bohr spoke as if the measurement apparatus disturbed the electron.
This paper had a significant influence on Bohr's line of thought. Apparently,
Bohr realized that speaking of disturbance seemed to indicate—as some of his
opponents may have understood him—that atomic objects were classical
particles with definite inherent kinematic and dynamic properties. After the EPR
paper he stated quite clearly: “the whole situation in atomic physics deprives of
all meaning such inherent attributes as the idealization of classical physics
would ascribe to such objects.”
Also after the EPR paper Bohr spoke about Heisenberg's “indeterminacy
relation” as indicating the ontological consequences of his claim that kinematic
and dynamic variables are ill-defined unless they refer to an experimental
outcome. Earlier he had often called it Heisenberg's “uncertainty relation”, as if
it were a question of a merely epistemological limitation. Furthermore, Bohr no
longer mentioned descriptions as being complementary, but rather phenomena or
information. He introduced the definition of a “phenomenon” as requiring a
complete description of the entire experimental arrangement, and he took a
phenomenon to be a measurement of the values of either kinematic or dynamic
Bohr's more mature view, i.e., his view after the EPR paper, on complementarity
and the interpretation of quantum mechanics may be summarized in the
following points:
    1. The interpretation of a physical theory has to rely on an experimental
    2. The experimental practice presupposes a certain pre-scientific practice of
       description, which establishes the norm for experimental measurement
       apparatus, and consequently what counts as scientific experience.
    3. Our pre-scientific practice of understanding our environment is an
       adaptation to the sense experience of separation, orientation, identification
       and reidentification over time of physical objects.

Physics and Philosophy                                          Musa Akrami

4. This pre-scientific experience is grasped in terms of common categories
   like thing's position and change of position, duration and change of
   duration, and the relation of cause and effect, terms and principles that are
   now parts of our common language.
5. These common categories yield the preconditions for objective
   knowledge, and any description of nature has to use these concepts to be
6. The concepts of classical physics are merely exact specifications of the
   above categories.
7. The classical concepts—and not classical physics itself—are therefore
   necessary in any description of physical experience in order to understand
   what we are doing and to be able to communicate our results to others, in
   particular in the description of quantum phenomena as they present
   themselves in experiments;
8. Planck's empirical discovery of the quantization of action requires a
   revision of the foundation for the use of classical concepts, because they
   are not all applicable at the same time. Their use is well defined only if
   they apply to experimental interactions in which the quantization of action
   can be regarded as negligible.
9. In experimental cases where the quantization of action plays a significant
   role, the application of a classical concept does not refer to independent
   properties of the object; rather the ascription of either kinematic or
   dynamic properties to the object as it exists independently of a specific
   experimental interaction is ill-defined.
10.The quantization of action demands a limitation of the use of classical
   concepts so that these concepts apply only to a phenomenon, which Bohr
   understood as the macroscopic manifestation of a measurement on the
   object, i.e. the uncontrollable interaction between the object and the
11.The quantum mechanical description of the object differs from the
   classical description of the measuring apparatus, and this requires that the
   object and the measuring device should be separated in the description,
   but the line of separation is not the one between macroscopic instruments
   and microscopic objects. It has been argued in detail (Howard 1994) that
   Bohr pointed out that parts of the measuring device may sometimes be
   treated as parts of the object in the quantum mechanical description.
12.The quantum mechanical formalism does not provide physicists with a
   ‘pictorial’ representation: the ψ-function does not, as Schrödinger had
   hoped, represent a new kind of reality. Instead, as Born suggested, the
   square of the absolute value of the ψ-function expresses a probability
   amplitude for the outcome of a measurement. Due to the fact that the

   Physics and Philosophy                                           Musa Akrami

      wave equation involves an imaginary quantity this equation can have only
      a symbolic character, but the formalism may be used to predict the
      outcome of a measurement that establishes the conditions under which
      concepts like position, momentum, time and energy apply to the
   13.The ascription of these classical concepts to the phenomena of
      measurements rely on the experimental context of the phenomena, so that
      the entire setup provides us with the defining conditions for the
      application of kinematic and dynamic concepts in the domain of quantum
   14.Such phenomena are complementary in the sense that their manifestations
      depend on mutually exclusive measurements, but that the information
      gained through these various experiments exhausts all possible objective
      knowledge of the object.

3. 4. 3. Bohr’s philosophical tendencies
Earlier generations of philosophers have often accused the Copenhagen
interpretation of being subjectivistic or positivistic. Today anyone who has
studied Bohr's essays carefully agrees that his view is neither. There are, as
many have noticed, both typically realist as well as antirealist elements involved
in it, and it has affinities to Kant or neo-Kantianism.
Bohr thought of the atom as real. Atoms are neither heuristic nor logical
constructions. A couple of times he emphasized this directly using arguments
from experiments in a very similar way to Ian Hacking and Nancy Cartwright
much later. What he did not believe was that the quantum mechanical formalism
was true in the sense that it gave us a literal (‘pictorial’) rather than a symbolic
representation of the quantum world. It makes much sense to characterize Bohr
in modern terms as an entity realist who opposes theory realism (Folse 1987). It
is because of the imaginary quantities in quantum mechanics (where the
commutation rule for canonically conjugate variable, p and q, introduces
Planck's constant into the formalism by pq - qp = ih/2π) that quantum mechanics
does not give us a ‘pictorial’ representation of the world. Neither does the theory
of relativity, Bohr argued, provide us with a literal representation, since the
velocity of light is introduced with a factor of i in the definition of the fourth
coordinate in a four-dimensional manifold (CC, p. 86 and p. 105). Instead these
theories can only be used symbolically to predict observations under well-
defined conditions. Thus Bohr was an antirealist or an instrumentalist when it
comes to theories.
In general, Bohr considered the demands of complementarity in quantum
mechanics to be logically on a par with the requirements of relativity in the

   Physics and Philosophy                                          Musa Akrami

theory of relativity. He believed that both theories were a result of novel aspects
of the observation problem, namely the fact that observation in physics is
context-dependent. This again is due to the existence of a maximum velocity of
propagation of all actions in the domain of relativity and a minimum of any
action in the domain of quantum mechanics. And it is because of these universal
limits that it is impossible in the theory of relativity to make an unambiguous
separation between time and space without reference to the observer (the
context) and impossible in quantum mechanics to make a sharp distinction
between the behavior of the object and its interaction with the means of
observation (CC, p. 105).
In emphasizing the necessity of classical concepts for the description of the
quantum phenomena, Bohr was influenced by Kant or neo-Kantianism. But he
was a naturalized or a pragmatized Kantian. The classical concepts are merely
explications of common concepts that are already a result of our adaptation to
the world. These concepts and the conditions of their application determine the
conditions for objective knowledge. The discovery of the quantization of action
has revealed to us, however, that we cannot apply these concepts to quantum
objects as we did in classical physics. Now kinematic and dynamic properties
(represented by conjugate variables) can be meaningfully ascribed to the object
only in relation to some actual experimental results, whereas classical physics
attributes such properties to the object regardless of whether we actually observe
them or not. In other words, Bohr denied that classical concepts could be used to
attribute properties to a physical world in-itself behind the phenomena, i.e.
properties different from those being observed. In contrast, classical physics
rests on an idealization, he said, in the sense that it assumes that the physical
world has these properties in-itself, i.e. as inherent properties, independent of
their actual observation.
The Copenhagen interpretation is first and foremost a semantic and
epistemological reading of quantum mechanics that carries certain ontological
implications. Bohr's view was, to phrase it in a modern philosophical jargon, that
the truth conditions of sentences ascribing a certain kinematic or dynamic value
to an atomic object are dependent on the apparatus involved, in such a way that
these truth conditions have to include reference to the experimental setup as well
as the actual outcome of the experiment. Hence, those physicists who accuse this
interpretation of operating with a mysterious collapse of the wave function
during measurements do not understand a word of it. Bohr accepted the Born
statistical interpretation because he believed that the ψ-function has only a
symbolic meaning and does not represent anything real. It makes sense to talk
about a collapse of the wave function only if, as Bohr put it, the ψ-function can
be given a pictorial representation, something he strongly denied.

   Physics and Philosophy                                        Musa Akrami

Indeed, Bohr, Heisenberg and many other physicists considered the Copenhagen
Interpretation to be the only rational interpretation of the quantum world. They
thought that it gave us the understanding of atomic phenomena that is in
accordance with the conditions for any physical description and the possible
objective knowledge of the world. Bohr believed that atoms are real, but it
remains a much debated point in the recent literature what sort of reality he
believed them to have, whether or not they are something beyond and different
from what they are observed to be (Folse 1985 and 1994; and Faye 1991).

References to Work by Bohr
ATDN Bohr, N. (1934/1987 ,)Atomic Theory and the Description of Nature ,
     reprinted as The Philosophical Writings of Niels Bohr, Vol. I ,
     Woodbridge: Ox Bow Press.
APHK Bohr, N. (1958/1987 ,)Essays 1932-1957 on Atomic Physics and Human
     Knowledge ,reprinted as The Philosophical Writings of Niels Bohr, Vol .
     II ,Woodbridge: Ox Bow Press.
Essays Bohr, N. (1963/1987 ,)Essays 1958-1962 on Atomic Physics and Human
       Knowledge ,reprinted as The Philosophical Writings of Niels Bohr, Vol .
       III ,Woodbridge: Ox Bow Press.
CC     Bohr, N. (1998 ,)Causality and Complementarity ,supplementary papers
       edited by Jan Faye and Henry Folse as The Philosophical Writings of
       Niels Bohr, Vol. IV ,Woodbridge: Ox Bow Press.

Other References
      Bunge, M. (1967), “The Turn of the Tide”, in Mario Bunge (ed ).Quantum
       Theory and Reality ,New York: Springer, pp. 1-12 .
      Chevalley, C. (1994), “Niels Bohr's Words and the Atlantis of
       Kantianism ,”in J. Faye and H. Folse (eds ,)Niels Bohr and Contemporary
       Philosophy ,pp. 33-55 .
      Faye, J. (1991) ,Niels Bohr: His Heritage and Legacy. An Antirealist View
       of Quantum Mechanics ,Dordrecht: Kluwer Academic .

Physics and Philosophy                                        Musa Akrami

   Faye, J., and Folse, H. (eds) (1994 ,)Niels Bohr and Contemporary
    Philosophy ,Boston Studies in the Philosophy of Science, vol. 158 ,
    Dordrecht: Kluwer Academic .
   Folse, H. (1985), The Philosophy of Niels Bohr. The Framework of
    Complementarity ,Amsterdam: North Holland .
   Folse, H. (1986), “Niels Bohr, Complementarity, and Realism”, in A. Fine
    and P. Machamer (eds) ,PSA 1986: Proceedings of the Biennial Meeting
    of the Philosophy of Science Association, vol. I ,East Lansing: PSA, pp.
    96-104 .
   Folse, H (1994), “Bohr's Framework of Complementarity and the Realism
    Debate”, in Faye and Folse (1994), pp. 119-139 .
   Held, C. (1994), “The Meaning of Complementarity ,”Studies in History
    and Philosophy of Science .893-871 ,25 ,
   Honner, J. (1987) ,The Description of Nature: Niels Bohr and The
    Philosophy of Quantum Physics ,Oxford: Clarendon Press .
   Hooker, C. A. (1972), “The Nature of Quantum Mechanical Reality”, in
    R. G .Colodny (ed.) ,Paradigms and Paradoxes ,Pittsburgh: University of
    Pittsburgh Press, pp. 67-305 .
   Howard, D. (1994), “What Makes a Classical Concept Classical? Toward
    a Reconstruction of Niels Bohr's Philosophy of Physics”, in Faye and
    Folse (1994 ,)pp. 201-229 .
   Kaiser, D. (1992), “More Roots of Complementarity: Kantian Aspects and
    Influences ,”Studies in History and Philosophy of Science .239-213 ,23 ,
   Murdoch, D. (1987) ,Niels Bohr's Philosophy of Physics ,Cambridge :
    Cambridge University Press .
   Petruccioli, S. (1993 ,)Atoms, Metaphors and Paradoxes ,Cambridge :
    Cambridge University Press .
   Plotnitsky, A. (1994 ,)Complementarity: Anti-Epistemology after Bohr
    and Derrida ,Durham: Duke University Press .
   Popper, K. R. (1967), “Quantum Mechanics Without ‘the Observer’”, in
    Mario Bunge (ed.) Quantum Theory and Reality ,New York: Springer, pp.

   Physics and Philosophy                                           Musa Akrami

Chapter4. Summary of some
philosophical and foundational issues
in quantum theories
        Introductory Remark
        Ever since quantum theory was born in 1900, it has been beset
        with interpretative difficulties. We shall pick out five main
        areas, which continue to be areas of active research. During the
        1920s, quantum theory took a definite shape as a result of
        intense work by physicists and mathematicians.

Quantum theory reached its canonical form in von Neumann's 1932 book
Mathematical Foundations of Quantum Mechanics. This book formulated
sharply two major interpretational issues:
(1) The problem of whether the statistical character of quantum theory is
epistemic or ontic in nature (also known as the problem of "hidden variables'');
 (2) The measurement problem.
(1): While von Neumann thought he had answered (1) definitively by
providing an "exact proof '' that the probabilistic character of quantum theory is
irreducible and cannot be thought of as a result of our ignorance, the issue
cannot be considered settled even today. One central aspect of this problem is
the question how to interpret the quantum probability calculus, which differs
from the classical Kolmogorovian probability calculus in crucial respects. Is
there a meaningful relative frequency interpretation of a probability measure
defined on the non-commutative event structure determined by quantum theory?
It has been claimed that quantum probabilities are not any sort of peculiar, exotic
probabilities: they are ordinary, classical conditional probabilities, conditioned
by the (also classical) events that certain measurements are carried out. Is this a
viable re-interpretation of quantum probability? If so, what philosophical
consequences does it entail?
(2): The measurement problem arises in quantum theory if one attempts to
describe the measuring process on the assumption that both the measured system
and the measuring apparatus are quantum systems and so described by quantum
theory. The problem is that accepting the so-called "eigenvalue eigenstate

   Physics and Philosophy                                          Musa Akrami

link'' rule, which specifies the conditions under which a quantity for a quantum
system has a definite value, leads to a paradoxical situation: after the
measurement interaction the joint system consisting of the measured+measuring
system ends up in a joint quantum state in which the measuring apparatus does
not have a sharp pointer value, i.e. does not in fact provide a definite result of
the measurement. Over the years since von Neumann's book, many solutions of
the measurement problem have been proposed: for example, appeals to the
environment of the measuring apparatus (decoherence), to "other worlds''
(i.e. Everettian interpretations), or to hidden variables, i.e. extra values for
quantities. (This last appeal can be made in various ways: one can postulate
once and for all that certain quantities, say positions, are definite, as in the
pilot-wave interpretation; or one can let which quantity is definite depend on the
quantum state, as in the modal interpretation.) But none of these solutions has
won assent; controversy still rages.
(3): Soon after von Neumann's book, the Einstein-Podolsky-Rosen (EPR)
paper of 1935, and later in the 1960s, the closely related work of J. Bell
articulated another area of interpretative difficulty: non-locality. The question
here is whether certain probabilistic correlations between spacelike separated
events predicted by quantum theory (and confirmed by experiments) can have a
causal explanation. Again, the subject has flourished since these
ground-breaking papers. For example, in 1989 Greenberger-Horne-Zeilinger
(GHZ) exhibited a new type of situation in which the quantum correlations
violate classical ideas in a non-probabilistic way. More philosophically, many
specifications of the notion of causal explanation have been proposed and
analyzed; most recently, using the idea of a branching space-time to represent
(4): Quantum logic was originally proposed in 1936 by G. Birkhoff and von
Neumann: the idea was that the lattice structure determined by the projections of
a quantum system should be interpreted as the logic of propositions about the
system. What notion of logic does this involve? In particular, does it mean that
logic is empirical? Since 1936, quantum logic has developed into an extremely
rich field, which is still expanding in several directions. Recently, research has
turned to the investigation of more abstract algebraic structures (e.g. quantum
MV algebras, unsharp quantum logic), and connections have also been made
between quantum logic and category theory.
Discussion of the conceptual status and philosophical significance of these
recent directions of research is much needed.
(5): Quantum field theories (QFT), especially relativistic ones, have been
developed since about 1930. There are many different approaches to these; but
foundational and philosophical attention has naturally focussed on

   Physics and Philosophy                                         Musa Akrami

mathematically rigorous approaches, especially the algebraic relativistic
quantum field theories (ARQFT) developed since the 1950s.
QFTs present us with new interpretative issues, in addition to those above,
which are common to all quantum theories. Two such issues are as follows.
(i): The notion of a particle. Various no-go results (many based on the
Reeh-Schlieder theorem) seem to entail that the notion of particle as sharply
localized in space or spacetime is incompatible with the basic assumptions of
QFT. What then is the notion of particle in QFT? And more generally: What
ontology is QFT compatible with? These questions have been addressed, for
example in the modal interpretation; but many questions remain open.
(ii): The QFT version of EPR-Bell correlations. In the last fifteen years, it has
been shown that various kinds of non-locality - more precisely, entanglement
between local algebras of observables pertaining to space-like separated
space-time regions - are generic in AQFT. Thus the problem arises whether one
can causally explain these correlations. Here again, many natural problems are
entirely open.

         Physics and Philosophy                                          Musa Akrami

   Chapter5. The Einstein-Podolsky-
   Rosen argument in quantum theory
5. 1. Can quantum mechanical description of physical reality be considered
5. 1. 1. Setting and prehistory
5. 1. 2. The argument in the text
5. 1. 3. Einstein's versions of the argument
5. 2. A popular form of the argument: Bohr's response
5. 3. Development of EPR
5. 3. 1. The Bohm version
5. 3. 2. Bell and beyond

                Introductory Remarks
                In the May 15, 1935 issue of Physical Review Albert Einstein
                co-authored a paper with his two postdoctoral research
                associates at the Institute for Advanced Study, Boris Podolsky
                and Nathan Rosen. The article was entitled "Can Quantum
                Mechanical Description of Physical Reality Be Considered
                Complete?" (Einstein et al. 1935).
                Generally referred to as "EPR", this paper quickly became a
                centerpiece in the debate over the interpretation of the quantum
                theory, a debate that continues today. This entry describes the
                argument of that 1935 paper, considers several different
                versions and reactions, and explores the ongoing significance of
                the issues they raise.

       By Arthur Fine, University of Washington

   Physics and Philosophy                                           Musa Akrami

5. 1. Can quantum mechanical description
of physical reality be considered complete?
5. 1. 1. Setting and prehistory
By 1935 the conceptual understanding of the quantum theory was dominated by
Bohr's ideas concerning complementarity. Those ideas centered on observation
and measurement in the quantum domain. According to Bohr's views at that
time, observing a quantum object involves a physical interaction with a classical
measuring device that results in an uncontrollable disturbance of both systems.
The picture here is of a tiny object banging into a big apparatus. The disturbance
this produces on the measuring instrument is what issues in the measurement
"result" which, because it is uncontrollable, can only be predicted statistically.
The disturbance experienced by the quantum object restricts those quantities that
can be co-measured with precision. According to complementarity when we
observe the position of an object, we disturb its momentum uncontrollably. Thus
we cannot determine precisely both position and momentum. A similar situation
arises for the simultaneous determination of energy and time. Thus
complementarity involves a doctrine of uncontrollable physical disturbance that,
according to Bohr, underwrites the Heisenberg uncertainty relations and is also
the source of the statistical character of the quantum theory.
Initially Einstein was enthusiastic about the quantum theory. By 1935, however,
his enthusiasm for the theory had been replaced by a sense of disappointment.
His reservations were twofold.
Firstly, he felt the theory had abdicated the historical task of natural science to
provide knowledge of, or at least justified belief in, significant aspects of nature
that were independent of observers or their observations. Instead the
fundamental understanding of the wave function (alternatively, the "state
function", "state vector", or "psi-function") in quantum theory was that it
provided probabilities only for "results" if appropriate measurements were made
(the Born Rule). The theory was simply silent about what, if anything, was
likely to be true in the absence of observation. In this sense it was irrealist.
Secondly, the quantum theory was essentially statistical. The probabilities built
into the state function were fundamental and, unlike the situation in classical
statistical mechanics, they were not understood as arising from ignorance of fine
details. In this sense the theory was indeterministic. Thus Einstein began to
probe how strongly the quantum theory was tied to irrealism and indeterminism.
He wondered whether it was possible, at least in principle, to ascribe certain
properties to a quantum system in the absence of measurement (and not just
probabilistically). Can we suppose, for instance, that the decay of an atom

   Physics and Philosophy                                          Musa Akrami

occurs at a definite moment in time even though such a definite time-value is not
implied by the quantum state function? That is, Einstein began to ask whether
the quantum mechanical description of reality was complete. Since Bohr's
complementarity provided strong support both for irrealism and indeterminism
and since it played such a dominant role in shaping the prevailing attitude
toward quantum theory, complementarity became Einstein's first target. In
particular, Einstein had reservations about the scope and uncontrollable effects
of the physical disturbances invoked by Bohr and about their role in fixing the
interpretation of the wave function. EPR was intended to support those
reservations in a particularly dramatic way.
Max Jammer (1974, pp. 166-181) describes the EPR paper as originating with
Einstein's reflections on a thought experiment he proposed in the 1930 Solvay
That experiment concerns a box that contains a clock which appears able to time
precisely the release (in the box) of a photon with determinate energy. If this
were feasible, it would appear to challenge the unrestricted validity of the
Heisenberg uncertainty relation that sets a lower bound on the simultaneous
uncertainty of energy and time.
The uncertainty relations, understood not just as a prohibition on what is co-
measurable, but on what is simultaneously real, were a central component in the
irrealist interpretation of the wave function.
Jammer (1974, p. 173) describes how Einstein's thinking about this experiment,
and Bohr's objections to it, evolved into a different photon-in-a-box
experiment, one that allows an observer to determine either the momentum or
the position of the photon indirectly, while remaining outside, sitting on the box.
Jammer associates this with the distant determination of either momentum or
position that, we shall see, is at the heart of the EPR paper. Carsten Held (1996)
cites a related correspondence with Paul Ehrenfest from 1932 in which Einstein
described an arrangement for the indirect measurement of a particle of mass m
using correlations with a photon established through Compton scattering.
Einstein's reflections here foreshadow the argument of EPR, along with noting
some of its difficulties.
    Thus without an experiment on m it is possible to predict freely, at will,
    either the momentum or the position of m with, in principle, arbitrary
    precision. This is the reason why I feel compelled to ascribe objective
    reality to both. I grant, however, that it is not logically necessary. (Held
    1998, p. 90)
Whatever their precursors, the ideas that found their way into EPR were worked
out in a series of meetings with Einstein and his two assistants, Podolsky and
Rosen. The actual text, however, was written by Podolsky and, apparently,
Einstein did not see the final draft (certainly he did not inspect it) before

   Physics and Philosophy                                         Musa Akrami

Podolsky submitted the paper to Physical Review in March of 1935, where it
was accepted for publication without changes. Right after it was published
Einstein complained that his central concerns were obscured by the overly
technical nature of Podolsky's development of the argument.
   For reasons of language this [paper] was written by Podolsky after several
   discussions. Still, it did not come out as well as I had originally wanted;
   rather, the essential thing was, so to speak, smothered by the formalism
   [Gelehrsamkeit]. (Letter from Einstein to Erwin Schrödinger, June 19,
   1935. In Fine 1996, p. 35.)
Thus in discussing the argument of EPR we should consider both the
argument in Podolsky's text and the argument that Einstein intended to
offer. We should also consider an argument presented in Bohr's reply to
EPR, which is possibly the best known version, although it differs
                                           significantly from the others.

5. 1. 2. The argument in the text
The EPR text is concerned, in the first instance, with the logical connections
between two assertions.
One asserts that quantum mechanics is incomplete.
The other asserts that incompatible quantities (those whose operators do
not commute, like a coordinate of position and linear momentum in that
direction) cannot have simultaneous "reality" (i.e., simultaneously real
The authors assert as a premise, later to be justified, that one or another of
these must hold.
It follows that if quantum mechanics were complete (so that the first option
failed) then the second option, that incompatible quantities cannot have
simultaneously real values, would hold.
However they also take as a second premise (also to be justified), that if
quantum mechanics were complete, then incompatible quantities (in particular
position and momentum) could indeed have simultaneous, real values.
They conclude that quantum mechanics is incomplete.
The conclusion certainly follows since otherwise (i.e., if the theory were
complete) one would have a contradiction.
Nevertheless the argument is highly abstract and formulaic and even at this point
in its development one can readily appreciate Einstein's disappointment with it.
EPR now proceed to establish the two premises, beginning with a discussion of
the idea of a complete theory.

   Physics and Philosophy                                           Musa Akrami

Here they offer only a necessary condition; namely, that for a complete theory
"every element of the physical reality must have a counterpart in the physical
Although they do not specify just what an "element of physical reality" is they
use that expression when referring to the values of physical quantities (positions,
momenta, and so on) under the following criterion (p. 777):
   If, without in any way disturbing a system, we can predict with certainty
   (i.e., with probability equal to unity) the value of a physical quantity, then
   there exists an element of reality corresponding to that quantity.
This sufficient condition is often referred to as the EPR Criterion of Reality.
With these terms in place it is easy to show that if, say, the values of position
and momentum for a quantum system were simultaneously real (i.e., were
elements of reality) then the description provided by the wave function of the
system would be incomplete, since no wave function contains counterparts for
both elements. (Technically, no state function is a simultaneous eigenstate for
both position and momentum.)
Thus they establish the first premise: either quantum theory is incomplete or
there can be no simultaneously real values for incompatible quantities.
They now need to show that if quantum mechanics were complete, then
incompatible quantities could have simultaneous real values, which is the second
premise. This, however, is not easily established. Indeed what EPR proceed to
do is very odd. Instead of assuming completeness and on that basis deriving that
incompatible quantities can have simultaneously real values, they simply set out
to derive the latter assertion without any completeness assumption at all.
This "derivation" turns out to be the heart of the paper and its most
controversial part. It attempts to show that in certain circumstances a
quantum system can have simultaneous values for incompatible quantities
(once again, for position and momentum), where these values also pass the
Reality Criterion's test for being "elements of reality".
They proceed by sketching a thought experiment. In the experiment two
quantum systems interact in such a way that two conservation laws hold. One is
the conservation of relative position. If we imagine the systems located along
the x-axis, then if one of the systems (we can call it Albert's) were found at
position q along the axis at a certain time, the other system (call it Niels') would
be found then a fixed distance d away, say at q′=q-d, where we may suppose that
the distance d between q and q′ is substantial. The other conservation law is that
the total linear momentum (along that same axis) is always zero. So when the
momentum of Albert's system along the x-axis is determined to be p, the
momentum of Niels' system would be found to be −p. The paper constructs an
explicit wave function for the combined (Albert+Niels) system that satisfies

   Physics and Philosophy                                           Musa Akrami

both conservation principles. Although commentators later raised questions
about the legitimacy of this wave function, it does appear to satisfy the two
conservation principles at least for a moment (Jammer 1974, pp. 225-38). In any
case, one can model the same conceptual situation in other cases that are clearly
well defined quantum mechanically.
At this point of the argument (p. 779) EPR make two critical assumptions,
although they do not call special attention to them.
The first assumption (separability) is that at the time when measurements will
be performed on Albert's system there is some reality that pertains to Niels'
system alone. In effect, they assume that Niels' system maintains its separate
identity even though it is linked with Albert's. They need this assumption to
make sense of another.
The second assumption is that of locality. This supposes that "no real change
can take place" in Niels' system as a consequence of a measurement made on
Albert's system. They gloss this by saying "at the time of measurement the two
systems no longer interact." Notice that this is not a general principle of no-
disturbance, but rather a principle governing change only in what is real with
respect to Niels' system.
On the basis of these two assumptions they conclude that Niels' system can
have real values ("elements of reality") for both position and momentum
There is no detailed argument for this in the text. Instead they use these two
assumptions to show how one could be led to assign both a position eigenstate
and a momentum eigenstate to Niels' system, from which the simultaneous
attribution of elements of reality is supposed to follow. Since this is the central
and most controversial part of the paper, it pays to go slowly here in trying to
reconstruct an argument on their behalf.
One attempt might go as follows. Separability holds that some reality pertains to
Niels' system. Suppose that we measure, say, the position of Albert's system.
The reduction of the state function for the combined systems then yields a
position eigenstate for Niels' system. That eigenstate applies to the reality there
and that eigenstate enables us to predict a determinate position for Niels' system
with probability one. Since that prediction only depends on a measurement made
on Albert's system, locality implies that the prediction of the position of Niels'
system does not involve any change in the reality of Niels' system.
If we interpret this as meaning that the prediction does not disturb Niels' system,
all the pieces are in place to apply The Criterion of Reality. It certifies that the
predicted position value, corresponding to the position eigenstate, is an element
of the reality that pertains to Niels' system. One could argue similarly with
respect to momentum.

   Physics and Philosophy                                            Musa Akrami

This line of argument, however, is deceptive and contains a serious confusion. It
occurs right after we apply locality to conclude that the measurement made on
Albert's system does not affect the reality pertaining to Niels' system. For, recall,
we have not yet determined whether the position inferred for Niels' system is
indeed an "element" of that reality. Hence it is still possible that the
measurement of Albert's system, while not disturbing the reality pertaining to
Niels' system, does disturb its position. To take the extreme case; suppose, for
example, that the measurement of Albert's system somehow brings the position
of Niels' system into being, or suddenly makes it well defined, and also allows
us to predict it with certainty. It would then follow from locality that the position
of Niels' system is not an element of the reality of that system, since it can be
affected at a distance. But, reasoning exactly as above, the Criterion would still
hold that the position of Niels' system is an element of the reality there, since it
can be predicted with certainty without disturbing the reality of the system.
What has gone wrong? It is that the Criterion provides a sufficient
condition for elements of reality and locality provides a necessary condition.
But, as above, there is no guarantee that these conditions will always match
consistently. To ensure consistency we need to be sure that what the Criterion
certifies as real is not something that can be influenced at a distance. One way to
do this, which seems to be implicit in the EPR paper, would be to interpret
locality in the EPR situation in such a way that measurements made on one
system are understood not to disturb those quantities on the distant, unmeasured
system whose values can be inferred from the reduced state of that system.
Given the two conservation laws satisfied in the EPR situation, this extended
way of understanding locality allows the Criterion to certify that position, as
well as momentum, when inferred for Niels' system, are real there.
As EPR point out, however, position and momentum cannot be measured
simultaneously. So even if each can be shown to be real in distinct contexts of
measurement, are they real at the same time? The answer is "yes", for the logical
force of locality is to decontextualize the reality of Niels' system from goings on
at Albert's. Thus when we infer from a certain measurement made on Albert's
system that Niels' system has an element of reality, locality kicks in and
guarantees that Niels' system would have that same element of reality even in
the absence of the measurement on Albert's system.
Put differently, locality entitles us to conclude that Niels' system has a real
position provided the conditional assertion "If a position measurement is
performed on Albert's system, then Niels' system has a real position" holds.
Similarly, Niels' system has a real momentum provided the conditional "If a
momentum measurement is performed on Albert's system, then Niels' system
has a real momentum" holds.

   Physics and Philosophy                                           Musa Akrami

As we have seen, given separability, locality and the Criterion of Reality both
conditionals hold. Hence locality implies that Niels' system has real values of
both position and momentum simultaneously, even though no simultaneous
measurement of position and momentum is allowed.
In the penultimate paragraph of EPR (p. 780) they address the problem of
getting real values for incompatible quantities simultaneously.
   Indeed one would not arrive at our conclusion if one insisted that two or
   more physical quantities can be regarded as simultaneous elements of
   reality only when they can be simultaneously measured or predicted. …
   This makes the reality [on the second system] depend upon the process of
   measurement carried out on the first system, which does not in any way
   disturb the second system. No reasonable definition of reality could be
   expected to permit this.
The unreasonableness to which EPR allude in making "the reality [on the second
system] depend upon the process of measurement carried out on the first system,
which does not in any way disturb the second system" is just the
unreasonableness that would be involved in renouncing locality itself. For it is
locality that enables one to overcome the incompatibility of position and
momentum measurements of Albert's system by requiring their joint
consequences for Niels' system to be incorporated in a single, stable reality
there. If we recall Einstein's acknowledgment to Ehrenfest that getting
simultaneous position and momentum was "not logically necessary", we can see
how EPR respond by making it become necessary once locality is assumed.

5. 1. 3. The key features of EPR
Here, then, are the key features of EPR.
       EPR is about the interpretation of state vectors ("wave
         functions") and employs the standard state vector reduction
         formalism (von Neumann's "projection postulate").
       The Criterion of Reality is only used to check, after state vector
         reduction assigns an eigenstate to the unmeasured system, that
         the associated eigenvalue constitutes an element of reality.
       (Separability) EPR make the tacit assumption that, because they
         are spatially separated, some "reality" pertains to the
         unmeasured component of the combined system.
       (Locality) EPR assume a principle of locality according to
         which, if two systems are far enough apart, the measurement of
         one system does not directly affect the reality that pertains to the
         unmeasured system. (This non-disturbance is understood to
         include those quantities on the distant, unmeasured system

   Physics and Philosophy                                          Musa Akrami

          whose values can be inferred from the reduced state of that
        Locality is critical in guaranteeing that simultaneous position
          and momentum values can be assigned to the unmeasured
          system even though position and momentum cannot be
          measured simultaneously on the other system.
        Assuming separability and locality, the demonstration of
          simultaneous position and momentum values depends on the
          state vector descriptions in conjunction with the Criterion of
        In summary, the argument of EPR shows that if interacting
          systems satisfy separability and locality, then the description of
          systems provided by state vectors is not complete. This
          conclusion rests on a common interpretive principle, state vector
          reduction, and the Criterion of Reality.
The EPR experiment with interacting systems accomplishes a form of indirect
measurement. The direct measurement of Albert's system yields information
about Niels' system; it tells us what we would find if we were to measure there
directly. But it does this at-a-distance, without any further physical interaction
taking place between the two systems. Thus the thought experiment at the heart
of EPR undercuts the picture of measurement as necessarily involving a tiny
object banging into a large measuring instrument.
If we look back at Einstein's reservations about complementarity, we can
appreciate that by focusing on a non-disturbing kind of measurement the EPR
argument targets Bohr's program for explaining central conceptual features of
the quantum theory. For that program relied on uncontrollable disturbances as a
necessary feature of any measurement in the quantum domain. Nevertheless the
cumbersome machinery employed in the EPR paper makes it difficult to see
what is central. It distracts from rather than focuses on the issues. That was
Einstein's complaint about Podolsky's text in his June 19, 1935 letter to
Schrödinger. Schrödinger responded on July 13 reporting reactions to EPR that
vindicate Einstein's concerns. With reference to EPR he wrote:
   I am now having fun and taking your note to its source to provoke the
   most diverse, clever people: London, Teller, Born, Pauli, Szilard, Weyl.
   The best response so far is from Pauli who at least admits that the use of
   the word "state" ["Zustand"] for the psi-function is quite disreputable.
   What I have so far seen by way of published reactions is less witty. … It
   is as if one person said, "It is bitter cold in Chicago"; and another
   answered, "That is a fallacy, it is very hot in Florida." (Fine 1996, p. 74)

   Physics and Philosophy                                            Musa Akrami

5. 1. 4. Einstein's versions of the argument
Einstein set about almost immediately to provide a clearer and more focused
version of the argument. He began that process just a few weeks after EPR was
published, in the June 19 letter to Schrödinger, and continued it in an article
published the following year (Einstein 1936). He returned to these ideas some
years later in a few other publications. Although his various expositions differ
from one another they all employ composite systems as a way of implementing
non-disturbing measurements-at-a-distance. None of Einstein's own accounts
contains the Criterion of Reality nor the tortured EPR argument over when
values of a quantity can be regarded as "elements of reality". The Criterion and
these "elements" simply drop out. Nor does Einstein engage in calculations, like
those of Podolsky, about the explicit form of the total wave function for the
composite system. Moreover, as early as June 19, 1935 Einstein makes it plain
that he is not especially interested in the question of simultaneous values for
incompatible quantities like position and momentum. The concern that he
expresses to Schrödinger is with the question of completeness, given the
resources of the quantum theory, in describing the situation concerning a single
variable (maybe position, maybe momentum). With respect to the treatment of
an incompatible pair he tells Schrödinger "ist mir wurst" — literally, it's sausage
to me; i.e., he couldn't care less. (Fine 1996, p. 38). In his writings subsequent to
EPR, Einstein probes an incompatibility between affirming locality and
separability, on the one hand, and completeness in the description of individual
systems by means of state functions, on the other. His argument is that we can
have at most one of these but never both. He frequently refers to this
dilemma as a "paradox".
In the letter to Schrödinger of June 19, Einstein sketches a simple argument for
the dilemma, roughly as follows. Consider an interaction between the Albert and
Niels systems that conserves their relative positions. (We need not worry about
momentum, or any other quantity.) Consider the evolved wave function for the
total (Albert+Niels) system. Now assume a principle of locality-separability
(Einstein calls it a Trennungsprinzip — separation principle): Whether a
physical property holds for Niels' system does not depend on what
measurements (if any) are made locally on Albert's system. If we measure the
position of Albert's system, the conservation of relative position implies that we
can immediately infer the position of Niels'; i.e., we can infer that Niels' system
has a determinate position. By locality-separability it follows that Niels' system
must already have had a determinate position just before Albert began that
measurement. At that time, however, Niels' system has no independent state
function. There is only a state function for the combined system and that total
state function does not predict with certainty the position one would find for

   Physics and Philosophy                                             Musa Akrami

Niels' system (i.e., it is not a product one of whose factors is an eigenstate for the
position of Niels' system).
Thus the description of Niels' system afforded by the quantum state function is
incomplete. A complete description would say (definitely yes) if a physical
property were true of Niels' system. (Notice that this argument does not even
depend on the reduction of the total state function for the combined system.)
In this formulation of the argument it is clear that locality-separability conflicts
with the eigenvalue-eigenstate link, which holds that a quantity of a system
has an eigenvalue if and only if the state of the system is an eigenstate of
that quantity with that eigenvalue. The "only if" part of the link would need to
be weakened order to interpret quantum state functions as complete descriptions.

Although this simple argument concentrates on what Einstein saw as the
essentials, stripping away most technical details and distractions, he had another
slightly more complex argument that he was also fond of producing. (It is
actually buried in the EPR paper, p. 779.) This second argument focuses clearly
on the interpretation of quantum state functions and not on any issues about
simultaneous values (real or not) for incompatible quantities. It goes like this.
Suppose, as in EPR, that the interaction between the two systems preserves
both relative position and zero total momentum and that the systems are far
apart. As before, we can measure either the position or momentum of Albert's
system and, in either case, we can infer the position or momentum for Niels'
system. It follows from the reduction of the total state function that, depending
on whether we measure the position or momentum of Albert's system, Niels'
system will be left (respectively) either in a position eigenstate or in a
momentum eigenstate.
Suppose too that separability hold for Niels; that is, that Niels' system has
some real physical state of affairs. If locality holds as well, then the
measurement of Albert's system does not disturb the assumed "reality" for Niels'
system. However, that reality appears to be represented by quite different state
functions, depending on which measurement of Albert's system one chooses to
carry out. If we understand a "complete description" to rule out that one and the
same physical state can be described by state functions with distinct physical
implications, then we can conclude that the quantum mechanical description is
incomplete. Here again we confront a dilemma between separability-locality and
completeness. Many years later Einstein put it this way (Schilpp 1949, p. 682):
    [T]he paradox forces us to relinquish one of the following two assertions:
    (1) the description by means of the psi-function is complete
    (2) the real states of spatially separate objects are independent of each

   Physics and Philosophy                                           Musa Akrami

It appears that the central point of EPR was to argue that in interpreting the
quantum state functions we are faced with these alternatives.
As we have seen, in framing his own EPR-like arguments for the incompleteness
of quantum theory, Einstein makes use of separability and locality, which are
also tacitly assumed in the EPR paper. He provides a clear statement of his ideas
here in a letter to Max Born,
    It is … characteristic of … physical objects that they are thought of as
    arranged in a space-time continuum. An essential aspect of this
    arrangement … is that they lay claim, at a certain time, to an existence
    independent of one another, provided these objects "are situated in
    different parts of space". … The following idea characterizes the relative
    independence of objects (A and B) far apart in space: external influence
    on A has no direct influence on B." (Born, 1971, pp. 170-71)
In the course of his correspondence with Schrödinger, however, Einstein
realized that assumptions about separability and locality were not necessary in
order to get the incompleteness conclusion that he was after; i.e., to show that
the state function of a system was not a complete description of the real state of
affairs with respect to the system.
Separability supposes that there is a real state of affairs (after the systems
separate) and locality suppose that one cannot directly influence it by acting at
a distance. What Einstein realized was that these two suppositions were already
part of the ordinary conception of a macroscopic object. Hence if one looks at
the interaction of a macro-system with a micro-system there would be no need to
frame additional assumptions in order to conclude that the quantum description
of the whole was incomplete with respect to its macroscopic part. Writing to
Schrödinger on August 8, 1935 Einstein says that he will show this by means of
a "crude macroscopic example".
   The system is a substance in chemically unstable equilibrium, perhaps a
   charge of gunpowder that, by means of intrinsic forces, can spontaneously
   combust, and where the average life span of the whole setup is a year. In
   principle this can quite easily be represented quantum-mechanically. In
   the beginning the psi-function characterizes a reasonably well-defined
   macroscopic state. But, according to your equation [i.e., the Schrödinger
   equation], after the course of a year this is no longer the case. Rather, the
   psi-function then describes a sort of blend of not-yet and already-exploded
   systems. Through no art of interpretation can this psi-function be turned
   into an adequate description of a real state of affairs; in reality there is just
   no intermediary between exploded and not-exploded. (Fine 1996, p. 78)

   Physics and Philosophy                                          Musa Akrami

The point is that after a year either the gunpowder will have exploded, or not.
(This is the "real state of affairs" which in the EPR situation requires one to
assume separability.) The state function, however, will have evolved into a
complex superposition over these two alternatives. Provided we maintain the
eigenvalue-eigenstate link, the quantum description by means of that state
function will yield neither conclusion, and hence the quantum description is
The reader may recognize the similarity between this exploding gunpowder
example and Schrödinger's cat.
In the case of the cat an unstable atom is hooked up to a lethal device that, after
an hour, is as likely to poison (and kill) the cat as not, depending on whether the
atom decays. After an hour the cat is either alive or dead, but the quantum state
of the whole atom-poison-cat system at this time is a superposition involving the
two possibilities and, just as in the case of the gunpowder, is not a complete
description of the situation (life or death) of the cat.
The similarity between the gunpowder and the cat is hardly accidental since
Schrödinger first produced the cat example in his reply of September 19, 1935 to
Einstein's August 8 gunpowder letter. There Schrödinger says that he has
himself constructed "an example very similar to your exploding powder keg",
and proceeds to outline the cat (Fine 1996, pp. 82-83). Although the "cat
paradox" is usually cited in connection with the problem of quantum
measurement and treated as a paradox separate from EPR, its origin is here as a
compact version of the EPR argument for incompleteness. Schrödinger's
development of "entanglement", the term he introduced as a general description
of the correlations that result when quantum systems interact, also began in this
correspondence over EPR.

5. 2. A popular form of the argument:
Bohr's response
The literature surrounding EPR contains yet another version of the argument, a
popular version that — unlike any of Einstein's — features the Criterion of
Assume again an interaction between our two systems that preserves both
relative position and zero total momentum, and suppose that the systems are far
apart. If we measure the position of Albert's system, we can infer that Niels'
system has a corresponding position. We can also predict it with certainty, given
the result of the position measurement of Albert's system. Hence, according to
the Criterion of Reality, the position of Niels' system constitutes an element of
reality. Similarly, if we measure the momentum of Albert's system, we can

   Physics and Philosophy                                        Musa Akrami

conclude that the momentum of Niels' system is an element of reality. The
argument now concludes that since we can choose freely to measure either
position or momentum, it "follows" that both must be elements of reality
Of course no such conclusion follows from our freedom of choice. It is not
sufficient to be able to choose at will which quantity to measure; for the
conclusion to follow from the Criterion alone one would need to be able to
measure both quantities at once. This is precisely the point that Einstein
recognized in his 1932 letter to Ehrenfest and that EPR addresses by assuming
locality and separability. What is striking about this version is that these
principles, central to the original EPR argument and to the dilemma at the heart
of Einstein's versions, disappear here. Instead, what we have is closer to a
caricature of the EPR paper than it is to a serious reconstruction.
Unfortunately, perhaps due in part to the difficulties presented by Podolsky's
text, this is the argument most commonly cited in the physics literature and
attributed to EPR themselves. Podolsky, however, should not get all the blame.
For this version of Podolsky's text has a prominent source in terms of which one
can more readily understand its popularity among physicists. It is Niels Bohr
By the time of the EPR paper many of the early interpretive battles over the
quantum theory had been settled, at least to the satisfaction of working
physicists. Bohr had emerged as the "philosopher" of the new theory and the
community of quantum theorists, busy with the development and extension of
the theory, were content to follow Bohr's leadership when it came to explaining
and defending its conceptual underpinnings (Beller 1999, Chapter 13).
Thus in 1935 the burden was on Bohr to explain what was wrong with the EPR
"paradox". The major article that he wrote in discharging this burden (Bohr
1935a) became the canon for how to respond to EPR. Unfortunately, Bohr's
summary of EPR in that article, which is the version just above, also became the
canon for what EPR contained by way of argument.
Bohr's response to EPR begins, as do many of his treatments of the conceptual
issues raised by the quantum theory, with a discussion of limitations on the
simultaneous determination of position and momentum. As usual, these are
drawn from an analysis of the possibilities of measurement if one uses an
apparatus consisting of a diaphragm connected to a rigid frame. Bohr
emphasizes that the question is to what extent we can trace the interaction
between the particle being measured and the measuring instrument. Following
the summary of EPR, Bohr then focuses on the Criterion of Reality which, he
says, "contains an ambiguity as regards the meaning of the expression ‘without
in any way disturbing a system’." Bohr concedes that the indirect measurement
of Niels' system achieved when one makes a measurement of Albert's system

   Physics and Philosophy                                         Musa Akrami

does not involve any "mechanical disturbance" of Niels' system. Still, he claims
that a measurement on Albert's system does involve "an influence on the very
conditions which define the possible types of predictions regarding the future
behavior of [Niels'] system." What Bohr may have had in mind is that when, for
example, we measure the position of Albert's system and get a result we can
predict the position of Niels' system with certainty. However, measuring the
position of Albert's system does not allow a similarly certain prediction for the
momentum of Niels' system. The opposite would be true had we measured the
momentum of Albert's system. Thus depending on which variable we
measure on Albert's system, we will be entitled to different predictions
about the results of further measurements on Niels' system.
There are two important things to notice about this response.
The first is that in conceding that Einstein's indirect method for determining,
say, the position of Niels' system does not mechanically disturb that system,
Bohr here departs from his original program of complementarity, which was to
base the uncertainty relations and the statistical character of quantum theory on
uncontrollable physical disturbances in a system, disturbances that were
supposed to arise inevitably in measuring some variable of the system. Instead
Bohr now distinguishes between a physical (or "mechanical") disturbance and
what one might call an "informational" disturbance; i.e., a disturbance in the
information available for predicting the future behavior of a system. He
emphasizes that only the latter arises in the EPR situation.
The second important thing to notice is how Bohr's response needs to be
implemented in order to block the type of arguments favored by Einstein, which
pose a dilemma between principles of locality and completeness. In Einstein's
arguments the locality principle makes explicit reference to the reality of the
unmeasured system (no direct influence on the reality there due to
measurements made here). Hence Bohr's pointing to an informational
disturbance would not affect the argument at all unless one includes the
information available for predicting the future behavior of the unmeasured
system as part of the reality of that system.
That would be implausible on two counts.
Firstly, because the information about Niels' unmeasured system is available
to those near Albert's system, which is someplace else, and to their contacts,
wherever they may be.
Secondly, because the very idea of "information about Niels' system" would
make little sense if what we designate by "Niels' system" includes that very
Nevertheless, this is the move that Bohr appears to make, maintaining that the
"conditions" (which define the possible types of predictions regarding the future

   Physics and Philosophy                                          Musa Akrami

behavior of Niels' system) "constitute an inherent element of the description of
any phenomena to which the term ‘physical reality’ can be properly attached"
(Bohr 1935a, p. 700). To be sure, if we include predictive information in the
"reality" of the unmeasured system, then the locality principle fails to hold
(although separability might) and so the EPR inference to the incompleteness of
the quantum theory would be blocked. Thus this way out concedes the validity
of the EPR argument and blocks its impact on the issue of completeness by
expanding the concept of physical reality in such a way as to make the quantum
theory highly nonlocal.
Despite Bohr's seeming endorsement of nonlocal interactions in his response to
EPR, in other places Bohr rejects nonlocality in the strongest terms. For
example in discussing an electron double slit experiment, which is Bohr's
favorite model for illustrating the novel conceptual features of quantum theory,
and writing at the same time as EPR, Bohr argues as follows.
    If we only imagine the possibility that without disturbing the phenomena
    we determine through which hole the electron passes, we would truly find
    ourselves in irrational territory, for this would put us in a situation in
    which an electron, which might be said to pass through this hole, would
    be affected by the circumstance of whether this [other] hole was open or
    closed; but … it is completely incomprehensible that in its later course
    [the electron] should let itself be influenced by this hole down there being
    open or shut. (Bohr 1935b)
Notice how close the language of disturbance here is to EPR. But here Bohr
defends locality and regards the very contemplation of nonlocality as
"irrational" and "completely incomprehensible". Since "the circumstance of
whether this [other] hole was open or closed" does affect the possible types of
predictions regarding the electron's future behavior, if we expand the concept of
the electron's "reality", as he appears to have suggested for EPR, by including
such information, we do "disturb" the electron around one hole by opening or
closing the other hole. That is, if we give to "disturb" the same sense here that
Bohr appears to give it when responding to EPR, then we are led to an
"incomprehensible" nonlocality, and into the territory of the irrational.
There is another way of trying to understand Bohr's position. According to one
common reading, after EPR Bohr embraced a relational (or contextual) account
of property attribution. On this account to speak of the position, say, of a system
presupposes that one already has already put in place an appropriate interaction
involving an apparatus for measuring position. Thus "the position" of the system
refers to a relation between the system and the measuring device. In the EPR
context this would seem to imply that before one measures the position of
Albert's system, talk of the position of Niels' system is out of place; whereas
after one measures the position of Albert's system, talk of the position of Niels'

   Physics and Philosophy                                            Musa Akrami

system is appropriate and, indeed, we can say truly that Niels' system "has" a
position. Similar considerations govern momentum measurements. It follows,
then, that local manipulations carried out on Albert's system, in a place we may
assume to be far removed from Niels' system, can directly affect what is
linguistically meaningful as well as factually true of Niels' system. Similarly, in
the double slit arrangement, it would follow that what can be said and said truly
about the position of the electron around the top hole would depend on the
context of whether the bottom hole is open or shut. One might suggest that such
relational actions-at-a-distance are harmless ones, perhaps merely "semantic";
like becoming the "best" when your only competitor — who might be miles
away — fails. Still, they embody precisely the sort of nonlocality already
discussed with respect to "informational disturbance", and that Bohr seemed to
In the light of all this it is difficult to know just what response can be attributed
to Bohr reliably that would derail EPR. Bohr may well have been aware of the
difficulty in framing the appropriate concepts clearly when, a few years after
EPR, he wrote,
   The unaccustomed features of the situation with which we are confronted
   in quantum theory necessitate the greatest caution as regard all questions
   of terminology. Speaking, as it is often done of disturbing a phenomenon
   by observation, or even of creating physical attributes to objects by
   measuring processes is liable to be confusing, since all such sentences
   imply a departure from conventions of basic language which even though
   it can be practical for the sake of brevity, can never be unambiguous.
   (Bohr 1939, p. 320.)

5. 3. Development of EPR
5. 3. 1. The Bohm version
For about fifteen years following its publication, the EPR paradox was discussed
at the level of a thought experiment whenever the conceptual difficulties of
quantum theory became an issue. In 1951 David Bohm, then an untenured
Assistant Professor at Princeton University, published a textbook on the
quantum theory in which he took a close look at EPR in order to develop a
response in the spirit of Bohr.
Bohm showed how one could mirror the conceptual situation in the EPR thought
experiment by looking at the dissociation of a diatomic molecule whose total
spin angular momentum is (and remains) zero; for instance, the dissociation of
an excited hydrogen molecule into a pair of hydrogen atoms by means of a

   Physics and Philosophy                                             Musa Akrami

process that does not change an initially zero total angular momentum (Bohm
1951, Sections 22.15-22.18).
In the Bohm experiment the atomic fragments separate after interaction, flying
off in different directions freely. Subsequently, measurements are made of their
spin components (which here take the place of position and momentum), whose
measured values would be anti-correlated after dissociation. In the so-called
singlet state of the atomic pair, the state after dissociation, if one atom's spin is
found to be positive with respect to the orientation of an axis at right angles to its
flight path, the other atom would be found to have a negative spin with respect
to an axis with the same orientation.
Like the operators for position and momentum, spin operators for different
orientations do not commute. Moreover, in the experiment outlined by Bohm,
the atomic fragments can move far apart from one another and so become
appropriate objects for assumptions that restrict the effects of purely local
actions. Thus Bohm's experiment mirrors the entangled correlations in EPR for
spatially separated systems, allowing for similar arguments and conclusions
involving locality, separability, and completeness.
A subsequent paper, co-authored with Aharonov (Bohm and Aharonov 1957)
goes on to sketch the machinery for a plausible experiment in which these
correlations could be verified. It has become customary to refer to experimental
arrangements involving determinations of spin components for spatially
separated systems, and to a variety of similar set-ups (especially ones for
measuring photon polarization), as "EPRB" experiments — "B" for Bohm.
Because of technical difficulties in creating and monitoring the atomic
fragments, however, there seem to have been no immediate attempts to perform
a Bohm version of EPR.

5. 3. 2. Bell and beyond
That was to remain the situation for almost another fifteen years, until John Bell
utilized the EPRB set-up to construct a stunning argument, at least as
challenging as EPR, but to a different conclusion (Bell 1964). Bell shows that,
under a given set of assumptions, certain of the correlations that can be
measured in runs of an EPRB experiment satisfy a particular set of constraints,
known as the Bell inequalities.
In these EPRB experiments, however, quantum theory predicts that the
measured correlations violate the Bell inequalities, and by an
experimentally significant amount.
Thus Bell shows that quantum theory is inconsistent with the given assumptions.
Prominent among these is an assumption of locality, similar to the locality
assumption tacitly assumed in EPR and explicitly assumed in Einstein's versions
(apart from the gunpowder case).

   Physics and Philosophy                                          Musa Akrami

Thus Bell's theorem is often characterized as showing that quantum theory
is nonlocal.
However, since several other assumptions are needed in any derivation of the
Bell inequalities (roughly, assumptions guaranteeing a classical representation of
the quantum probabilities), one should be cautious about singling out locality as
necessarily in conflict with the quantum theory.
Bell's results were explored and deepened by various theoretical investigations
and they have stimulated a number of increasingly sophisticated and delicate
EPRB-type experiments designed to test whether the Bell inequalities hold
where quantum theory predicts they should fail.
With a few anomalous exceptions, the experiments confirm the quantum
violations of the inequalities. (Baggott 2004 contains a readable account of the
major refinements and experiments; but see Hess and Philipp 2004 for some
reservations.) The confirmation is quantitatively impressive and, although there
are still viable ways of reconciling the experimental results with frameworks that
embody locality and separability, many conjecture that as experiments are
improved such frameworks will not stand the test of time. While the exact
significance of these experimental tests of the Bell inequalities thus remains a
matter of continued controversy, the techniques developed in the experiments,
and related theoretical ideas for utilizing the entanglement associated with
EPRB-type interactions, have become important in their own right. These
techniques and ideas, stemming from EPR and the Bell theorem, have
applications now being advanced in several relatively new fields of investigation
— quantum cryptography, teleportation and computing.
To go back to the EPR dilemma between locality and completeness, it would
appear from the Bell theorem that Einstein's strategy of maintaining locality, and
thereby concluding that the quantum description is incomplete, may have fixed
on the wrong horn. Even though the Bell theorem does not rule out locality
conclusively, it should certainly make one wary of assuming it. On the other
hand, since Einstein's exploding gunpowder argument (or Schrödinger's cat)
supports incompleteness without assuming locality, one should be wary of
adopting the other horn of the dilemma, affirming that the quantum state
descriptions are complete and "therefore" that the theory is nonlocal. It may well
turn out that both horns need to be rejected: that the state functions do not
provide a complete description and that the theory is also nonlocal (although
possibly still separable; see Winsberg and Fine 2003). There is at least one well-
known approach to the quantum theory that makes a choice of this sort, the de
Broglie-Bohm approach (see Bohmian Mechanics). Of course it may also be
possible to break the EPR argument for the dilemma plausibly by questioning
some of its other assumptions (e.g., separability, the reduction postulate, or the

   Physics and Philosophy                                           Musa Akrami

eigenvalue-eigenstate link). That would lead to the remaining option, to regard
the theory as both local and complete.
      Baggott, J., 2004 ,Beyond Measure: Modern Physics, Philosophy and the
       Meaning of Quantum Theory ,Oxford: Oxford University Press .
      Bell, J.S., 1964, "On the Einstein-Podolsky-Rosen Paradox ,"Physics ,
        ,211-19195reprinted in Bell 1987 .
       ,1987 -----Speakable and Unspeakable in Quantum Mechanics ,New
       York: Cambridge University Press .
      Beller, M., 1999 ,Quantum Dialogue: The Making of a Revolution ,
       Chicago: University of Chicago Press .
      Bohm, D., 1951 ,Quantum Theory ,New York: Prentice Hall .
      Bohm, D., and Aharonov, Y., 1957, "Discussion of Experimental Proof
       for the Paradox of Einstein, Rosen and Podolski ,"Physical Review ,
      Bohr, N., 1935a, "Can Quantum-Mechanical Description of Physical
       Reality Be Considered Complete ,"?Physical Review .712-696 :48 ,
      1935 -----b, "Space and Time in Nuclear Physics", Mss 14, March 21 ,
       Manuscript Collection ,Archive for the History of Quantum Physics ,
       American Philosophical Society, Philadelphia .
      " ,1939 -----The causality problem in atomic physics" in Bohr, 1996, pp .
       ,1996 -----Collected Works ,Vol. 7, Amsterdam: North Holland .
      Born, M., (ed.), 1971 ,The Born-Einstein Letters ,New York; Walker .
      Einstein, A. 1936, "Physik und Realität ,"Journal of the Franklin Institute ,
        347-313 :221reprinted in translation in Einstein 1954 .
       1954 -----Ideas and Opinions ,New York: Crown .
      Einstein, E., Podolsky, B., and Rosen, N., 1935, "Can Quantum-
       Mechanical Description of Physical Reality Be Considered Complete ,"?
       Physical Review .781-479777 ,
      Fine, A., 1996 ,The Shaky Game: Einstein, Realism and the Quantum
       Theory2 ,nd Edition, Chicago: University of Chicago Press .

Physics and Philosophy                                          Musa Akrami

   " ,1982 ,-----Hidden Variables, Joint Probability and the Bell
    Inequalities ,"Physical Review Letters .295-291 :48 ,
   Halvorson, H., 2000, "The Einstein-Podolsky-Rosen State Maximally
    Violates Bell's Inequality ,"Letters in Mathematical Physics .329-321 :53 ,
   Held, C., 1998 ,Die Bohr-Einstein-Debatte: Quantenmechanik und
    Physikalische Wirklichkeit, Paderborn: Schöningh .
   Hess, K and Philipp, W., 2004, "Breakdown of Bell's Theorem for Certain
    Objective Local Parameter Spaces ,"Proceedings of The National
    Academy of Science .1815-11191799 ,
   Jammer, M., 1974 ,The Philosophy of Quantum Mechanics ,New York :
    Wiley .
   Larsson, J,-A, 1999, "Modeling the Singlet State with Local Variables ,"
    Physics Letters A .252-245 :256 ,
   Malley, J., 2004, "All Quantum Observables in A Hidden-Variable Model
    Must Commute Simultaneously ,"Physical Review A .3-12211891 ,69
   Schilpp, P.A., (ed.), 1949 ,Albert Einstein: Philosopher-Scientist ,La
    Salle, IL: Open Court .
   Schrödinger, E., 1935a, "Die gegenwärtige Situation in der
    Quantenmechanik ",Naturwissenschaften-844 ,828-823 ,812-817 :23 ,
     ;849English translation in Trimmer, 1980 .
   Schrödinger, E., 1935b. "Discussion of Probability Relations between
    Separated Systems ,"Proceedings of the Cambridge Philosophical Society ,
   Szabo, L. and Fine, A., 2002, "A Local Hidden Variable Theory for the
    GHZ Experiment ,"Physics Letters A .241-229 :295 ,
   Trimmer, J. D., 1980, "The Present Situation in Quantum Mechanics: A
    Translation of Schrödinger's ‘Cat Paradox’ Paper ,"Proceedings of the
    American Philosophical Society 338-323 :124 ,
   von Neumann, J., 1955 ,Mathematical Foundations of Quantum
    Mechanics ,trans. Robert T. Geyer, Princeton: Princeton University Press .
   Winsberg, E., and Fine, A., 2003, "Quantum Life: Interaction,
    Entanglement and Separation ,"Journal of Philosophy ,C:80-97

      Physics and Philosophy                                            Musa Akrami

  Chapter6. Bohmian Mechanics
6. 1. The completeness of the quantum mechanical description
6. 2. The impossibility of hidden variables ... or the inevitability of
6. 3. History

             Introductory Remarks
             Bohmian mechanics, which is also called the de Broglie-
             Bohm theory, the pilot-wave model, and the causal
             interpretation of quantum mechanics, is a version of
             quantum theory discovered by Louis de Broglie in 1927 and
             rediscovered by David Bohm in 1952. It is the simplest
             example of what is often called a hidden variables
             interpretation of quantum mechanics.
             In Bohmian mechanics a system of particles is described in part
             by its wave function, evolving, as usual, according to
             Schrödinger's equation. However, the wave function provides
             only a partial description of the system. This description is
             completed by the specification of the actual positions of the
             particles. The latter evolve according to the "guiding equation,"
             which expresses the velocities of the particles in terms of the
             wave function. Thus, in Bohmian mechanics the configuration
             of a system of particles evolves via a deterministic motion
             choreographed by the wave function. In particular, when a
             particle is sent into a two-slit apparatus, the slit through which
             it passes and where it arrives on the photographic plate are
             completely determined by its initial position and wave function.
             Bohmian mechanics inherits and makes explicit the nonlocality
             implicit in the notion, common to just about all formulations
             and interpretations of quantum theory, of a wave function on
             the configuration space of a many-particle system. It
             accounts for all of the phenomena governed by nonrelativistic
             quantum mechanics, from spectral lines and scattering theory to
             superconductivity, the quantum Hall effect and quantum
             computing. In particular, the usual measurement postulates of

   By Sheldon Goldstein

   Physics and Philosophy                                          Musa Akrami

        quantum theory, including collapse of the wave function and
        probabilities given by the absolute square of probability
        amplitudes, emerge from an analysis of the two equations of
        motion - Schrödinger's equation and the guiding equation -
        without the traditional invocation of a special, and somewhat
        obscure, status for observation.

6. 1. The completeness of the quantum
mechanical description
Despite its extraordinary predictive successes, quantum mechanics has, since its
inception some seventy years ago, been plagued by conceptual difficulties. The
basic problem, plainly put, is this: It is not at all clear what quantum mechanics
is about. What, in fact, does quantum mechanics describe?
It might seem, since it is widely agreed that any quantum mechanical system is
completely described by its wave function, that quantum mechanics is
fundamentally about the behavior of wave functions. Quite naturally, no
physicist wanted this to be true more than did Erwin Schrödinger, the father of
the wave function. Nonetheless, Schrödinger ultimately found this impossible to
believe. His difficulty was not so much with the novelty of the wave function
(Schrödinger 1935): "That it is an abstract, unintuitive mathematical construct is
a scruple that almost always surfaces against new aids to thought and that carries
no great message." Rather, it was that the "blurring" suggested by the spread out
character of the wave function "affects macroscopically tangible and visible
things, for which the term ‘blurring’ seems simply wrong."
For example, in the same paper Schrödinger noted that it may happen in
radioactive decay that
    the emerging particle is described ... as a spherical wave ... that impinges
    continuously on a surrounding luminescent screen over its full expanse.
    The screen however does not show a more or less constant uniform
    surface glow, but rather lights up at one instant at one spot ....
And he observed that one can easily arrange, for example by including a cat in
the system, "quite ridiculous cases" with
   the -function of the entire system having in it the living and the dead cat
   (pardon the expression) mixed or smeared out in equal parts.

   Physics and Philosophy                                           Musa Akrami

It is thus because of the "measurement problem," of macroscopic
superpositions, that Schrödinger found it difficult to regard the wave function as
"representing reality." But then what does? With evident disapproval,
Schrödinger describes how
   the reigning doctrine rescues itself or us by having recourse to
   epistemology. We are told that no distinction is to be made between the
   state of a natural object and what I know about it, or perhaps better, what I
   can know about it if I go to some trouble. Actually -- so they say -- there
   is intrinsically only awareness, observation, measurement.
Many physicists pay lip service to the Copenhagen interpretation -- that
quantum mechanics is fundamentally about observation or results of
measurement. But it is becoming increasingly difficult to find any who, when
pressed, will defend this interpretation.
It seems clear that quantum mechanics is fundamentally about atoms and
electrons, quarks and strings, not those particular macroscopic regularities
associated with what we call measurements of the properties of these things. But
if these entities are not to be somehow identified with the wave function itself --
and if talk of them is not merely shorthand for elaborate statements about
measurements -- then where are they to be found in the quantum description?
There is, perhaps, a very simple reason why there has been so much difficulty
discerning in the quantum description the objects we believe quantum mechanics
should be describing. Perhaps the quantum mechanical description is not the
whole story, a possibility most prominently associated with Albert Einstein.
As we told, in 1935 Einstein, Boris Podolsky and Nathan Rosen argued for this
possibility in the famous EPR paper (Einstein et al. 1935), which they concluded
with the following:
    While we have thus shown that the wave function does not provide a
    complete description of the physical reality, we left open the question of
    whether or not such a description exists. We believe, however, that such a
    theory is possible.
The argument given in the EPR paper for this conclusion invoked quantum
correlations and an assumption of locality.
Later, on the basis of more or less the same considerations as those of
Schrödinger quoted above, Einstein again concluded that the wave function
does not provide a complete description of individual systems, an idea he
called "this most nearly obvious interpretation" (Einstein 1949, p. 672). In
relation to a theory incorporating a more complete description, Einstein
remarked that "the statistical quantum theory would ... take an approximately
analogous position to the statistical mechanics within the framework of classical

   Physics and Philosophy                                              Musa Akrami

mechanics." It is perhaps worth noting here that Bohmian mechanics, as we
shall see, exactly fits this description.

6. 2. The impossibility of hidden variables ...
or the inevitability of nonlocality?
John von Neumann, one of the greatest mathematicians of the twentieth century,
claimed to have mathematically proven that Einstein's dream, of a deterministic
completion or reinterpretation of quantum theory, was mathematically
impossible. He concluded that (von Neumann 1932, p. 325 of the English
   It is therefore not, as is often assumed, a question of a re-interpretation of
   quantum mechanics -- the present system of quantum mechanics would
   have to be objectively false, in order that another description of the
   elementary processes than the statistical one be possible.
This claim of von Neumann was almost universally accepted among
physicists and philosophers of science. For example, Max Born, who
formulated the statistical interpretation of the wave function, assured us that
(Born 1949, p. 109)
   No concealed parameters can be introduced with the help of which the
   indeterministic description could be transformed into a deterministic one.
   Hence if a future theory should be deterministic, it cannot be a
   modification of the present one but must be essentially different.
Bohmian mechanics is, quite clearly, a counterexample to the claims of von
Neumann, so something has to be wrong with von Neumann's argument. In fact,
according to John Bell (Mermin 1993, p. 805), von Neumann's assumptions
(about the relationships among the values of quantum observables that must be
satisfied in a hidden-variables theory) are so unreasonable that the "the proof of
von Neumann is not merely false but foolish!" Nonetheless, some physicists
continue to rely on von Neumann's proof, although in recent years it is more
common to find physicists citing the Kochen-Specker Theorem and, more
frequently, Bell's inequality as the basis of this refutation. We still find, a quarter
of a century after the rediscovery of Bohmian mechanics in 1952, statements
such as these (Wigner 1976):
    The proof he [von Neumann] published ..., though it was made much
    more convincing later on by Kochen and Specker, still uses assumptions
    which, in my opinion, can quite reasonably be questioned. ... In my
    opinion, the most convincing argument against the theory of hidden
    variables was presented by J. S. Bell (1964).

   Physics and Philosophy                                         Musa Akrami

Now there are many more statements of a similar character that could have been
cited. This quotation owes its significance to the fact that Wigner was not only
one of the leading physicists of his generation, but, unlike most of his
contemporaries, he was also profoundly concerned with the conceptual
foundations of quantum mechanics and wrote on the subject with great clarity
and insight.
There was, however, one physicist who wrote on this subject with even greater
clarity and insight than Wigner himself, namely the very J. S. Bell whom
Wigner praises for demonstrating the impossibility of a deterministic
completion of quantum theory such as Bohmian mechanics. Here's how Bell
himself reacted to Bohm's discovery (Bell 1987, p. 160):
   But in 1952 I saw the impossible done. It was in papers by David Bohm.
   Bohm showed explicitly how parameters could indeed be introduced, into
   nonrelativistic wave mechanics, with the help of which the indeterministic
   description could be transformed into a deterministic one. More
   importantly, in my opinion, the subjectivity of the orthodox version, the
   necessary reference to the ‘observer,’ could be eliminated. ...
   But why then had Born not told me of this ‘pilot wave’? If only to point
   out what was wrong with it? Why did von Neumann not consider it? More
   extraordinarily, why did people go on producing ‘‘impossibility’’ proofs,
   after 1952, and as recently as 1978? ... Why is the pilot wave picture
   ignored in text books? Should it not be taught, not as the only way, but as
   an antidote to the prevailing complacency? To show us that vagueness,
   subjectivity, and indeterminism, are not forced on us by experimental
   facts, but by deliberate theoretical choice?
Wigner to the contrary notwithstanding, Bell did not establish the impossibility
of a deterministic reformulation of quantum theory, nor did he ever claim to
have done so. On the contrary, over the course of the past several decades, until
his untimely death in 1990, Bell was the prime proponent, for a good part of
this period almost the sole proponent, of the very theory, Bohmian mechanics,
that he is supposed to have demolished.
Bohmian mechanics is of course as much a counterexample to the Kochen-
Specker argument for the impossibility of hidden variables as it is to the one
of von Neumann. It is obviously a counterexample to any such argument.
However reasonable the assumptions of such an argument, some of them must
fail for Bohmian mechanics.
Wigner was quite right to suggest that the assumptions of Kochen and Specker
are more convincing than those of von Neumann. They appear, in fact, to be
quite reasonable indeed. However, they are not. The impression that they are
arises from a pervasive error, a naive realism about operators, that will be

   Physics and Philosophy                                          Musa Akrami

discussed below in the sections on quantum observables, on spin, and on
One of the achievements of John Bell was to replace the "arbitrary axioms"
(Bell 1987, page 11) of Kochen-Specker and others by an assumption of
locality, of no action-at-a-distance. It would be hard to argue against the
reasonableness of such an assumption, even if one were so bold as to doubt its
inevitability. Bell showed that any hidden-variables formulation of quantum
mechanics must be nonlocal, as, indeed, Bohmian mechanics is. But he showed
much much more.
In a celebrated paper published in 1964, Bell showed that quantum theory
itself is irreducibly nonlocal. This fact about quantum mechanics, based as it is
on a short and mathematically simple analysis, could have been recognized soon
after the discovery of quantum theory in the 1920's. That this did not happen is
no doubt due in part to the obscurity of orthodox quantum theory and to the
ambiguity of its commitments. It was, in fact, his examination of Bohmian
mechanics that led Bell to his nonlocality analysis. In the course of his
investigation of Bohmian mechanics he observed that (Bell 1987, p. 11):
   in this theory an explicit causal mechanism exists whereby the disposition
   of one piece of apparatus affects the results obtained with a distant piece.
   Bohm of course was well aware of these features of his scheme, and has
   given them much attention. However, it must be stressed that, to the
   present writer's knowledge, there is no proof that any hidden variable
   account of quantum mechanics must have this extraordinary character. It
   would therefore be interesting, perhaps, to pursue some further
   "impossibility proofs," replacing the arbitrary axioms objected to above
   by some condition of locality, or of separability of distant systems.
In a footnote, Bell added that "Since the completion of this paper such a proof
has been found." This proof was published in his 1964 paper, "On the Einstein-
Podolsky-Rosen Paradox," in which he derives Bell's inequality, the basis of his
conclusion of quantum nonlocality.
It is worth stressing that Bell's analysis indeed shows that any account of
quantum phenomena must be nonlocal, not just any hidden variables account.
Bell showed that nonlocality is implied by the predictions of standard
quantum theory itself. Thus if nature is governed by these predictions, then
nature is nonlocal. (That nature is so governed, even in the crucial EPR-
correlation experiments, has by now been established by a great many
experiments, the most conclusive of which is perhaps that of Aspect (Aspect et
al., 1982).)
Bell, too, stressed this point (by determinism Bell here means hidden variables):

   Physics and Philosophy                                            Musa Akrami

   It is important to note that to the limited degree to which determinism
   plays a role in the EPR argument, it is not assumed but inferred. What is
   held sacred is the principle of ‘local causality’ -- or ‘no action at a
   It is remarkably difficult to get this point across, that determinism is not a
   presupposition of the analysis. (Bell 1987, p. 143)
   Despite my insistence that the determinism was inferred rather than
   assumed, you might still suspect somehow that it is a preoccupation with
   determinism that creates the problem. Note well then that the following
   argument makes no mention whatever of determinism. ... Finally you
   might suspect that the very notion of particle, and particle orbit ... has
   somehow led us astray. ... So the following argument will not mention
   particles, nor indeed fields, nor any other particular picture of what goes
   on at the microscopic level. Nor will it involve any use of the words
   ‘quantum mechanical system’, which can have an unfortunate effect on
   the discussion. The difficulty is not created by any such picture or any
   such terminology. It is created by the predictions about the correlations in
   the visible outputs of certain conceivable experimental set-ups. (Bell
   1987, p. 150)
The "problem" and "difficulty" to which Bell refers above is the conflict
between the predictions of quantum theory and what can be inferred, call it C,
from an assumption of locality in Bohm's version of the EPR argument, a
conflict established by Bell's inequality. C happens to concern the existence of a
certain kind of hidden variables, what might be called local hidden variables, but
this fact is of little substantive importance. What is important is not so much the
identity of C as the fact that C is incompatible with the predictions of quantum
theory. The identity of C is, however, of great historical significance: It is
responsible for the misconception that Bell proved that hidden variables are
impossible, a belief until recently almost universally shared by physicists, as
well as for the view, even now almost universally held, that what Bell's result
does is to rule out local hidden variables, a view that is misleading.
Here again is Bell, expressing the logic of his two-part demonstration of
quantum nonlocality, the first part of which is Bohm's version of the EPR
    Let me summarize once again the logic that leads to the impasse. The
    EPRB correlations are such that the result of the experiment on one side
    immediately foretells that on the other, whenever the analyzers happen to
    be parallel. If we do not accept the intervention on one side as a causal
    influence on the other, we seem obliged to admit that the results on both
    sides are determined in advance anyway, independently of the

   Physics and Philosophy                                         Musa Akrami

   intervention on the other side, by signals from the source and by the local
   magnet setting. But this has implications for non-parallel settings which
   conflict with those of quantum mechanics. So we cannot dismiss
   intervention on one side as a causal influence on the other. (Bell 1987, p.

6. 3. History
The pilot-wave approach to quantum theory was initiated, even before the
discovery of quantum mechanics itself, by Einstein, who hoped that interference
phenomena involving particle-like photons could be explained if the motion of
the photons were somehow guided by the electromagnetic field -- which would
thus play the role of what he called a Führungsfeld or guiding field (Wigner
1976, p. 262). While the notion of the electromagnetic field as guiding field
turned out to be rather problematical, the possibility that for a system of
electrons the wave function might play this role, of guiding field or pilot wave,
was explored by Max Born in his early paper founding quantum scattering
theory (Born 1926) -- a suggestion to which Heisenberg was profoundly
Not long after Schrödinger's discovery, in 1926, of wave mechanics, i.e., of
Schrödinger's equation, Louis de Broglie in effect discovered Bohmian
mechanics: In 1927, de Broglie found an equation of particle motion equivalent
to the guiding equation for a scalar wave function (de Broglie 1928, p. 119), and
he explained at the 1927 Solvay Congress how this motion could account for
quantum interference phenomena. However, de Broglie responded poorly to an
objection of Wolfgang Pauli (Pauli 1928) concerning inelastic scattering, no
doubt making a rather bad impression on the illustrious audience gathered for
the occasion.
Born and de Broglie very quickly abandoned the pilot-wave approach and
became enthusiastic supporters of the rapidly developing consensus in favor
of the Copenhagen interpretation.
Bohmian mechanics was rediscovered in 1952 by David Bohm (Bohm 1952),
the first person genuinely to understand its significance and implications. Its
principal proponent during the sixties, seventies and eighties was John Bell.

      Albert, D. Z., 1992 ,Quantum Mechanics and Experience ,Cambridge ,
       MA: Harvard University Press

Physics and Philosophy                                          Musa Akrami

   Aspect, A., Dalibard, J., and Roger, G., 1982, "Experimental test of Bell's
    inequalities using time-varying analyzers ",Phys. Rev. Lett 1817-1814 :46
   Bell, J. S., 1964, "On the Einstein-Podolsky-Rosen Paradox ",Physics :
     ;211-195reprinted in Bell 1987 and in Wheeler and Zurek 1983
   Bell, J. S., 1966, "On the Problem of Hidden Variables in Quantum
    Theory ",Rev. Mod. Phys ;452-447 :13 .reprinted in Bell 1987 and in
    Wheeler and Zurek 1983
   Bell, J. S., 1987 ,Speakable and Unspeakable in Quantum Mechanics ,
    Cambridge: Cambridge University Press
   Beller, M., 1999 ,Quantum Dialogue: The Making of a Revolution ,
    Chicago: University of Chicago Press
   Berndl, K., Daumer, M., Dürr, D., Goldstein, S., and Zanghì, N., 1995, "A
    Survey of Bohmian Mechanics ",Il Nuovo Cimento115 B.751-737 :
    [Preprint (in Postscript) available online.]
   Berndl, K., Dürr, D., Goldstein, S., Peruzzi, G., and Zanghì, N., 1995, "On
    the Global Existence of Bohmian Mechanics ",Commun. Math. Phys :171 .
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    Experimental Gravity and Measurement Theory ,New York: Plenum

   Physics and Philosophy                                          Musa Akrami

Chapter7. Early Philosophical
Interpretations of General Relativity
7. 1. The Search for Philosophical Novelty
7. 2. Machian Positivism
        7. 2. 1. In the Early Einstein
        7. 2. 2. A "Relativization of Inertia"?
        7. 2. 3. Positivism and the "Hole Argument"
        7. 2. 4. An Emerging Anti-Positivism
7. 3. Kantian and Neo-Kantian Interpretations
        7. 3. 1. Neo-Kantians on Special Relativity
        7. 3. 2. Immunizing Strategies
        7. 3. 3. Rejecting or Refurbishing the Transcendental Aesthetic
      7.3. 4. General Covariance: A Synthetic Principle of "Unity of
7. 4. Logical Empiricism
        7.4. 1. Lessons of Methodology?
        7. 4. 2. From the "Relativized A priori to the "Relativity of Geometry"
        7. 4. 3. Critique of Reichenbachian Metric Conventionalism
7. 5. "Geometrization of Physics": Realism and Transcendental Idealism
        7. 5. 1. Differing Motivations
        7.5. 2. "Geometrizing" Gravity: the Initial Step
        7.5.3. Extending "Geometrization"
        7. 5. 4. Eddington's "World Geometry"
        7.5. 5. Meyerson on "Pangeometrism"
        7. 5. 6. "Structural Realism"?

By Thomas A. Ryckman

    Physics and Philosophy                                           Musa Akrami

Introductory remark
Each of the following philosophical interpretations of general relativity selected
certain aspects of that theory for favored recognition. While followers of Mach
lauded Einstein's attempt to implement a "relativization of inertia" in the general
theory, they were much more comfortable with Einstein's operationalist
treatment of concepts in the special theory. Kantians and neo-Kantians, if freed
from strict fealty to the doctrine of the Transcendental Aesthetic, pointed to the
surpassing importance of certain synthetic "intellectual forms" in the general
theory, such as the principle of general covariance. For logical empiricism, the
philosophical significance of relativity theory was largely methodological, that
conventions must first be laid down in order to express the empirical content of a
physical theory. Finally, within a few years of its completion in 1915, attempts
were made to extend general relativity's "geometrization" of gravitation to non-
gravitational fields. The first of these, by Weyl, and shortly thereafter by
Eddington, may be distinguished from others, in particular the many attempts of
Einstein, in that they aimed not at a unified field theory, in the sense of a
completely geometrical field theory of all fundamental interactions, but at
reconstructing general relativity from the epistemological perspectives of
transcendental idealism.

 7. 1. The Search for Philosophical Novelty
 Extraordinary public clamor greeted an announcement of the joint meeting of
 the Royal Society of London and the Royal Astronomical Society on the 6th of
 November, 1919. To within acceptable margin of error, astronomical
 observations during the solar eclipse the previous May 29 th revealed the
 displacement of starlight passing near the surface of the sun predicted by
 Einstein's gravitational theory of curved spacetime. By dint of having
 "overthrown" such a permanent fixture of the cognitive landscape as Newtonian
 gravitational theory, the general theory of relativity at once became a principal
 focus of philosophical interest and inquiry. Although some physicists and
 philosophers initially opposed it, mostly on non-physical grounds, surveyed here
 are the principal philosophical interpretations of the theory accepting it as a
 definite advance in physical knowledge. Even so, these include positions ill-
 informed as to the mathematics and physics of the theory. Further lack of clarity
 stemmed from the scientific literati who provided differing, and at times,

   Physics and Philosophy                                            Musa Akrami

conflicting mathematical or physical accounts of the theory's fundamental
principles. These are: the principles of equivalence, of general relativity, of
general covariance, and finally what Einstein termed "Mach's Principle" of the
complete relativization of inertia. In one or another form, all of these
controversies have continued into the present literature of physics and
philosophy of physics. (See e.g., Ohanian (1977); Norton (1993); Friedman
(1983); Barbour and Pfister (1995).) This is not unusual: physical theories, if
sufficiently robust, are rarely, if ever, without unproblematic aspects, often taken
to say different things at different stages of development. But the very fluidity of
physical and mathematical meaning lent interpretative latitude for inherently
antagonistic philosophical viewpoints seeking vindication, confirmation or
illumination by the revolutionary new theory. Perhaps only semi-facetiously,
Russell (1926, 331) observed that
    There has been a tendency, not uncommon in the case of a new scientific
    theory, for every philosopher to interpret the work of Einstein in
    accordance with his own metaphysical system, and to suggest that the
    outcome is a great accession of strength to the views which the
    philosopher in question previously held. This cannot be true in all cases;
    and it may be hoped that it is true in none. It would be disappointing if so
    fundamental a change as Einstein has introduced involved no
    philosophical novelty.
It cannot be denied that general relativity proved a considerable stimulus to
"philosophical novelty". But then the question as to whether it particularly
supported any one line of philosophical interpretation over another also must
take into account the fact that schools of interpretation in turn "evolved" to
accommodate what were regarded as its philosophically salient features. A
classic instance of this is the assertion, to become a cornerstone of logical
empiricism, that relativity theory had shown the untenability of any "philosophy
of the synthetic a priori", despite the fact that early works on relativity theory by
both Reichenbach and Carnap were written from within that broad perspective.
It will be seen that, however ideologically useful, this claim by no means
"follows" from relativity theory although, as physicist Max von Laue noted in
his early text on general relativity (1921, 42), "not every sentence of The
Critique of Pure Reason" might still be held intact. What does "follow" from
scrutiny of the various philosophical appropriations of general relativity is rather
a consummate illustration that, due to the evolution and mutual interplay of
physical, mathematical and philosophical understandings of a revolutionary
physical theory, significant "philosophical interpretations" often are works in
progress, extending over many years.

   Physics and Philosophy                                           Musa Akrami

7. 2. Machian Positivism
7. 2. 1. In the Early Einstein
In 1912, Einstein's name, together with those of the Göttingen mathematicians
David Hilbert and Felix Klein, was prominently displayed (in the
Naturwissenschaftliche Rundschau 27, 336) among those joining Mach's in a
call for the formation of a "Society for Positivist Philosophy". Citing the
pressing need of science "but also of our age in general" for a "comprehensive
world view based on the material facts accumulated in the individual sciences",
the appeal appears above all to have been an orchestrated attempt to buttress
Mach's positivist conception of science in the face of recent realist criticisms of
Mach by Max Planck, then Germany's leading theoretical physicist. More a
declaration of allegiance than an act of scholarly neutrality, it provides but
further evidence of Einstein's youthful enthusiasm for Mach's writings. Late in
life (1949a, 21), Einstein wrote of the "profound influence" that Mach's Science
of Mechanics (1883) exercised upon him as a student as well as of the "very
great influence" in his "younger years" of "Mach's epistemological position".
Indeed, in first decade or so of relativity theory, these influences are highly
visible. Already in the special theory of relativity (1905), Einstein's operational
definition of the "simultaneity" of distantly separated events, whereby clocks are
synchronized by sending and receiving light signals, is closely modeled on the
operational definition of "mass" in Mach's Mechanics. Moreover, occasional
epistemological and methodological pronouncements indicated a broad
consensus with core parts of Mach's epistemology of science, e.g., "The concept
does not exist for the physicist until he has the possibility of discovering whether
or not it is fulfilled in an actual case" (1917a/1955, 22). Thus relativity theory
was widely viewed as fully compliant with Mach's characterization of
theoretical concepts as merely economical shorthand for concrete observations
or operations.

7. 2. 2. A "Relativization of Inertia"?
Machian influences specific to the general theory of relativity appeared even
more extensive. In papers leading up to the definitive presentation of the general
theory of relativity in 1916, Einstein made no secret of the fact that Mach had
been the inspiration for his epistemologically mandated generalization of the
principle of relativity. Holding, with Mach, that no observable facts could be
associated with the notions of "absolute acceleration" or "absolute inertia" (i.e.,
resistance to acceleration), the generalization mandated that the laws of nature
be completely independent of the state of motion of any chosen reference
system. On Mach's death, Einstein wrote, in a warm obituary, of how close

   Physics and Philosophy                                           Musa Akrami

Mach himself had been, years before, to demanding a general theory of
relativity, quoting extensively from the famous passages in the latter parts of the
Mechanics critical of Newton's "absolute" concepts of space, time and motion
(1916b, 102-3). With this reference in mind, the physicist Phillip Frank, later to
be associated with the Vienna Circle, observed (1917/1949, 68) that "it is
universally known today that Einstein's general theory of relativity grew
immediately out of the positivistic doctrine of space and motion". In fact, there
are both genuine and spurious Machian motivations connected with Einstein's
principle of general relativity, a mixture complicated by Einstein's own puzzling
remarks regarding the principle of general covariance.

7. 2. 3. Positivism and the "Hole Argument"
A passage from §3 of Einstein's first complete exposition of the general theory
of relativity (1916a) appeared to provide further grist for the mill of Machian
positivism. There Einstein grandly declared that his requirement of general
covariance for the gravitational field equations (i.e., that they remain unchanged
under arbitrary, but suitably continuous, transformation of the spacetime
coordinates), "takes away from space and time the last remnant of physical
objectivity". An accompanying heuristic "reflection" on the reasoning behind
this claim seemed nothing less than an endorsement of Mach's phenomenalism.
"All our space-time verifications", Einstein wrote, "invariably amount to a
determination of space-time coincidences....". This is because, Einstein
presumed, all results of physical measurement ultimately amount to verifications
of such coincidences, such as the observation of the coincidence of the second
hand of a clock with a mark on its dial. Observing that such (topological)
relations alone are preserved under arbitrary coordinate transformation, Einstein
concluded that "all our physical experience can ultimately be reduced to such
coincidences". To Mach's followers, Einstein's illustrative reflection was nothing
less than an explicit avowal of the centerpiece of Mach's phenomenalist
epistemology, that sensations (Empfindungen), directly experienced sensory
perceptions, alone are real and knowable. Thus Josef Petzoldt, a Machian
philosopher and editor of the 8th edition of Mach's Mechanics , the first to appear
after the general theory of relativity, noted that Einstein's remarks meant that the
theory "rests, in the end, on the perception of the coincidence of sensations" and
so "is fully in accord with Mach's world-view, which is best characterized as
relativistic positivism" (1921, 516).
However, contemporary scholarship has shown that Einstein's remarks here
were but elliptical references to an argument (the so-called "Hole Argument")
that has only fully been reconstructed from his private correspondence. Its
conclusion is that, if a theory is generally covariant, the points of the spacetime
manifold can have no inherent primitive individuality (inherited say, from the

   Physics and Philosophy                                          Musa Akrami

underlying topology), and so no reality independent of physical fields (Stachel
(1980); Norton (1984), (1993)). Thus for a generally covariant theory, no
physical reality accrues to "empty space" (or "spacetime") in the absence of
physical fields. This means that the spacetime coordinates are nothing more than
arbitrary labels for the identification of physical events, or, with rhetorical
embellishment, that space and time have lost "the last remnant of physical
objectivity". Hence this passage was not an endorsement of positivist
To be sure, for a number of years Einstein expressed the ambition of the general
theory of relativity to fully implement Mach's program for the relativization of
all inertial effects, even appending the so-called "cosmological constant" to his
field equations (1917b) for this purpose. This real point of contact of Mach's
influence was clearly identified only in 1918, when Einstein distinguished what
he baptized as "Mach's Principle" (roughly, that inertial effects stem from an
interaction of bodies) from the principle of general relativity which he now
interpreted as the principle of general covariance. Taken together with the
principle of the equivalence, Einstein asserted that the three principles, were
three "points of view" on which his theory rested, even if they could not be
thought completely independent of one another. Despite Einstein's intent, there
is considerable disagreement about the extent to which, if at all, general
relativity conforms to "Mach's Principle". In part this is due to vagaries
regarding what the Principle actually asserts and then again, to difficulties in
comprehending what physical mechanism might implement the Principle,
however interpreted. How, for instance, could a body's inertial mass be
accounted due to the influence of all other bodies in the universe? (See the
discussions in Barbour and Pfister (1995)).

7. 2. 4. An Emerging Anti-Positivism
As Einstein's principal research activity turned, after 1919, to the pursuit of a
geometrical "unified theory of fields", his philosophical pronouncements
increasingly took on a realist or at least anti-positivist coloration. Already in
(1922, 28) lecturing at the Sorbonne, Einstein pronounced Mach "un bon
mécanicien" (no doubt in reference to Mach's views of the relativity of inertia)
but "un déplorable philosophe". Increasingly, Einstein's retrospective portrayals
of the genesis of general relativity centered almost entirely on considerations of
mathematical aesthetics (see Norton (2000) and §5). On the other hand,
positivists and operationalists alike adopted the Einstein analysis of simultaneity
as relativity theory's fundamental methodological feature. One, ruefully noting
the difficulty of giving an operationalist analysis of the general theory, even
suggested that the requirement of general covariance "conceals the possibility of
disaster" (Bridgman (1949), 354). Finally there was, for Einstein, an

   Physics and Philosophy                                          Musa Akrami

understandable awkwardness in learning of Mach's surprising disavowal of any
role as forerunner to relativity theory in the "Preface", dated 1913, to his
posthumous book (1921) on physical optics, published by Mach's son Ludwig.
Though Einstein died without knowing differently, a recent investigation has
built a strong case that this statement was forged after Mach's death by his son
Ludwig, under the influence of a rival guardian of Mach's legacy and opponent
of relativity theory, the philosopher Hugo Dingler (Wolters, 1987).

7. 3. Kantian and Neo-Kantian
7. 3. 1. Neo-Kantians on Special Relativity
In the universities of Imperial and early Weimar Germany, the philosophy of
Kant, particularly the various neo-Kantian schools, held pride of place. Of these,
the "Marburg School" of Hermann Cohen and Paul Natorp, later Ernst Cassirer,
exhibited a special interest in the philosophy of the physical sciences and of
mathematics. But prior to the general theory of relativity (1915-1916), Kantian
philosophers accorded relativity theory only cursory attention. This may be seen
in two leading Marburg works appearing in 1910, Cassirer's Substanzbegriff und
Funktionsbegriff. and Natorp's Die Logischen Grundlagen der Exakten
Wissenschaften. Both conform to the characteristic Marburg modification of
Kant that greatly extended the scope of "transcendental logic", bringing under
"pure thought" or "intellectual forms" what Kant had sharply distinguished as
"pure intuition" and a conceptual faculty of understanding. Of course, this
revisionist tendency greatly transformed the meaning of Kant's Transcendental
Aesthetic and with it Kant's conviction that space and time were "forms of
sensibility" or "pure intuitions a priori" and so as well, his accounts of
arithmetic and geometry. As will be seen, it enabled Cassirer, some ten years
later, to view even the general theory of relativity as a striking confirmation of
the fundamental tenets of transcendental idealism. In 1910, however, Cassirer's
brief but diffuse discussion of "the problem of relativity" mentions neither the
principle of relativity nor the light postulate nor the names of Einstein, Lorentz
or Minkowski. Rather it centers on the question of whether space and time are
aggregates of sense impressions or "independent intellectual (gedankliche)
forms". Having decided in favor of the latter, Cassirer goes on to argue how and
why these ideal mathematical presuppositions are necessarily related to
measurable, empirical notions of space, time, and motion (1910, 228-9; 1923,

   Physics and Philosophy                                          Musa Akrami

Natorp's treatment, though scarcely six pages is far more detailed (1910, 399-
404). In Marburg revisionist fashion, the "Minkowski (sic) principle of
relativity" was welcomed as a more consistent (as avoiding "Newtonian
absolutism") carrying through of the distinction between transcendentally ideal
and purely mathematical concepts of space and time and the relative physical
measures of space and time. The relativization of time measurements, in
particular, showed that Kant, shorn of the psychologistic error of "pure
intuition", had correctly maintained that time is not an object of perception.
Natorp further alleged that from this relativization it followed that events are
ordered, not in relation to an absolute time, but as lawfully determined
phenomena in mutual temporal relation to one another. This is close to a
Leibnizian relationism about time. Similarly, the light postulate had a two-fold
significance within the Marburg conception of natural science. On the one hand,
the uniformity of the velocity of light, deemed an empirical presupposition of all
space- and time-measurements, reminded that absolute determinations of these
measures, unattainable in empirical natural science, would require a
correspondingly absolute bound. Then again, as an upper limiting velocity for
physical processes, including gravitational force, the light postulate eliminated
the "mysterious absolutism" of Newtonian action-at-a-distance. Natorp regarded
the requirement of invariance of laws of nature with respect to the Lorentz
transformations as "perhaps the most important result of Minkowski's
investigation". However, little is said about this, and in fact there is some
confusion regarding these transformations and the Galilean ones they supercede
(the former are seen as a "broadening (Erweiterung) of the old supposition of the
invariance of Newtonian mechanics for a translatory or circular (zirkuläre,
emphasis added) motion of the world coordinates"(403)). He concluded with an
observation that the appearance of non-Euclidean and multi-dimensional
geometries in physics and mathematics are to be understood only as "valuable
tools in the treatment of special problems". In themselves, they furnish no new
insight into the (transcendental) logical meaning and ground of the purely
mathematically determined concepts of space and time; still less do they require
the abandonment of these concepts.

7. 3. 2. Immunizing Strategies
Following the experimental confirmation of the general theory in 1919, few
Kantians attempted to retain, unadulterated, all of the components of Kant's
epistemological views. Several examples will suffice to indicate characteristic
"immunizing" strategies (see Hentschel (1990). The Habilitationsschrift of E.
Sellien (1919), read by Einstein in view of his criticism expressed in an October,
1919 letter to Moritz Schlick (Howard (1984),625), declared that Kant's views
on space and time pertained solely to "intuitive space" and so were not touched

   Physics and Philosophy                                           Musa Akrami

by the measurable spaces and times of Einstein's empirical theory. The work of
another young Kantian philosopher, Ilse Schneider, personally known to
Einstein, affirmed that Kant merely had held that the space of three-dimensional
Euclidean geometry is the space in which Newton's gravitational law is valid,
whereas an analogous situation obtains in general relativity. Furthermore,
Einstein's cosmology (1917b) of a finite but unbounded universe could be seen
as in complete accord with the "transcendental solution" to the First Antinomy in
the Second Book of the Transcendental Dialectic. Her verdict was that the
apparent contradictions between relativity theory and Kantian philosophy
disappear on closer examination of both doctrines (1921, 71-75).

7. 3. 3. Rejecting or Refurbishing the
Transcendental Aesthetic
But most Kantian philosophers did not attempt to immunize Kant from an
apparent empirical refutation by the general theory. Rather, their concern was to
establish how far-reaching the necessary modifications of Kant must be and
whether, on implementation, anything distinctively Kantian remained. Certainly,
most at risk appeared to be the claim, in the Transcendental Aesthetic, that all
objects of "outer" intuition, and so all physical objects, conform to the space of
Euclidean geometry. Since the general theory of relativity employed non-
Euclidean (Riemannian) geometry for the characterization of physical
phenomena, the conclusion seemed inevitable that any assertion of the
necessarily Euclidean character of physical space in finite, if not "infinitesimal",
regions, is simply false.
Winternitz (1924) is an example of this tendency that may be singled out on the
grounds that it was deemed significant enough to be the subject of a rare book
review by Einstein (1924) . Winternitz argued that the Transcendental Aesthetic
is inextricably connected to the claim of the necessarily Euclidean character of
physical space and so stood in direct conflict with Einstein's theory. It must
accordingly be totally jettisoned as a confusing and unnecessary appendage of
the fundamental transcendental project of establishing the a priori logical
presuppositions of physical knowledge. Indeed, these presuppositions have been
confirmed by the general theory: They are spatiality and temporality as
"unintuitive schema of order" in general (as distinct from any particular
chronometrical relations), the law of causality and presupposition of continuity,
the principle of sufficient reason, and the conservation laws. Remarkably, the
necessity of each of these principles was, rightly or wrongly, soon to be
challenged by the new quantum mechanics. (For a challenge to the law of
conservation of energy, see Bohr, Kramers, and Slater (1924)). According to
Winternitz, the ne plus ultra of transcendental idealism lay in the claim that the

   Physics and Philosophy                                              Musa Akrami

world "is not given but posed (nicht gegeben, sondern aufgegeben) (as a
problem)" out of the given material of sensation. Interestingly, Einstein, late in
life, returns to this formulation as comprising the fundamental Kantian insight
into the character of physical knowledge (1949b, 680).
However, a number of neo-Kantian positions, of which that of Marburg was
only the best known, did not take the core doctrine of the Transcendental
Aesthetic, that space and time are a priori intuitions, à la lettre. Rather,
resources broadly within it were sought for preserving an updated "critical
idealism". In this regard, Bollert (1921) merits mention for its technically adroit
presentation of both the special and the general theory. Bollert argued that
relativity theory had "clarified" the Kantian position in the Transcendental
Aesthetic by demonstrating that not space and time, but spatiality
(determinateness in positional ordering) and temporality (in order of succession)
are a priori conditions of physical knowledge. In so doing, general relativity
theory with its variably curved spacetime, brought a further advance in the steps
or levels of "objectivation" lying at the basis of physics. In this process,
corresponding with the growth of physical knowledge since Galileo, each higher
level is obtained from the previous through elimination of subjective elements
from the concept of physical object. This ever-augmented and revised advance
of conditions of objectivity is alone central to critical idealism. For this reason, it
is "an error" to believe that "a contradiction exists between Kantian a priorism
and relativity theory" (1921,64). As will be seen, these conclusions are quite
close to those of the much more widely known monograph of Cassirer (1921). It
is worth noting that Bollert's interpretation of critical idealism was cited
favorably by Gödel (1946/9-B2, 240, n.24) much later during the course of
research which led to his famous discovery of rotating universe solutions to
Einstein's gravitational field equations (1949). This investigation had been
prompted by Gödel's curiosity concerning the similar denials, in relativity theory
and in Kant, of an absolute time.

7.3. 4. General Covariance: A Synthetic
Principle of "Unity of Determination"
The most influential of all neo-Kantian interpretations of general relativity was
Ernst Cassirer's Zur Einsteinschen Relativitätstheorie (1921). Cassirer regarded
the theory as a crucial test for Erkenntniskritik, the preferred term for the
epistemology of Marburg's transcendental idealism. The question, posed right at
the beginning, is whether the Transcendental Aesthetic offered a foundation
"broad enough and strong enough" to bear the general theory of relativity.
Recognizing the theory's principal epistemological significance to lie in the
requirement of general covariance ("that the general laws of nature are not

   Physics and Philosophy                                          Musa Akrami

changed in form by arbitrary changes of the space-time variables"), Cassirer
directed his attention to Einstein's remarks, cited in §2 above, that general
covariance "takes away from space and time the last remnant of physical
objectivity". Cassirer correctly construed the gist of this passage to mean that in
the general theory of relativity, space and time coordinates have no further
importance than to be mere labels of events ("coincidences"), independent
variables of the mathematical (field) functions characterizing physical state
magnitudes. Furthermore,in accord with central tenets of the Marburg Kant
interpretation noted above, Cassirer maintained that the requirement of generally
covariant laws was a vindication of the transcendental ideality of space and time,
not, indeed, as "forms of intuition" but as "objectifying conditions" that further
"de-anthropomorphized" the concept of object in physics, rendering it "purely
symbolic". In this regard, the requirement of general covariance had
significantly improved upon Kant in bringing out far more clearly the
exclusively methodological role of these conditions in empirical cognition, a
role Kant misleadingly assigned to "pure intuition". Not only has it has shown
that space and time are not "things", it has also clarified that they are "ideal
principles of order" applying to the objects of the physical world as a necessary
condition of their possible experience. According to Cassirer, Kant's intention
with regard to "pure intuition" was simply to express the methodological
presupposition that certain "intellectual forms" (Denkformen), among which are
the purely ideal concepts of coexistence and succession, enter into all physical
knowledge. According to the development of physics since the 17 th century
chronicled in Substanzbegriff und Functionsbegrif, these forms have
progressively lost their "fortuitous" (zufälligen) anthropomorphic features, and
more and more take on the character of "systematic forms of unity". From this
vantage point, general covariance is but the most recent refinement of the
methodological principle of "unity of determination" governing the constitution
of objects of physical knowledge, completing the transposition in physics from
concepts of substance into functional and relational concepts. In its wake, the
fundamental concept of object in physics no longer pertains to particular entities
or processes in space and time but rather to "the invariance of relations among
(physical state) magnitudes". For this reason, Cassirer concluded, the general
theory of relativity exhibits "the most determinate application and carrying
through within empirical science of the standpoint of critical idealism"
(1921/1957, 71; 1923, 412).

   Physics and Philosophy                                           Musa Akrami

7.4. Logical Empiricism
7.4. 1. Lessons of Methodology?
Logical empiricism's philosophy of science was conceived under the guiding
star of Einstein's two theories of relativity, as may be seen from the early
writings of its founders, for purposes here, Moritz Schlick, Rudolf Carnap, and
Hans Reichenbach. The small monograph of Schlick, Space and Time in
Contemporary Physics, appearing in 1917, initially in successive issues of the
scientific weekly Die Naturwissenschaften, served as a prototype. Among the
first of a host of "philosophical examinations" of the general theory of relativity,
it was distinguished both by the comprehensibility of its largely non-technical
physical exposition and by Einstein's enthusiastic praise of its philosophical
appraisal, favoring Poincaré's conventionalism over both neo-Kantianism and
Machian positivism. The transformation of the concept of space by the general
theory of relativity was the subject of Rudolf Carnap's dissertation at Jena in
1921. Appearing as a monograph in 1922, it also evinced a broadly
conventionalist methodology combined with elements of Husserlian
transcendental phenomenology. Distinguishing clearly between intuitive,
physical and purely formal conceptions of space, Carnap argues that, subject to
the necessary constraints of certain a priori phenomenological conditions of the
topology of intuitive space, the purely formal and the physical aspects of
theories of space, can be adjusted to one another so as to preserve any
conventionally chosen aspect. In turn, Hans Reichenbach was one of five
intrepid attendees of Einstein's first seminar on general relativity given at Berlin
University in the tumultuous winter of 1918-1919; his detailed notebooks
survive. The general theory of relativity was the particular subject of
Reichenbach's neo-Kantian first book (1920), which is dedicated to Albert
Einstein, as well as of his next two books (1924), (1928), and of numerous
papers in the 1920s.
But Einstein's theories of relativity provided far more than the subject matter for
these philosophical examinations; rather logical empiricist philosophy of science
was itself fashioned by lessons allegedly drawn from relativity theory in
correcting or rebutting neo-Kantian and Machian perspectives on general
methodological and epistemological questions of science. Several of the most
characteristic doctrines of logical empiricist philosophy of science — the
interpretation of a priori elements in physical theories as conventions, the
treatment of the role of conventions in linking theory to observation and in
theory choice, the insistence on verificationist definitions of theoretical terms —
were taken to have been conclusively demonstrated by Einstein in fashioning his
two theories of relativity. In particular, Einstein's 1905 analysis of the

   Physics and Philosophy                                           Musa Akrami

conventionality of simultaneity in the special theory of relativity became
something of a methodological paradigm, prompting Reichenbach's own method
of "logical analysis" of physical theories into "subjective" (definitional,
conventional) and "objective" (empirical) components. The overriding concern
in the logical empiricist treatment of relativity theory was to draw broad lessons
from relativity theory for scientific methodology and philosophy of science
generally, although issues more specific to the philosophy of physics were also
addressed. Only the former are considered here; for a discussion of the latter, we
may refer to Ryckman (forthcoming b).

7. 4. 2. From the "Relativized A priori to the
"Relativity of Geometry"
A cornerstone of Reichenbach's "logical analysis" of the theory of general
relativity is the thesis of "the relativity of geometry", that an arbitrary geometry
may be ascribed to spacetime (holding constant the underlying topology) if the
laws of physics are correspondingly modified through the introduction of
"universal forces". This particular argument for metric conventionalism has
generated substantial controversy on its own, but is better understood through an
account of its genesis in Reichenbach's early neo-Kantianism. Independently of
that genesis, the thesis becomes the paradigmatic illustration of Reichenabch's
broad methodological claim that conventional or definitional elements, in the
form of "coordinative definitions" associating mathematical concepts with
"elements of physical reality", are a necessary condition of empirical cognition
in science. At the same time, however, Reichenbach's thesis of metrical
conventionalism is part and parcel of an audacious program of epistemological
reductionism regarding spacetime structures. This was first attempted in his
"constructive axiomatization" (1924) of the theory of relativity on the basis of
"elementary matters of fact"(Elementartatbestande) regarding the observable
behavior of lights rays, and rods and clocks. Here, and in the more widely read
treatment(1928), metrical properties of spacetime are deemed less fundamental
than topological ones, while the latter are derived from the concept of time
order. But time order in turn is reduced to that of causal order and so the whole
edifice of structures of spacetime is considered epistemologically derivative,
resting upon ultimately basic empirical facts about causal order and a prohibition
against action-at-a-distance. The end point of Reichenbach's epistemological
analysis of the foundations of spacetime theory is then "the causal theory of
time", a type of relational theory of time that assumes the validity of the causal
principle of action-by-contact (Nahwirkungsprinzip).
However, Reichenbach's first monograph on relativity (1920) was written from
within a neo-Kantian perspective. As Friedman (1999) and others have

   Physics and Philosophy                                            Musa Akrami

discussed in detail (Ryckman, forthcoming a), Reichenbach's innovation, a
modification of the Kantian conception of synthetic a priori principles, rejecting
the sense of "valid for all time" while retaining that of "constitutive of the object
(of knowledge)", led to the conception of a theory-specific "relativised a priori".
According to Reichenbach, any physical theory presupposes the validity of
systems of certain, usually quite general, principles, which may vary from theory
to theory. Such "coordinating principles", as they are then termed, are
indispensable for the ordering of perceptual data; they define "the objects of
knowledge" within the theory. The epistemological significance of relativity
theory, according to the young Reichenbach, is to have shown, contrary to Kant,
that these systems may contain mutually inconsistent principles, and so require
emendation to remove contradictions. Thus a "relativization" of the Kantian
conception of synthetic a priori principles is the direct epistemological result of
the theory of relativity. But this finding is also taken to signal a transformation
in the method of epistemological investigation of science. In place of Kant's
"analysis of Reason", "the method of analysis of science"(der
wissenschaftsanalytische Methode) is proposed as "the only way that affords us
an understanding of the contribution of our reason to knowledge" (1920, 71;
1965, 74). The method's raison d'être is to sharply distinguish between the
"subjective" role of (coordinating) principles — "the contribution of Reason" —
and the "contribution of objective reality", represented by theory-specific
empirical laws and regularities ("axioms of connection") which in some sense
have been "constituted" by the former. Relativity theory itself is a shining
exemplar of this method for it has shown that the metric of spacetime describes
an "objective property" of the world, once the subjective freedom to make
coordinate transformations (the coordinating principle of general covariance) is
recognized (1920, 86-7; 1965, 90). The thesis of metric conventionalism had yet
to appear.
But soon it did. Still in 1920, Schlick objected, both publicly and in private
correspondence with Reichenbach, that "principles of coordination" were
precisely statements of the kind that Poincaré had termed "conventions" (see
Coffa, 1991, 201ff.). Moreover, Einstein, in lecture of January, 1921, entitled
"Geometry and Experience", appeared to lend support to this view. Einstein
argued that the question concerning the nature of spacetime geometry becomes
an empirical question only on certain pro tem stipulations regarding the
"practically rigid body" of measurement (pro tem in view of the inadmissibility
in relativity theory of the concept "actually rigid body"). In any case, by 1922,
the essential pieces of Reichenbach's "mature" conventionalist view had
emerged. The argument is canonically presented in §8 (entitled "The Relativity
of Geometry") of Der Philosophie der Raum-Zeit-Lehre (completed in 1926,
published in 1928). In a move superficially similar to the argument of Einstein's

   Physics and Philosophy                                            Musa Akrami

"Geometry and Experience", Reichenbach maintained that questions concerning
the empirical determination of the metric of spacetime must first confront the
fact that only the whole theoretical edifice comprising geometry and physics
admits of observational test. Einstein's gravitational theory is such a totality.
However, unlike Einstein, Reichenbach's "method of analysis of science", later
re-named "logical analysis of science", is directed to the epistemological
problem of factoring this totality into its conventional or definitional and its
empirical components.
This is done as follows. The empirical determination of the spacetime metric by
measurement requires choice of some "metrical indicators": this can only be
done by laying down a "coordinative definition" stipulating, e.g., that the
metrical notion of a "length" is coordinated to some physical object or process.
A standard choice coordinates "lengths" with "infinitesimal measuring rods"
supposed rigid (e.g., Einstein's "practically rigid body"). This however is only a
convention, and other physical objects or processes might be chosen. (In
Schlick's fanciful example, the Dali Lama's heartbeat could be chosen as the
physical process establishing units of time.) Of course, the chosen metrical
indicators must be corrected for certain distorting effects (temperature,
magnetism, etc.) due to the presence of physical forces. Such forces are termed
"differential forces" to indicate that they affect various materials differently.
However, Reichenbach argued, the choice of a rigid rod as standard of length is
tantamount to the claim that there are no non-differential — "universal" —
distorting forces that affect all bodies in the same way and cannot be screened
off. In the absence of "universal forces" the coordinative definition regarding
rigid rods can be implemented and the nature of the spacetime metric
empirically determined, for example, finding that paths of light rays through
solar gravitational field are not Euclidean straight lines. Thus, the theory of
general relativity, on adoption of the coordinative definition of rigid rods
("universal forces = 0"), affirms that the geometry of spacetime in this region is
of a non-euclidean kind. The point, however, is that this conclusion rests on the
convention governing measuring rods. One could, alternately, maintain that the
geometry of spacetime was Euclidean by adopting a different coordinative
definition, for example, holding that measuring rods expanded or contracted
depending on their position in spacetime, a choice tantamount to the supposition
of "universal forces". Then, consistent with all empirical phenomena, it could be
maintained that Euclidean geometry was compatible with Einstein's theory if
only one allowed the existence of such forces. Thus whether general relativity
affirms a Euclidean or a non-euclidean metric in the solar gravitational field
rests upon a conventional choice regarding the existence of "universal forces".
Either hypothesis may be adopted since they are empirically equivalent
descriptions; their joint possibility is referred to as "the relativity of geometry".

   Physics and Philosophy                                            Musa Akrami

Just as with the choice of "standard synchrony" in Reichenbach's analysis of the
conventionality of simultaneity, also held to be "logically arbitrary",
Reichenbach recommends the "descriptively simpler" alternative in which
"universal forces" do not exist. To be sure, "descriptive simplicity has nothing to
do with truth", i.e., has no bearing on the question of whether spacetime has a
non-Euclidean structure (1928, 47; 1958, 35).

7. 4. 3. Critique of Reichenbachian Metric
In retrospect, it is rather difficult to understand the significance that has been
accorded this argument. Carnap, for example, in his "Introductory Remarks"
(1958, vii) to the posthumous English translation of this work, singled it out on
account of its "great interest for the methodology of physics". Reichenbach
himself deemed "the philosophical achievement of the theory of relativity" to lie
in this methodological distinction between conventional and factual claims
regarding spacetime geometry (1928, 24; 1958, 15), and he boasted of his
"philosophical theory of relativity" as an incontrovertible "philosophical result":
   the philosophical theory of relativity, i.e., the discovery of the definitional
   character of the metric in all its details, holds independently of
   experience….a philosophical result not subject to the criticism of the
   individual sciences." (1928, 223; 1958, 177)
Yet this result is neither incontrovertible nor an untrammeled consequence of
Einstein's theory of gravitation. There is, first of all, the shadowy status accorded
to "universal forces". A sympathetic reading (e.g., Dieks (1987)) suggests that
the notion serves usefully in mediating between a traditional a priori
commitment to Euclidean geometry and the view of modern geometrodynamics,
where gravitational force is "geometrised away" (see §5). For, as Reichenbach
explicitly acknowledged, gravitation is itself a "universal force", coupling to all
bodies and affecting them in the same manner (1928, 294-6; 1958, 256-8).
Hence the choice recommended by "descriptive simplicity" is merely a
stipulation that metrical appliances, regarded as "infinitesimal", be considered as
"differentially at rest" in an inertial system (1924, 115; 1969, 147). This is a
stipulation that spacetime measurements always take place in regions that are to
be considered small Minkowski spacetimes (arenas of gravitation-free physics).
By the same token, however, consistency required an admission that "the
transition from the special theory to the general one represents merely a
renunciation of metrical characteristics" (1924, 115; 1969, 147), or, even more
pointedly, that "all the metrical properties of the spacetime continuum are
destroyed by gravitational fields" where only topological properties remain
(1928, 308; 1958, 268-9). To be sure, these conclusions are supposed to be

   Physics and Philosophy                                            Musa Akrami

rendered more palatable in connection with the epistemological reduction of
spacetime structures in the causal theory of time.
Despite the influence of this argument on the subsequent generation of
philosophers of science, Reichenbach's analysis of spacetime measurement
treatment is plainly inappropriate, manifesting a fallacious tendency to view the
generically curved spacetimes of general relativity as stiched together from little
bits of flat Minskowski spacetimes. Besides being mathematically inconsistent,
this procedure offers no way of providing a non-metaphorical physical meaning
for the fundamental metrical tensor gμν, the central theoretical concept of general
relativity, nor to the series of curvature tensors derivable from it and its
associated affine connection. Since these sectional curvatures at a point of
spacetime are empirically manifested and the curvature components can be
measured, e.g., as the tidal forces of gravity, they can hardly be accounted as due
to conventionally adopted "universal forces". Furthermore, the concept of an
"infinitesimal rigid rod" in general relativity cannot really be other than the
interim stopgap Einstein recognized it to be. For it cannot actually be "rigid" due
to these tidal forces; in fact, the concept of a "rigid body" is already forbidden in
special relativity as allowing instantaneous causal actions. Secondly, such a rod
must indeed be "infinitesimal", i.e., a freely falling body of negligible thickness
and of sufficiently short extension, so as to not be stressed by gravitational field
inhomogeneities; just how short depending on strength of local curvatures and
on measurement error (Torretti (1983), 239). But then, as Reichenbach appeared
to have recognized in his comments about the "destruction" of the metric by
gravitational fields, it cannot serve as a coordinately defined general standard for
metrical relations. In fact, as Weyl was the first to point out, precisely which
physical objects or structures are most suitable as measuring instruments should
be decided on the basis of gravitational theory itself. From this enlightened
perspective, measuring rods and clocks are objects that are far too complicated.
Rather, the metric in the region around any observer O can be empirically
determined from freely falling ideally small neutral test masses together with the
paths of light rays. More precisely stated, the spacetime metric results from the
affine-projective structure of the behavior of neutral test particles of negligible
mass and from the conformal structure of light rays received and issued by the
observer. (Weyl, 1921) Any purely conventional stipulation regarding the
behavior of "measuring rods" as physically constitutive of metrical relations in
general relativity is then otiose (Weyl, 1923a; Ehlers, Pirani and Schild (1973)).
Alas, since Reichenbach reckoned the affine structure of the gravitational-
inertial field to be just as conventional as, on his view, its metrical structure, he
was not able to recognize this method as other than an equivalent, but by no
means necessarily preferable, account of the empirical determination of the

   Physics and Philosophy                                           Musa Akrami

metric through the use of rods and clocks (Coffa, 1979; Ryckman (1994),

7. 5. "Geometrization of Physics": Realism
and Transcendental Idealism
7. 5. 1. Differing Motivations
In the decade or so following the appearance of the general theory of relativity,
there was much talk of a "geometrization" of physics (Weyl (1918b), (1919);
Haas (1920); Lodge (1921)). While these discussions were largely, and
understandably, confined to scientific circles, they nonetheless brought distinctly
philosophical issues — of methodology, but also of epistemology and
metaphysics — together with technical matters. General relativity revived a
geometrizing tendency essentially dormant within physics since the 17th
century. In so doing, it opened up the prospect of a "geometrization" of physics,
the possibility of finding a unifying representation of all of known physics
within a single geometrical theory of the spacetime continuum. Einstein himself,
however, was not the first to embark on this audacious quest. Rather he initially
followed in the mathematical footsteps of Hermann Weyl, Arthur Stanley
Eddington, and Theodore Kaluza, only gradually (1925) devising the first of his
own "homegrown" geometrical "unified field theories". Still, by 1923, Einstein
had become the recognized leader of the unification program. (Vizgin (1994),
The first phase of the geometrical unification program essentially ended with
Einstein's "distant parallelism" theory of 1928-1931 (1929), perhaps Einstein's
final public sensation (Fölsing (1997, 605)). Needless to say, none of these
efforts met with success. In a lecture at the University of Vienna on October 14,
1931, Einstein forlornly referred to these failed attempts, each conceived on a
different differential geometrical basis, as a "graveyard of dead hopes" (Einstein,
1932). By this time, certainly, the prospects for the geometrical unification
program had considerably waned. A consensus emerged among nearly all
leading theoretical physicists that while the geometrical unification of the
gravitation and electromagnetic fields might be attained in formally different
ways, the problem of matter, treated with undeniable empirical success by the
new quantum theory, was not to be resolved within the confines of spacetime
geometry. In any event, from the early 1930s, any unification program appeared
greatly premature, in view of the wealth of data produced by the new physics of
the nucleus.

   Physics and Philosophy                                          Musa Akrami

As many will know, the unsuccessful pursuit of the goal of geometrical
unification absorbed Einstein, and his various research assistants, for more than
three decades, up to Einstein's death in 1955. In the course of it, Einstein's
methodology of research diametrically changed. In place of physical or heuristic
principles to guide theoretical construction, such as the principle of equivalence,
which put him on the path to general relativity, he increasingly relied on
considerations of mathematical aesthetics, such as "logical simplicity" and the
inevitability of certain mathematical structures under variously adopted
constraints. In a talk entitled "On the Method of Theoretical Physics" at Oxford
in 1933, the transformation was stated dramatically:
    Experience remains, of course, the sole criterion of the physical utility of
    a mathematical construction. But the creative principle resides in
    mathematics. In a certain sense, therefore, I hold it true that pure thought
    can grasp reality, as the ancients dreamed. (274)
Moreover, the advent and accumulating empirical successes of the new quantum
theory did not dislodge Einstein's core metaphysical belief in a physical reality
conceived as a continuous "total field" whose components are functions of the
spacetime variables, a geometrical conception of physical reality implied, to be
sure, by general relativity (e.g., (1950), 348). Yet, whatever may have been
Kaluza's philosophical motivations in putting forward his proposal for
geometrical unification, neither Einstein's mathematical realism nor his
metaphysics guided either Weyl or Eddington, a fact that has often been
obscured or ignored in historical treatments. The geometrical unifications of
Weyl (1918a,b) and Eddington (1921) were above all explicit attempts to
comprehend the nature of physical theory, in the light of general relativity, from
systematic epistemological standpoints that were neither positivist nor realist. As
such they comprise "early philosophical interpretations" of that theory, although
they intertwine philosophy, geometry and physics in a manner unprecedented
since Descartes. Before turning attention to their "interpretations", it will be
helpful to see how the geometrizing tendency arises within general relativity
itself and to note a few details of the geometrical unification program that
followed in its wake.

7.5. 2. "Geometrizing" Gravity: the Initial Step
Einstein's so-called "geometrization" of gravitational force in 1915 gave the
geometrization program its first, partial, realization as well as its subsequent
impetus. In Einstein's theory, the fundamental or "metric" tensor
g<SUB&MU;&NU; of Riemannian geometry appears in a dual role which
thoroughly fuses its geometrical and its physical meanings. As is apparent from
the expression for the "interval" between neighboring spacetime events, ds2 =

   Physics and Philosophy                                          Musa Akrami

gμν dxμ dxν (here, and below there is an implicit summation over repeated
upper and lower indices), the metric tensor is at once the geometrical quantity
underlying measurable metrical relations of lengths and times. In this role it ties
a mathematical theory of events in four-dimensional "curved" spacetime to
observations and measurements in space and time. But it is also the "potential"
of the gravitational (or "metrical") field whose value, at any point of spacetime,
depends, via the Einstein Field Equations (see below), on the presence of
physical quantities of mass-momentum-stress in the immediate region. In the
new view, the idea of strength of gravitational "force" is replaced by that of
degree of "curvature" of spacetime. Such a curvature is manifested, for example,
by the "tidal force" of the Earth's gravitational field that occasions two freely
falling bodies, released at a certain height and at fixed separation, to approach
one another. A freely falling body is no longer to be regarded as moving through
space according to the "pull" of an attractive gravitational "force", but simply as
tracing out the "laziest" track along the bumps and hollows of spacetime itself.
The Earth's mass (or equivalently, energy) determines a certain spacetime
curvature and so becomes a source of gravitational action. At the same time, the
gross mechanical properties of bodies, comprising all gravitational-inertial
phenomena, can be derived as the solution of a single system of generally
covariant partial differential equations, the Einstein equations of the
gravitational field. According to these equations, spacetime and matter stand in
dynamical interaction. One abbreviate way of characterizing the dual role of the
gμν is to say that in the general theory of relativity, gravitation, which includes
mechanics, has become "geometrized", i.e., incorporated into the geometry of

7.5.3. Extending "Geometrization"
In making spacetime curvature dependent on distributions of mass and energy,
general relativity is indeed capable of encompassing all (non-quantum) physical
fields. However, in classical general relativity there remains a fundamental
asymmetry between gravitational and non-gravitational fields, in particular,
electromagnetism, the only other fundamental physical interaction definitely
known at the time. This shows up visibly in one form of the Einstein field
equations in which, on the left-hand side, a geometrical object (Gμν, the Einstein
tensor) built up from the uniquely compatible linear symmetric ("Levi-Civita")
connection associated with the metric tensor gμν, and representing the curvature
of spacetime, is set identical to a tensorial but non-geometrical
phenomenological representation of matter on the right-hand side.
   Gμν = k Tμν, where Gμν = Rμν − 1/2 gμν R

   Physics and Philosophy                                          Musa Akrami

The expression on the right side, introduced by a coupling constant,
mathematically represents the non-gravitational sources of the gravitational field
in a region of spacetime in the form of a stress-energy-momentum tensor (an
"omnium gatherum" in Eddington's pithy phrase (1919, 63)). As the geometry of
spacetime principally resides on the left-hand side, this situation seems
unsatisfactory. Late in life, Einstein likened his famous equation to a building,
one wing of which (the left) was built of "fine marble", the other (the right) of
"low grade wood" (1936, 311). In its classical form, general relativity accords
only the gravitational field a direct geometrical significance; the other physical
fields reside in spacetime; they are not of spacetime.
Einstein's dissatisfaction with this asymmetrical state of affairs was palpable at
an early stage and was expressed with increasing frequency beginning in the
early 1920s. A particularly vivid declaration of the need for geometrical
unification was made in his "Nobel lecture" of July, 1923:
The mind striving after unification of the theory cannot be satisfied that two
fields should exist which, by their nature, are quite independent. A
mathematically unified field theory is sought in which the gravitational field and
the electromagnetic field are interpreted as only different components or
manifestations of the same uniform field,… The gravitational theory, considered
in terms of mathematical formalism, i.e. Riemannian geometry, should be
generalized so that it includes the laws of the electromagnetic field."(489)
It might be noted that the tacit assumption, evident here, that incorporation of
electromagnetism into spacetime geometry requires a generalization of the
Riemannian geometry of general relativity, though widely held at the time, is not
quite correct (Rainich (1925); Misner and Wheeler (1962); Geroch (1966)).
5.4 A "Pure Infinitesimal Geometry"
Still, it wasn't Einstein, but the mathematician Hermann Weyl who first
addressed the asymmetry in 1918 in the course of refashioning Einstein's theory
on the preferred epistemological basis of a "pure infinitesimal geometry" (Reine
Infinitesimalgeometrie). Holding that direct — evident, in the sense of
Husserlian phenomenology --comparisons of length or duration could be made at
neighboring points of spacetime, but not, as the Riemannian geometry of
Einstein's theory permitted, "at a distance", Weyl discovered additional terms in
his geometry that he identified with the potentials of the electromagnetic field.
From these, the electromagnetic field strengths can be immediately derived and
so electromagnetism as well as gravitation could be expressed solely within the
terms of spacetime geometry. As no other interactions were definitely known to
occur, Weyl proudly declared that the concepts of geometry and physics were
the same. Hence, everything in the physical world was a manifestation of
spacetime geometry.

   Physics and Philosophy                                             Musa Akrami

(The) distinction between geometry and physics is an error, physics extends not
at all beyond geometry: the world is a (3+1) dimensional metrical manifold, and
all physical phenomena transpiring in it are only modes of expression of the
metric field, …. (M)atter itself is dissolved in "metric" and is not something
substantial that in addition exists "in" metric space (1919, 115-16).
By the winter of 1919-1920, for both physical and philosophical reasons (the
latter having to do with his conversion to Brouwer's "intuitionist" views about
the mathematical continuum, in particular, the continuum of spacetime), Weyl
(1920) surrendered the belief, expressed here, that matter, with its corpuscular
structure, might be derived within spacetime geometry. Thus he gave up the
Holy Grail of the nascent unified field theory program almost before it had
begun. Nonetheless, he actively defended his theory well into the 1920s,
essentially on the grounds of Husserlian transcendental phenomenology, that his
geometry and its central principle, "the epistemological principle of relativity of
magnitude" comprised a superior epistemological framework for general
relativity. Weyl's postulate of a "pure infinitesimal" non-Riemannian metric for
spacetime, according to which it must be possible to independently choose a
"gauge" (scale of length or duration) at each spacetime point, met with intense
criticism. No observation spoke in favor of it; to the contrary, Einstein pointed
out that according to Weyl's theory, the atomic spectra of the chemical elements
should not be constant, as indeed they are observed to be. Although Weyl
responded to this objection forcefully, and with some subtlety (Weyl, 1923a), he
was able to persuade neither Einstein, nor any other leading relativity physicist,
with the exception of Eddington. However, the idea of requiring "gauge
invariance" of fundamental physical laws was revived and vindicated by Weyl
himself in a different form later on (Weyl (1929);see also O'Raifeartaigh

7. 5. 4. Eddington's "World Geometry"
Despite Weyl's failure to win many friends for his theory, his guiding example
of unification launched the geometrical program of "unified field theory",
initiating a variety of efforts, all aimed at finding a suitable generalization of the
Riemannian geometry of Einstein's theory to encompass as well non-
gravitational physics (Vizgin (1994), ch.4). In December, 1921, the Berlin
Academy published Theodore Kaluza's novel proposal for unification of
gravitation and electromagnetism upon the basis of a five-dimensional
Riemannian geometry. But earlier that year, in February, came Arthur Stanley
Eddington's further generalization of Weyl's four-dimensional geometry,
wherein the sole primitive geometrical notion is the non-metrical comparison of
direction or orientation at the same or neighboring points. In Weyl's geometry

   Physics and Philosophy                                            Musa Akrami

the magnitude of vectors at the same point, but pointing in different directions,
might be directly compared to one another; in Eddington's, comparison was
immediate only for vectors pointing in the same direction. His "theory of the
affine field" included both Weyl's geometry and the semi-Riemannian geometry
of Einstein's general relativity as special cases. Little attention was paid
however, to Eddington's claim, prefacing his paper, that his objective had not
been to "seek (the) unknown laws (of matter)" as befits a unified field theory.
Rather it lay "in consolidating the known (field) laws" wherein "the whole
scheme seems simplified, and new light is thrown on the origin of the
fundamental laws of physics" (1921, 105).
Eddington was persuaded that Weyl's "principle of relativity of length" was "an
essential part of the relativistic conception", a view he retained to the end of his
life (e.g., (1939, 28)). But he was also convinced that the largely antagonistic
reception accorded Weyl's theory was due to its confusing formulation. The flaw
lay in Weyl's failure to make transparently obvious that his locally scale
invariant ("pure infinitesimal") "world geometry" was not the physical geometry
of actual spacetime, but an entirely mathematical geometry inherently serving to
specify the ideal of an observer-independent external world. To remedy this,
Eddington devised a general method of deductive presentation of field physics in
which "world geometry" is developed mathematically as conceptually separate
from physics. A "world geometry" is a purely mathematical geometry the
derived objects of which possess only the structural properties requisite to the
ideal of a completely impersonal world; these are objects, as he wrote in Space,
Time and Gravitation (1920), a semi-popular best-seller, represented "from the
point of view of no one in particular". Naturally, this ideal had changed with the
progress of physical theory. In the light of relativity theory, such a world is
indifferent to specification of reference frame and, after Weyl, of gauge of
magnitude (scale). A "world geometry" is not the physical theory of such a
world but a framework or "graphical representation" in whose terms existing
physical theory might be displayed, essentially by the mathematical
identification of known tensors of the existing physical laws of gravitation and
electromagnetism, with tensors of the world geometry. Such a geometrical
representation of physics cannot really be said to be "right" or "wrong", for it
only implements, if it can, current ideas governing the conception of objects and
properties of an impersonal objective external world. But when existing physics,
in particular, Einstein's theory of gravitation, is set in the context of Eddington's
world geometry, it yields a surprising consequence: The Einstein law of
gravitation appears as a definition! In the form Rμν = 0 it defines what in the
"world geometry" appears to the mind as "vacuum" while in the form of the
Einstein field equation noted above, it defines what is there encountered by the
mind as "matter". This result is what was meant by his stated claim of throwing

   Physics and Philosophy                                          Musa Akrami

"new light on the origin of the fundamental laws of physics". Eddington's
notoriously difficult and opaque later works (1936), (1946), took their
inspiration from this argumentation in attempting to carry out a similar, but
algebraic, program of deriving fundamental physical laws, and the constants
occurring in them, from epistemological principles.

7.5. 5. Meyerson on "Pangeometrism"
Within physics the idealist currents lying behind the "world geometries" of Weyl
and Eddington were largely ignored, whereas within philosophy, with the
notable exception of Émile Meyerson's La Déduction Relativiste (1925),most
philosophers lacked the tools to connect these readily discernible currents with
their geometrical theories. Meyerson, who had no doubt of the basic realist
impetus of science, carefully distinguished Einstein's "rational deduction of the
physical world" from the geometrical unifications of gravitation and
electromagnetism of Weyl and Eddington. These theories, as affirmations of a
complete panmathematicism, or rather of a pangeometrism (§§ 157-58), were
compared to the rational deductions of Hegel's Logic. That general relativity
succeeded in partly realizing Descartes' program of reducing the physical to the
spatial through geometric deduction, is due to the fact that Einstein "followed in
the footsteps" of Descartes, not Hegel (§133). But pan-geometrism is also
capable of overreaching itself and this is the transgression committed by Weyl
and Eddington. Weyl in particular is singled out for criticism for seemingly to
have reverted to Hegel's monistic idealism, and so to be subject to its fatal flaw.
In regarding nature as completely intelligible, Weyl had abolished the thing-in-
itself and so promoted the identity of self and non-self, the great error of the
Though he had "all due respect to the writings of such distinguished scientists"
as Weyl and Eddington, Meyerson took their overt affirmations of idealism to be
misguided attempts "to associate themselves with a philosophical point of view
that is in fact quite foreign to the relativistic doctrine" (§150). That "point of
view" is in fact two distinct species of transcendental idealism. It is above all
"foreign" to relativity theory because Meyerson cannot see how it is possible to
"reintegrate the four-dimensional world of relativity theory into the self". After
all, Kant's own argument for Transcendental Idealism proceeded "in a single
step", in establishing the subjectivity of the space and time of "our naïve
intuition". But this still leaves "the four dimensional universe of relativity
independent of the self". Any attempt to "reintegrate" four-dimensional
spacetime into the self would have to proceed at a "second stage" where,
additionally, there would be no "solid foundation" such as spatial and temporal
intuition furnished Kant at the first stage. Perhaps, Meyerson allowed, there is

   Physics and Philosophy                                          Musa Akrami

indeed "another intuition, purely mathematical in nature", lying behind spatial
and temporal intuition, and capable of "imagining the four-dimensional universe,
to which, in turn, it makes reality conform". This would make intuition a "two-
stage mechanism". While all of this is not "inconceivable", it does appear,
nonetheless, "rather complex and difficult if one reflects upon it". In any case,
this is likely to be unnecessary, for considering the matter "with an open mind",
one would seem to be led to the position of those who believe that relativity
theory tends to destroy the concept of Kantian intuition (§§ 151-2).
Meyerson had come right up to the threshold of grasping the Weyl-Eddington
geometric unification schemes in something like the sense in which they were
intended. The stumbling block for him, and for others, is the conviction that
transcendental idealism can be supported only from an argument about the
nature of intuition, and intuitive representation. To be sure, the geometric
framework for Weyl's construction of the objective four-dimensional world of
relativity is based upon the Evidenz available in "essential insight", which is
limited to the simple linear relations and mappings in what is basically the
tangent vector space to a point in a manifold. Thus in Weyl's differential
geometry there is a fundamental divide between integrable and non-integrable
relations of comparison. The latter are primitive and epistemologically
privileged, but nonetheless not justified until it is shown how the infinitesimal
homogenous spaces, corresponding to the "essence of space as a form of
intuition", are compatible with the large-scale inhomogenous spaces
(spacetimes) of general relativity. And this required not a philosophical
argument about the nature of intuition, but one formulated in group-theoretic
conceptual form. (Weyl, 1923a,b). Eddington, on the other hand, without the
cultural context of Husserlian phenomenology or indeed of philosophy
generally, jettisoned the intuitional basis of transcendental idealism altogether,
as if unaware of its prominence. Thus he sought a superior and completely
general conceptual basis for the objective four-dimensional world of relativity
theory by constituting that world within a geometry (its "world structure"
(1923)) based upon a non-metrical affine (i.e., linear and symmetric) connection.
He was then free to find his own way to the empirically confirmed integrable
metric relations of Einstein's theory without being hampered by the conflict of a
"pure infinitesimal" metric with the observed facts about rods and clocks.

7. 5. 6. "Structural Realism"?
It has been routinely assumed that all the attempts at a "geometrization of
physics" in the early unified field theory program shared something of Einstein's
hubris concerning the ability of mathematics to "grasp" the fundamental
structure of the external world. The geometrical unified field theory program

   Physics and Philosophy                                           Musa Akrami

thus appears to be inseparably stitched to a form of scientific realism, recently
termed "structural realism", with perhaps even an inspired turn toward
Platonism. According to "structural realism", whatever the "nature" of the
fundamental entities comprising the physical world, only their "structure" can be
known as that structure is represented in the equations of the theory. The sole
ontological continuity across changes in fundamental physical theory is a
continuity of structure, as the equations of the earlier theory can be derived,say
as limit cases, from those of the later. Geometrical unification theories seems
tailored for this kind of realism. For if a geometrical theory is taken to give a
true or approximately true representation of the physical world, what is
geometrically represented has the definite structure of the fundamental
geometrical relations. But for Weyl and Eddington, geometrical unification was
not, nor could be, such a representation, for essentially the reasons articulated
two decades before by Poincaré (1906,14):
Does the harmony the human intelligence thinks it discovers in nature exist
outside of this intelligence? No, beyond doubt, a reality completely independent
of the mind which conceives it, sees or feels it, is an impossibility. A world as
exterior as that, even if it existed, would for us be forever inaccessible. But what
we call objective reality is, in the last analysis, what is common to many
thinking beings, and could be common to all; this common part,...,can only be
the harmony expressed by mathematical laws. It is this harmony then which is
the sole objective reality....
In Weyl and Eddington, geometrical unification was an attempt to cast the
"harmony" of the Einstein theory of gravitation in a new epistemological and
explanatory light, by displaying the great field laws of gravitation and
electromagnetism within the common frame of a geometrically represented
objective reality. Their unorthodox manner of philosophical argument, cloaked,
perhaps necessarily, in the language of differential geometry, has tended to
conceal or obscure conclusions about the significance of a "geometrized
physics" that push in considerably different directions from either
instrumentalism or scientific realism.

Barbour, J., and Pfister, H. (eds.) (1995). Mach's Principle: From Newton's
Bucket to Quantum Gravity. (Boston, Basel, Berlin: Birkhäuser).
Carnap, R. (1956). "Introductory Remarks to the English Edition", dated July,
1956, in H. Reichenbach (1958), v- vii.
Cassirer, E. (1910). Substanzbegriff und Funktionsbegriff. (Berlin: Bruno
Cassirer). translated by W.C. Swabey and M.C. Swabey in Substance and

   Physics and Philosophy                                        Musa Akrami

Function and Einstein's Theory of Relativity. (Chicago: Open Court, 1923);
reprint (New York: Dover, 1953), 1-346.
Coffa, J.A. (1979). "Elective Affinities: Weyl and Reichenbach", in W. Salmon
(ed.), Hans Reichenbach: Logical Empiricist (Dordrecht: D. Reidel), 267-304.
----- (1991).The Semantic Tradition from Kant to Carnap: To the Vienna Station
(Cambridge: Cambridge University Press).
Eddington, A, S.(1936). The Relativity Theory of Protons and Electrons.
(Cambridge: Cambridge University Press).
----- (1939). The Philosophy of Physical Science.(The Tarner Lectures, 1938).
(Cambridge: Cambridge University Press)
----- (1948). Fundamental Theory. (Cambridge: Cambridge University Press).
Posthumously published.
Friedman, M. (1983). Foundations of Space-Time Theories. (Princeton:
Princeton University Press).
Howard, D., and Stachel, J. (eds.) (1989). Einstein and the History of General
Relativity. (Boston, Basel, Berlin: Birkhäuser).
Norton, J. (2000). "‘Nature is the Realisation of the Simplest Conceivable
Mathematical Ideas’: Einstein and the Canon of Mathematical Simplicity",
Studies in the History and Philosophy of Modern Physics 31, 135-170.
O'Raifeartaigh, L. (1997). The Dawning of Gauge Theory. (Princeton: Princeton
University Press).
Reichenbach, H. (1920). Relativitätstheorie und Erkenntnis Apriori. (Berlin: J.
Springer). Translation by M. Reichenbach, The Theory of Relativity and A Priori
Knowledge. (Berkeley and Los Angeles: University of California Press, 1965).
----- (1924) Axiomatik der relativistischen Raum-Zeit-Lehre. (Braunschweig:
Vieweg). Translation by M. Reichenbach, Axiomatization of the Theory of
Relativity (Berkeley and Los Angeles: University of California Press, 1969).
----- (1928). Philosophie der Raum-Zeit Lehre. (Berlin: Walter de Gruyter).
Translation, with omissions, by M.Reichenbach and J. Freund, The Philosophy
of Space and Time. (New York: Dover, 1958).
Ryckman, T. (1994). "Weyl, Reichenbach and the Epistemology of Geometry",
Studies in the History and Philosophy of Modern Physics, 25,831-870.
Torretti, R. (1983). Relativity and Geometry (Oxford: Pergamon Press).
Vizgin, V. (1994) Unified Field Theories in the first third of the 20th Century.
Translated from the Russian by J. B. Barbour (Basel, Boston, Berlin: Birkäuser).

   Physics and Philosophy                                         Musa Akrami

Chapter8. Cosmology:
Methodological Debates in the 1930s
and 1940s
8. 1. Introduction
8. 2. The Lead-up to the Debate
       8. 2. 1. Einstein's General Theory of Relativity
       8. 2. 2. Hubble's Expanding Universe
8. 3. Cosmology and its philosophy
       8. 3. 1. Relativistic Cosmology: the majority philosophy
       8.3. 2. Milne's Philosophical Challenge
       8.3. 3. Kinematic Relativity—an alternative cosmology
8. 4. The Great Cosmological Debate Begins: 1933-1934
       8. 4. 1. Dingle's First Attacks
       8.4. 2. Two Ways to Disagree with Milne
       8.4. 3. Milne Makes Philosophical Improvements
      8.4. 4. A Major Philosophical Issue: What makes a scientific theory
       8. 4. 5. How to Choose Among Theories and Philosophies?
8. 5. The Triumph of Milne's Methods 1935-36
       8. 5. 1. McCrea, Walker and Robertson Adopt Milne's Methods
       8. 5. 2. But Eddington Scoffd…
8. 6. Dingle's Denoument
       8. 6. 1. Modern Aristotles?
       8.6. 2. Dingle as ‘True Believer’
       8. 6. 3. Wrong from the Very Start
       8. 6. 4. The Debate Goes Very Public
       8. 6. 5. The Counterattack

By George Gale, University of Missouri/Kansas City

   Physics and Philosophy                                           Musa Akrami

      8. 6. 6. The Coolest Voice
8. 7. The Calm Between the Storms
       8. 7. 1. Two Equal Competitors
       8. 7. 2. The Origin and Evolution of Theories
      8. 7. 3. Milne's Ultimate Success
8. 8. Steady-state Cosmology
      8. 8. 1. Bondi's Philosophical Origins
      8. 8. 2. Enter Popper
      8. 8. 3. But It's Milne In the End
      8. 8. 4. Return of the Cosmological Principle
      8. 8.5. A Popperian Conclusion

Introductory remark
Sometimes, philosophy drives science. Cosmology between 1932-48 provides an
excellent example how explicitly philosophical considerations directed the
evolution of a modern science during a crucial period of its development. The
following article exhibits these philosophical aspects of cosmological thinking in
detail, beginning with a brief sketch of the historical development of general
relativity cosmology until 1932. Following this, the historical participants in the
philosophical debate are introduced, along with the basic ideas of their
competing positions. Then the critical stages of the debate -- 1935-37 -- are
closely explored by focussing directly upon the arguments of the participating
scientists and philosophers. Finally, the concluding stage of the philosophical
debate, namely, the emergence of the steady-state theory of the Universe, is
presented in the context of its development from Popper's philosophy of science.

8. 1. Introduction
One of the most vigorous philosophical debates of the century broke out among
cosmologists during the 1930s and 1940s. At the peak of the debate, 1936-37,
many of the most prominent scientists in Britain, as well as several leading
philosophers of science, had gotten themselves publically involved. Their
arguments, attacks and rebuttals were chronicled in many of the leading

   Physics and Philosophy                                           Musa Akrami

scientific journals, including a special edition of the foremost general scientific
journal, Nature, devoted entirely to philosophical arguments and counter-
Methodology was the central issue of the debate, although metaphysical
questions also arose, particularly those concerning the actual reality of certain
structures and forces imputed to the Universe by the new cosmological theories
and observations. But in the end, methodology was the real goad spurring on
most of the participants.
At bottom, there were just two opposing positions in the debate, each of which
comprised a two-point stance. On one side were those scientists who had their
roots mostly in the experimental side of natural science. To them, there was one
and only one legitimate method for science. Theory construction, they believed,
involved two closely-linked steps. First, one began from the empirical
observations, that is, from measurements, manipulations, experiments, whose
results were evident to the human senses; this is classic empiricist epistemology.
Observational results would then suggest possible hypotheses to examine via
further empirical testing. When enough data concerning the hypothesis had been
gathered, logical generalization could be carried out, thereby producing a
theory; this is classic inductivist logic.
Opposing these inductive-empiricist scientists were those whose roots were
mostly in the theoretical side of natural science, most especially mathematical
physics. To them, there was another, more logically sound, method to construct
theories. First, hypotheses could be generated in any fashion, although most
believed that imagining hypotheses which were based upon very general, very
reasonable concepts—that the Universe's physical processes had simple
mathematical descriptions, for example—was the best place to begin; this is
classic rationalist epistemology. Once the hypothesis had been generated, strict
analytical reasoning could be used to make predictions about observations; this
is classic deductivist logic. Scientists who held this view came to be called
hypothetico-deductivists; their views about both hypothesis generation and
deductive predictions were each strongly opposed by the inductive-empiricists.
Part of the controversy may be laid to the fact that cosmology was a new
science, and disputes about methodology in new sciences are not rare in the
history of the sciences. What is rare about this case, however, is the vigor,
sometimes even bitterness, with which the philosophical controversy was
waged. Another reason for the controversy lies in the fact that cosmology is a
data-poor science: observations are hard-won and rare, and they frequently must
be run through elaborate theoretical manipulations and corrections in order to
make sense at all. With a paucity of data results, scientists must rely upon
philosophical argument to undergird their views about how the scientific work
should be done.

   Physics and Philosophy                                           Musa Akrami

One final feature of the debate must be noted. The participants are almost
universally scientists, and not philosophers. Yet this does not much affect the
level of philosophical thinking going on; these scientists knew their philosophy
well, and they wielded philosophy's weapons and defenses with great skill. In
the end, their debate shaped cosmology into the science we know today.
It will be useful to look briefly at the history of cosmology leading up to the

8. 2. The Lead-up to the Debate
Since about 1700 theories about the nature and structure of the Universe were
derived from Newtonian theory, most especially his theory of gravitation, which
was used to account for the behavior of heavenly bodies and their systems.
Newton's theory hypothesized a force—gravitation—acting upon material
bodies, free to move over time within the passive, inert ‘container’ of three-
dimensional space. Bodies, paths, and space itself exemplified the classical
geometry of Euclid. All these features changed with the publication of Einstein's
General Theory of Relativity, 1915-17.

8. 2. 1. Einstein's General Theory of Relativity
Einstein's intended his theory to replace Newton's theory of gravitation
completely. In Einstein's view, gravity was not a force existing independently of
the spatial ‘container’; rather, gravitation arises as a curvature of the space (and
time, which is necessarily connected to space in the new theory), which means
that geometry and gravity and astronomical behavior are all intimately
connected. For example, near the sun the geometrical structure, the curvature, of
spacetime changes radically, which expresses itself as an increasing velocity of
incoming orbiting bodies such as comets or satellites. One immediate, and to
some, puzzling, consequence of Einstein's theory is that the geometry of the
Universe is no longer taken to be Euclidean. Although there are several different
candidates for the actual geometry of space, it was not known which is correct.
It was not recognized at first that the General Theory of Relativity could be
applied to the Universe as a single, whole, individual object, thereby producing a
new cosmological theory, one completely different from its predecessors.
Although the mathematics involved are extremely difficult, two solutions, one
by Einstein himself, the other by the Dutch astronomer Willem de Sitter, were
produced in just a short time in 1917. Unfortunately, the universes predicted by
the two solutions were extreme: Einstein's universe would be densely packed
with matter, whereas de Sitter's would be essentially empty.

   Physics and Philosophy                                           Musa Akrami

Obviously, the universe as observed by astronomers did not conform at all to the
description provided by either solution, a fact many found troubling. Moreover,
no additional solutions were forthcoming (even though both Friedmann and
LeMaître had developed alternatives, they remained unknown and unnoticed).
For nearly twelve years, the new cosmology appeared to be going nowhere.
Then Hubble at California's Mt. Palomar made public his astonishing
observations of a cosmic Doppler shift, a shift toward the red in the color of light
coming from the most distant star systems.

8. 2. 2. Hubble's Expanding Universe
Most cosmologists—with the interesting exception of Hubble himself—came to
the immediate conclusion that the red shift could only mean that the universe
was expanding. Immediately the relativity theorists were able to interpret the
expansion as a continuous change in the geometry of spacetime, which was
thoroughly accounted for by the General Theory of Relativity. After over a
decade of stagnation in face of the meager choice between just two models of
the cosmos, Hubble's observations spurred theorists on to the construction of a
melange of new models, each vying in competition with the other.
In the end, it was the Belgian astronomer Georges LeMaître's theory of an
expanding universe that came to be accepted. LeMaître's model was publically
proclaimed as appropriate and generally correct during a special session of the
British Association for the Advancement of Science, 31 Oct 1931. Modern
scientific cosmology had been officially born; because of its birth within the
context of Einstein's theory of relativity, the new cosmology became quickly and
broadly known as Relativistic Cosmology. The model of this cosmology is most
famously that of the blowing up of a balloon painted with dots to represent
galaxies. Over time, the radius of the model's spherical space (the balloon)
increases, thereby decreasing the curvature of the space (the balloon's skin), and
increasing the distance between the dots.
Although cosmologists came from Europe and America as well as Britain, most
of the work in theoretical cosmology took place in London, Cambridge and
Oxford. Americans Hubble, Tolman and Robertson did their work at CalTech in
Pasadena, but were frequently in England; and most of the European and British
workers cycled through Pasadena at one time or another. De Sitter, from
Holland, and LeMaître, from Belgium, spent important periods in England, as
did various of the German workers. Thus, even though cosmology was done
throughout the Western world, its major concentrating point was England; our
focus in what follows will be the same.

   Physics and Philosophy                                          Musa Akrami

8.3. Cosmology and its philosophy
Because it represented such a radical departure from previous scientific thinking
about the Universe, relativistic cosmology needed to work out its philosophical
underpinnings, most especially in regard to its methodology. ‘How is this new
science to be conducted?’ was thus a compelling question. But method, of
course, is always linked to metaphysics and epistemology. A full-blown
philosophical discussion was evidently required. It came soon enough: within a
span of less than a year, a vigorous debate between two philosophically opposed
camps developed. The debate required nearly two decades to reach its full
resolution. But, with the resolution, cosmology had philosophically certified its
methodology within the context of a concensus metaphysics and epistemology.
Before going into the details of the debate, however, several general points
should be noted. Let us turn to the details of the origin of the debate.

8. 3. 1. Relativistic Cosmology: the majority
To begin with, the cosmological thinking of the majority of scientists—
including Eddington, de Sitter, Robertson, Tolman, and their colleagues—had
betrayed a relatively unexamined, and apparently uncontroversial cluster of
philosophical perspectives: on the metaphysical side they held a modest sort of
explanatory realism—if an accepted theory referred to entity x, then x was
acceptable as a genuinely, physically real object; to this metaphysical stance was
coupled a methodology exhibiting a classic sort of inductive empiricism—
scientific knowledge consisted of generalizations built up from individual
empirical observations. But this cluster of views did not go long unchallenged.
In early July 1932, just nine months after relativistic cosmology became the
concensus during the British Association meeting, Oxford astrophysicist E. A.
Milne published a short article in Nature which directly attacked the current
philosophical tenets, proposing their replacement by a new cluster of views, one
as radical as the new science it purported to undergird.

8.3. 2. Milne's Philosophical Challenge
Milne's metaphysical views were based in positivism, most especially in
operationalism: only those objects whose properties could be directly revealed
by some observational procedure, or operation, were to be counted among the
real. Thus, for Milne, reality did not contain the usual relativistic cosmology
referents “curved space”, “expanding space” or even “four-dimensional
spacetime”, simply because none of these entities were operationalizable. Milne
held that ‘what you saw was what you got’; since “curved space” of various

   Physics and Philosophy                                           Musa Akrami

geometries couldn't be observed, space was just as it looked—Euclidean. In the
same way, the expanding of the Universe was a genuine expanding—each
galaxy was retreating from each other—not just a change in the geometry of the
curvature, as it was for the relativists. Moreover, in place of relativistic
cosmology's inductive empiricism, Milne opted for a hypothetico-deductive
rationalism. Cosmologists, Milne believed, were bound to dream up any and all
possible models of a universe, and then deduce what, if any, observable
consequences followed from their hypotheses. Hypothesizing could be based
upon just about anything, although Milne believed that certain very general
rational principles derived from aesthetic beliefs about universal order and
regularity would be the most fruitful. His ‘cosmological principle’, namely, that
every cosmologist in the universe should look out upon the same cosmos, was
the prime example of such thinking. Later, Bondi would found Steady-state
Cosmology on an even more general version of Milne's principle, which he
called the ‘perfect cosmological principle.’

8.3. 3. Kinematic Relativity—an alternative
Milne's philosophy of cosmology came with a closely associated cosmological
model, kinematic relativity, so-called because of its tight links to the kinematics
of Einstein's Special Theory of Relativity. Kinematics, in Einstein's Special
Theory, is especially concerned with observers trying to make measurements of
the behavior of objects moving in systems relative to themselves. According to
Milne's understanding, these measurements could only be made by the observers
signalling among themselves using light or other electromagnetic radiation,
using clocks to time the signals. In the end, all measurement—even space and
velocity—reduced to timing the signals as they went from one observer to
another. This idea of measurement represented a revolutionary simplification of
previous ideas, and held philosophical interest for that reason alone. There were
practical consequences as well. As Bondi later remarked, “Milne's idea led
straightaway to the radar speed gun!”
Milne's kinematic relativity and its underlying philosophy both immediately
brought careful scrutiny, not to mention controversy.

8.4. The Great Cosmological Debate Begins:
Eddington was the first to attack Milne's views. In a series of lectures given at
Harvard during late ‘32 and published early in the new year as The Expanding

   Physics and Philosophy                                           Musa Akrami

Universe, Eddington denied the efficacy of both operationalism and hypothetico-
deductivism, and not only defended explanatory realism, but strengthened his
ontological position heroically: the theoretical entities of relativistic cosmology
were not just plausible, they were so necessary to understanding the universe,
that cosmological knowledge was essentially impossible without them.
(Eddington 1932, p. 19)

8. 4. 1. Dingle's First Attacks
Few others would ever go so far as Eddington's ontological heroism; yet
epistemological and methodological heroism in the fight against Milne was not
rare. Chief hero in this aspect of the attack on Milne was Herbert Dingle, a
highly respected astrophysicist, and then-secretary of the Royal Astronomical
Society. Dingle's initial foray appeared as a response to Milne's first detailed
presentation of kinematic relativity. (Milne 1933) After claiming that while
kinematic relativity did not differ appreciably from relativistic cosmology in its
mathematical formalism or observable consequences, Dingle asserted that, on
the other hand, it invited special criticism because it renounced “the fundamental
principles of scientific method,” namely, “Newton's principle of induction from
phenomena.”(Dingle 1933 p178) Dingle was never to relent in his attacks upon
Milne's hypothetico-deductivism, at all times rejecting the methodology as even
a possible candidate for acceptance by genuine science.
Dingle's article appeared back-to-back with an appraisal of kinematic relativity
by the important American cosmologist H. P. Robertson. (Robertson 1933a)
Robertson focussed upon Milne's hypothetico-deducivism as well, noting that
the cosmological principle in kinematic relativity functions as an a priori rule,
rather than as an empirical generalization, its status in relativistic cosmology.
Robertson otherwise is not especially taken with Milne's theory, limiting himself
to remarks suggesting that, where they can be compared, kinematic relativity
and relativistic cosmology apparently are similar in physical content. As we
shall shortly see, Robertson's later work strongly belied this earlier apparent
indifference to Milne's theory.

8.4. 2. Two Ways to Disagree with Milne
Right from the start, cosmologists differed in their opinions about both the
physical content of Milne's theory, and its underlying philosophy. Dingle
disliked Milne's methods, but found the theory itself of not much interest.
Robertson initially agreed with Dingle, but within a short time had significant
changes of heart. Eddington disliked both the theory and its philosophy, finding
them far too deviant from what was typical, i.e., relativistic cosmology and its
mainstream philosophy. Younger cosmologists such as McVittie and McCrea,
students, respectively, of Eddington and Whittaker, soon joined the fray.

   Physics and Philosophy                                           Musa Akrami

McVittie initially found the physics of kinematic relativity quite interesting, and
quite different from the physics of relativistic cosmology. (McVittie 1933b) But
Milne's philosophy was something else; the strict empiricism McVittie had
earlier revealed (McVittie 1933a) made him equally unhappy with both Milne's
rationalism and his hypothetico-deductivism.
McCrea's remarks were among the most perceptive and favorable. (Kermack and
McCrea 1933) While he thought that Milne's operationalist criticisms of curved
and expanding space were of little import, McCrea was the first to notice the
parsimony and elegance of Milne's strictly kinematic solution to the problem of
the origin of the universe's expansion. Since a search for such a solution had
vexed relativistic cosmology for several years (McVittie 1931), McCrea
suggested that Milne's mechanism should be immdiately shown to be part of
relativistic cosmology. (Kermack and McCrea 1933 p. 529)
Clearly, the so-recently won consensus about relativistic cosmology and its
philosophy had dissolved into confusion and controversy over Milne and his

8.4. 3. Milne Makes Philosophical
Over the next year or so, Milne made strenuous efforts to elucidate both
kinematic relativity's physics and its philosophy, beginning, as would be his
wont, with the philosophy. In October, Milne addressed the Philosophical
Association, giving an explicit and detailed analysis not only of his
philosophical views, but also of their history, which, he claimed, extended back
to Locke and Hume (Milne 1934a) His description of the two opposed
methods—inductive empiricism vs. hypothetico-deductivism—is quite clear and
   Strictly speaking, physics has no philosophy. It has method…Now the
   methods of theoretical physics seem to be reducible to two species, the
   method of starting with concepts and the method of starting with things
   observed. …When a subject is developed from concepts the concepts play
   the part of the terms occurring in the axioms of geometry…. The concepts
   are undefined save as being governed by propositions of which they are
Milne's commitment to axiomatization is notable here. It was based in his earlier
admiration for the work of Whitehead and Russell (Crowther 1970);
commitment to axiomatization in cosmology, once having been initiated by
Milne, would be an enduring hallmark of the work of many, including both
Robertson and Walker.

   Physics and Philosophy                                           Musa Akrami

Three weeks after this address, Milne spoke on related topics at the monthly
meeting of the Royal Astronomical Society. His main point was that theories
differed only insofar as their concepts could be cashed out in observations
deduced from them. Eddington took strong exception to Milne's arguments,
claiming in response that kinematic relativity and relativistic cosmology differed
more importantly in their ontology than in their consequences. Eddington was
especially concerned with differences in the spacetime-geometry each theory
ascribed to the world. For Eddington and his colleagues, the equivalence of
gravitation and spacetime geometry was a genuine reality, a feature of the
physical world, just as real as suns and moons and stars.

8.4. 4. A Major Philosophical Issue: What
makes a scientific theory ‘good’?
Milne was having none of it. In the next month's Observatory—the informal
monthly publication of the Royal Astronomical Society—he took Eddington and
his theoretical-realist colleagues to task, concluding that “theories differ simply
and solely when their predictions as to phenomena differ”; most importantly,
“this method of comparison avoids all reference to distance-assignments, world-
geometry, schemes of projection or the like.” (Milne 1934b) In other words,
metaphysics was to be avoided in cosmology; space, spacetime, geometry and
the like were to be rejected as scientific realities, replaced by reference simply
and solely to observations. The only realities, according to Milne, were what
could be reported among observers about light signals and clocks.
During 1934 Milne worked together with his new student A.G. Walker. Walker
never evinced much interest in the philosophical aspects of kinematic relativity,
choosing instead to focus tightly upon working out the physical details of the
theory itself. He had immediate success. (Walker 1934) One of his important
conclusions was that other authors, specifically McVittie and Robertson, were
wrong to conclude that the physics of Milne's theory ultimately corresponded to
relativistic cosmology: “Milne's system is fundamentally different from that of
general relativity.” (Walker 1934 p. 489; emphasis in original)

8. 4. 5. How to Choose Among Theories and
In an important review of the entire confused situation between kinematic
relativity and relativistic cosmology, McVittie confessed that “experimentally it
seems hopeless to discriminate between them…at present the choice is almost
entirely a matter of personal taste.” (McVittie 1934 p. 29) At almost the same
time, de Sitter took on Milne in serious fashion. (deSitter 1934) Responding to
Milne's methodological challenge, he showed that, indeed, it is possible to

   Physics and Philosophy                                          Musa Akrami

formulate relativistic cosmology in axiomatic fashion, just as Milne had
formulated kinematic relativity “from concepts.” But de Sitter explicitly rejected
Milne's philosophical use of the cosmological principle, “which asserts that
statistically the world pictures of two different observers must be the same.” His
objection is founded on the matter-of-fact that “we have, however, no means of
communicating with other observers, situated on faraway stars, or moving with
excessive velocities.” (deSitter 1934 p. 598) So much for rational principles as
The year in cosmology ended almost as confused as it had begun, with one
exception: Milne had gotten much clearer about his philosophical views, and
was applying them to an exhaustive presentation of his cosmology, theory and
philosophy. His book Relativity, Gravitation and World Structure (Milne 1935)
would be published in just a few months.

8. 5. The Triumph of Milne's Methods 1935-
The new year marked a sudden change. In short order, McCrea, Walker and
Robertson succumbed to Milne's methodological recommendations: first, to
carry out an operationalist paring of non-observational concepts, then, secondly,
to embed the resulting minimalist concept set in an axiomatic hypothetical-
deductive structure. Thus was the famous Robertson-Walker spacetime metric

8. 5. 1. McCrea, Walker and Robertson Adopt
Milne's Methods
McCrea's effort operationalized the concept of “distance”, principally and
originally by comparison of certain elements of Newtonian cosmology and de
Sitter's axiomatized version of relativistic cosmology. (McCrea 1935) Walker's
paper specifically eschewed use of “any indefinable concepts”, in particular, he
did not assume that the “associated metric [of relativistic cosmology] has any a
priori physical significance.” (Walker 1935) Robertson's article, the first of
three, is the most important, both in its content, and in the signal it sends,
namely, that one of the original mainstream relativistic cosmology proponents
has adopted a major element of Milne's new philosophy for cosmology.
(Robertson 1935) Robertson's conclusion exhibits this point clearly and

   Physics and Philosophy                                           Musa Akrami

   We have examined, from the operational standpoint, the problem of
   determining the most general kinematical background suitable for an
   idealized universe in which the cosmological principle holds. Allowing
   the fundamental observers the use only of clocks and theodolites, and
   granting them the possibility of sending and receiving we have shown that
   for each given mode of motion x(t) there necessarily exists a quadratic
   line element which is invariant, in form as well as in fact, under
   transformation fqrom one fundamental observer to another. (Robertson
   1935 p. 300)
Unlike de Sitter, Robertson accepts the cosmological principle, replete with its
observers on far-separated particles. Moreover, as this statement shows,
Robertson is intimately familiar with Milne's latest operationalist reduction:
space is to be reduced to time measurements given by clock readings on signals
exchanged between observers. Robertson gets this idea from Milne's book,
which he had earlier reviewed (but which was only subsequently published) for
Astrophysical Journal. (Robertson 1936)

8. 5. 2. But Eddington Scoffd…
Eddington disparages these same methods. In his scathing Nature review of
Milne's book, he rejects Milne's hypothetico-deductivism, his cosmological
principle, and, above all, his operationalism: “When I visit the Cavendish
Laboratory, I do not find its occupants engaged in flashing light-signals at each
other, but I find practically everyone employing rigid scales or their equivalent.”
(Eddington 1935, p. 636) Whittaker's review was not so negative as Eddington's.
(Whittaker 1935) While the senior physicist rejects Milne's operationalism and
attacks upon the geometrical commitments of relativistic proponents, he is
considerably more forgiving about Milne's hypothetico-deductivism, and even
goes so far as to remark Milne's “brilliant record in astrophysical discovery.”
Nonetheless, Milne's break with a tradition including at least “Einstein, de Sitter,
Friedmann, LeMaître, Weyl, Eddington, H.P. Robertson and others” is to be
regretted. (Whittaker 1935 p. 179) Perhaps, along with Eddington, Whittaker
hopes that soon “Professor Milne will return to orthodoxy.” (Eddington 1935, p.
But Whittaker's view on Milne must be put into the perspective he held on the
whole ongoing debate. As he saw it
    …a lively debate is in progress at the present moment between Sir Arthur
    Eddington and Dr Harold Jeffreys of Cambridge, Professor Milne of
    Oxford, Sir James Jeans, and Professor Dingle of the Imperial College,
    the subject being the respective shares of reason and observation in the
    discovery of the laws of nature. (Whittaker 1941, p. 160)

   Physics and Philosophy                                           Musa Akrami

But lively debate is far too gentlemanly a description for what now occurred.
After holding his ire somewhat in check for—as he saw it—already far too long,
Dingle finally erupted.

1. 6. Dingle's Denoument
Controversy over Milne and his philosophy reached a crescendo in mid-1937.
Dingle, his stew having finally boiled over, wrote privately to the editor of
Nature, first castigating the rampant cosmological ‘mysticism’ passing itself off
for science, and then offering to produce an article taking the sword to the
mystics themselves. His offer was immediately accepted. The result was
Dingle's notorious “Modern Aristotelianism”, a polemical diatribe chiefly
against Milne, but aimed as well at Eddington and Dirac on account of their
“betrayal” of the scientific method of Newton and his fellow members of the
Royal Society. (Dingle 1937)

8. 6. 1. Modern Aristotles?
The article is remarkable both for its style and for its content. Dingle's style in
the article is vituperative. Thus, emotionally-loaded terms such as “paralysis of
reason,” “intoxication of the fancy,” “‘Universe’ mania”, and the like frequently
appear, these to be topped only by references to “delusions,” “traitors,” and, of
course, “treachery,” each associated with one or more of the guilty parties.
(Dingle 1937, p. 786)
Above and beyond his extreme language, Dingle makes certain substantive
claims bearing directly upon central philosophical questions. The issue, as he
sees it, is nothing more than the question “Whether the foundation of science
shall be observation or invention” (Dingle 1937, p. 786). As always, talk about
‘foundations’ is philosophical talk. The two opposing positions Dingle here calls
“foundational” involve views on both method and epistemology, suitably
tangled together. Dingle delineates the opposed alternatives as follows. The way
of true science, he claims, shows that “the first step in the study of Nature should
be sense observation, no general principles being admitted which are not derived
by induction therefrom.” (Dingle 1937, p. 784) Stated more explicitly, Dingle
here argues that authentic science is empiricist in epistemology (scientific
knowledge is founded in sensory observation), and inductivist in method
(general principles are reached via inductive logic). Opposed to this view, he
argues, is “the doctrine that Nature is the visible working-out of general
principles known to the human mind apart from sense perception.” (Dingle
1937, p.787) As representative of this latter view Dingle cites Milne, and refers
in particular to Milne's claim that “it is, in fact, possible to derive the laws of

   Physics and Philosophy                                          Musa Akrami

dynamics rationally…without recourse to experience.” (Milne 1937, p. 329)
Obviously, Dingle is here arguing against the view, Milne's view, that authentic
science may be rationalist in epistemology (scientific knowledge is founded in
pure theoretical reasoning apart from sense perception), and hypothetico-
deductive in method (general principles are justified by their deductively
implying correct observations).
Along with Milne, Dingle indicts Eddington, and, by implication, Dirac, all three
of whom, Dingle believes, are guilty of inventing scientific hypotheses by free
mental imaginings rather than by strict immersion in observations and
observational data.

8.6. 2. Dingle as ‘True Believer’
What is going on here? Put bluntly, Dingle is an old-fashioned empiricist and
inductivist. He believes that the only way to do true science is to first collect
data, then, and only then, to hypothesize on the basis of that data. Observation,
then hypothesis. As he sees it, Eddington, Milne and Dirac have got it exactly
backwards. They first (as he terms it) assume an hypothesis, then, and only then,
go about collecting data. Except, according to his lights, the data isn't ever
collected: “to [the Aristotelians'] modern representatives it seems as though a
fancy is no sooner in the head than it is on paper and sent for publication.”
(Dingle 1937, p. 785) Obviously Dingle is simply wrong; it never occurred to
his opponents that hypotheses would not be followed immediately by attempts
at deductive prediction of observational consequences. But it was enough, in
Dingle's mind, that they didn't use induction, for them to come under blame.

8. 6. 3. Wrong from the Very Start
But there is something else at work here as well. Dingle doesn't object solely to
his opponents' lack of inductive logic. Of equal importance is the fact that they
find the source of their hypotheses in fairly general principles, wide-ranging
rational proposals about the structure of the universe at large. These principles
Dingle takes to be a priori, in the most pejorative sense of that term. They are
phantasms, “chimeras” he calls them, which seduce the imaginations of his
opponents, and lead them and their dumb-struck admirers away from the
genuine, authentic method of science. This is what really sticks in Dingle's craw.
In turn, Eddington, Milne and Dirac are chastised, each for something slightly
different, but at bottom the same, namely, they one and all “appear as a victim of
the great ‘Universe’ mania.” (Dingle 1937, p. 786) In the end, Dingle believes,
the danger of this new ‘methodology’ is real, and serious. As he notes in
   Nor are we dealing with a mere skin disease which time itself will heal.
   Such ailments are familiar enough; every age has its delusions and every

   Physics and Philosophy                                           Musa Akrami

   cause its traitors. But the danger here is radical. Our leaders themselves
   are bemused, so that treachery can pass unnoticed and even think itself
   fidelity. It is the noblest minds that are o'erthrown…the very council of
   the elect can violate its charter and think it is doing science service.
   (Dingle 1937, p. 786)
Here Dingle obviously goes over the top. Yet overblown as it is, there is no
doubting his sincerity: Milne and the other cosmologists have betrayed the true
science bequeathed them by their ancestors in the Royal Society.
How could Dingle be answered?

8. 6. 4. The Debate Goes Very Public
The response arrived three months later, on 12 June. On this particular Saturday
in June, Nature published a fifteen-page special supplement as No. 3528.
Contained within were contributions from sixteen “representative investigators”,
as the editor referred to them, each responding to “Modern Aristotelianism”
Nature's Editor, R.A. Gregory, introduces the occasion by noting that “in Nature
of May 8, we published an article by Dr. Herbert Dingle entitled ‘Modern
Aristotelianism’”. Because the article, as Gregory goes on to say, “created
considerable interest”, Nature “decided to invite further contributions on the
subject from a number of representative investigators.”
“Created considerable interest” is, to understate the issue, an understatement.
Some of the contributors were quite obviously livid with rage and other volatile
emotions. Others, such as Milne himself, who had come in for particularly
scathing criticism in Dingle's article, were patient and careful in rebuttal. Each
of the sixteen contributors to the special article chose a side in the controversy,
either pro Dingle's inductive empiricism, and con Milne et al.'s rationalist
hypothetico-deductivism, or vice versa. Remarks made by the participants
exhibit the full diversity of philosophy of science in their contemporary
community. Dingle's views, in particular, were not without favor.
Harold Jeffreys, F.R.S., noted geologist and astronomer, and author of a well-
regarded philosophy of science book Scientific Inference (1957), led off with a
nice ad hominem: “Without using induction, Milne and Eddington could not
order their lives for a day, and what they are really asserting is that they are
entitled to use special axioms in physics, for which no need has been shown.”
Jeffreys' criticism here of course ignores the role of deductive observations in
justifying the “special” axioms. The problem, as Jeffreys sees it, originates in the
perpetrators' “belief that there is some special virtue in mathematics.” L.N.G.
Filon, F.R.S., vice-chancellor of the University of London agrees on this point,
noting that “some men of science appear to think that they can solve the whole
problem of Nature by some all-inclusive mathematical intuition.” R.A.
Sampson, the Astronomer Royal, focusses upon the rationalistic aspects of the

   Physics and Philosophy                                           Musa Akrami

‘modern Aristotelians’, to wit, for their “framing a theory independent of
experience, such as is denounced in Dr. Dingle's article”, which produces work
not unlike that “of a poet or other humanist, who gives us at most a number of
illustrative cases.”

8. 6. 5. The Counterattack
But Milne, Eddington, and Dirac had their supporters as well. N.R. Campbell,
whose theory of science was already well-known, makes an uncontroversial
interpretation of the affair. “Science” he begins, “(or at least physics) has long
consisted of two distinct but complementary activities”, one of which is
experimental and empirical; “its procedure is induction.” The other activity
attempts to provide explanations of scientific laws, which explanations have the
“pecularity” that “they often (not always) predict new laws in addition to
explaining old ones.” Campbell cannot resist ending on an ad hominem of his
own: “If he [Dingle] does not deem it important to observe the distinction
between what is and what is not demonstrable experiment, surely he should
welcome a movement to amalgamate the Royal with the Aristotelian Society.”
G.J. Whitrow, then a young lecturer at Christ Church, Oxford, returns to the
mathematical theme. Dingle, he argues, “not only attacks the particular methods
adopted by contemporary mathematical investigators in relativistic cosmology,
but even refuses to admit that this subject is worthy of scientific investigation as
it is based not only on experience but also on reason.” Hypotheses, by this light,
may originate rationalistically as well as any other way, certainly there is no
problem with this.

8. 6. 6. The Coolest Voice
The clearest, most temperate discription of the issues at hand is given by young
cosmologist William McCrea, then professor of mathematics at Queen's, Belfast,
and editor of the R.A.S.'s Observatory. Not to be outdone by Jeffreys, McCrea
begins with an ad hominem of his own: “Dr. H. Dingle's objection to ‘modern
Aristotelianism’ seems to be itself what he would call Aristotelian rather than
Galilean.” In other words, Dingle raises a non-empirical objection about Milne
et al.'s non-empiricism! But McCrea soon gets to the heart of the matter, the role
of hypothetico-deductivism in mathematical physics:
    What Dr. Dingle has done is to reopen the question of the relation of
    mathematical physics to experimental physics, since he claims to detect a
    new and perverted point of view in the former. Now a system of
    mathematical physics, apart from the alleged perversion, is the working
    out of the mathematical consequences of certain hypotheses. The worth of
    the theory is judged…by the closeness of the agreement of its predictions

   Physics and Philosophy                                               Musa Akrami

   with the results of observation, and also the number of phenomena which
   it can so predict from the one set of hypotheses. The scientific attitude is,
   not to cavil at the attempt, but to see if it is successful.
This is an absolutely standard interpretation of how the H-D method works.
Throughout his own writings, beginning right from his inaugural lecture in
Oxford (Milne 1929), Milne had subscribed to precisely the same interpretation
of the Hypothetico-Deductive (H-D) method. Whatever the controversy is about,
the issue is not how to interpret hypothetico-deductivism. That much is evident.
Moreover, it is quite clear that Dingle et al. are not mounting opposition to
something we, today, would consider philosophically radical; rather, they are
objecting to what, today, would be considered completely unobjectionable.
Given today's acceptance of the H-D method, yet its rejection by otherwise well-
regarded scientists at that time, it seems to follow that it was, at least in part, this
debate and its followup which settled the issue. In any case, Dingle and his
supporters generally went silent, restricting their activities for the most part to
books, or relatively positive statements of their own positions. (A.D.R. 1938,
Dingle 1938) Things settled down, just in time for the War.

8. 7. The Calm Between the Storms
During the next several years, it became evident that Milne's methods, and
kinematic relativity as well, had reached respectability. One important sign of
this progress was exhibited at an early 1939 joint meeting between the Royal
Astronomical Society and the Physical Society of London, The meeting had as
its goal a thorough review of the situation in cosmology. McVittie was chosen to
present the observational situation; his report was soon published. (McVittie,
1939) Reviewing the theoretical situation was George Temple, one of the most
highly respected mathematicians of the time. Temple's report saw print almost
immediately. (Temple 1939) Within a short time, Temple's paper took on the
role of successor to Robertson's definitive 1933 “Relativistic Cosmology.”
(Robertson 1933b)

8. 7. 1. Two Equal Competitors
Both McVittie and Temple presented kinematic relativity and relativistic
cosmology as equal competitors in accounting for the cosmological
observations. Unfortunately, as McVittie noted, observations could not, at that
time, discriminate between the two theories. Temple's analysis of Milne's work
praises its simplicity and elegance, and refers in particular to its operationalism
and axiomatization, which “start from a completely novel discussion of the

   Physics and Philosophy                                                   Musa Akrami

correlation of measurements made by different observers in terms of light
signals only.” (Temple 1939, p. 468) Throughout the rest of his discussion of the
two theories, Temple utilizes Milne's light-signal correlation method, explicitly
rejecting rigid-rod transport for distance measurement. Milne's methods have
Later that year McCrea publishes an important paper in Philosophy of Science.
(McCrea 1939) Put most simply, the paper starts out to defend Milne's methods,
but ends up by presenting a full-blown and interesting, although quite
unhistorical, account of the evolution and structure of physical theories.

8. 7. 2. The Origin and Evolution of Theories
McCrea's overall view is that theories are set up to be hypothetico-deductive in
structure. His account is based on his view of the evolution of theories of space-
time and mechanics, beginning with Newton, through the General Theory of
Relativity and ending in kinematic relativity. His argument reduces to the claim
that, insofar as Milne and e.g., Newton, can be shown to follow the same
procedure, any attack upon Milne is also an attack upon Newton. First, he states
his goals in the paper.
The first goal is to emphasise how each theory leaves us in a position in which
the succeeding one appears as a perfectly natural next step in the development of
ideas. (McCrea 1939, p. 137) McCrea embeds this argument in an account of
how analogue models (à la Campbell) are used to set up new theories—this is
essentially an account of how discovery might proceed in linking an older theory
with its successor.The second goal is to show how, in spite of superficial
differences in character, the theories in question all necessarily possess the same
general structure constituted by the presence of hypotheses, from which certain
general mathematical relations are deduced, which in their turn are used to predict relations
between observable quantities. As McCrea notes, “this study may claim an
interest of its own, but it is presented also for a further reason” namely, that
    it has been contended [by Dingle, most especially] that theories like
    Milne's represent a fundamentally new outlook on the part of some
    theorists, in that such theories are purely mental constructs divorced from
    experince of the physical world. We shall see that on the contrary Milne's
    theory is easily brought into line with the others in such a way that this
    criticism is neither more nor less true of it than of the rest. (McCrea 1939,
    p. 138)
In McCrea's discussion of the theories he asserts that “the consituents [of the
theories themselves] which are of physical significance are sets of mathematical
relations, coupled with sets of rules of interpretation” which yield, “after
observational test, descriptions rather than explanations of physical phenomena.”

   Physics and Philosophy                                            Musa Akrami

According to McCrea, one real advantage of his view is that it “leads to simple
criteria for comparing the merits of different theories.” Finally, on the
metaphysics of the original hypotheses, McCrea claims that “the initial
hypotheses from which the mathematical relations are deduced do not ultimately
have any direct physical significance.”
McCrea's paper, published in the leading philosophy of science journal of the
time, is the final imprimateur on Milne's views.

8. 7. 3. Milne's Ultimate Success
Three years later, Milne was awarded the James Scott prize, the most prestigious
award for ‘natural philosophy’ in the Anglophone world. Milne's lecture title is
telling: “Fundamental Concepts of Natural Philosophy.” (Milne 1943) Although
Milne does concede to Dingle that he no longer believes that it is possible to
deduce physics completely in the absence of reference to phenomena, for the
most part his award lecture is a long reiteration of his previous twelve years'
work in cosmology.
One year later, Milne received his ultimate accolade, election as president of the
Royal Astronomical Society. In his inaugural lecture, Milne again reviews his
work, but adds two remarks of interest. First, he modifies his earlier view that
theories are acceptable solely on the basis of their successful predictive power;
to this, he now adds that a theory cannot be accepted as satisfactory unless it is
philosophically satisfying. (Milne 1943, p. 120) Secondly, on a personal note, he
admits that he is still amazed at the outcry that his theory and its philosophy
caused. Milne here is being a bit disingenuous. In many places in his letters he
not only recognizes the outcry, he delights in it, and seeks to provoke it even
more. (Milne 1932-37, 12 May 35; 28 Jul 36)
From this point onward, cosmology's philosophy is no longer directly influenced
by Milne himself. Moreover, kinematic relativity began to stagnate as a research
programme; except for Whitrow, Milne had no new students, and failed to
attract any new converts to the theory. His work was done. But his philosophical
influence didn't end, in fact it wasn't to crest until the end of the 40s in the work
of another man, Hermann Bondi. Again, however, a storm was generated by
Milne's methods, even though they were now in the hands of another.

8. 8. Steady-state Cosmology
In 1948, a young mathematician, Herman Bondi, in concert with two close
friends Thomas Gold and Fred Hoyle, proposed a radical new cosmological
theory, the Steady State theory. This theory differs from the basic picture shared
by both kinematic relativity and relativistic cosmology, namely, that of a

   Physics and Philosophy                                              Musa Akrami

universe with a definite origin in a small, dense knot, followed by evolution into
the universe we have today. According to Bondi's theory, the universe as far
back into the past as we might look would always look the same; there was no
evolution, there could be no “fossils”, as Bondi called putative evidence of a
universe different in the past from our present one. What we observe today is the
same state of a universe that has been and always will be steady. Bondi came to
his notion of the steady state primarily from his commitment to the philosophical
components of Milne's work, most especially the methodology of rationalism
plus hypothetico-deductivism; additionally, Bondi coupled to these Milnean
notions some ideas taken directly from the philosophy of Karl Popper.

8. 8. 1. Bondi's Philosophical Origins
Bondi reveals his philosophical commitments in several ways. First, he argues
against induction and extrapolation from small-scale experiment, that is, against
the inductive empiricism of Dingle et al. Secondly, he argues in favor of
hypothesis and deduction, that is, in favor of Milne et al. Finally, he specifically
remarks the excellence of Milne's Methods, and the theory—kinematic
relativity—created therefrom, and remarks the significance of these elements in
the creation of his version of the new steady-state cosmology.
From the very beginning Bondi admits the validity of both positions in the
methodological debate:
    In particular, there are two important approaches to the subject
    [cosmology] so different from each other that it is hardly surprising that
    they lead to different answers...The contrast between the ‘extrapolating’
    and the ‘deductive’ attitudes to cosmology is very great indeed. (Bondi
    1960), p. 3-5)
The extrapolating approach, which Bondi sometimes calls the empirical school,
is represented by Dingle, McVittie, and their colleagues. Opposed to the
extrapolative approach is the deductive approach, which “is reached from
investigations in the borderland between physics and philosophy.” Milne is
obviously the major proponent of this view. Although Bondi finds good points
in both approaches, he also finds problems in both approaches. In the end,
cosmology is the worse for excesses from either end of the spectrum:
   Just as some adherents of the ‘empirical’ school tend to regard cosmology
   as a testing ground for their extrapolations and as a legitimate playground
   for the geometers, so some adherents of the deductive approach appear to
   regard cosmology as a purely logical subject. (Bondi 1960, p. 7)
In this latter case, the deductive extremists, in their mathematical zeal, seem to
forget that cosmology, after all, should have some relation to observation: “To
them all that is of interest in a theory is its logical character, not its relevance to

   Physics and Philosophy                                           Musa Akrami

the interpretation of observational data.” Obviously, this danger must be
avoided: according to Bondi, deductivism can be a scientific approach in
cosmology only if its postulates (or axioms) are candidates for disproof.

8. 8. 2. Enter Popper
Clearly, with this reference to the connection between science and disproof,
Bondi has added a distinctly Poppererian element to the deductivist
methodology, one which had not previously appeared in the works of any of the
earlier members of the hypothetico-deductive school. According to Popper's
philosophy of science, a theory can legitimately be called “scientific” only if that
theory makes a prediction that, in principle, can be shown to be false, or
falsified, to use Popper's own term. Thus astrology, for example, fails to be a
scientific theory because it cannot be falsified: although astrology seems to
make predictions, these statements about the future are so vague, so general and
abstract, that they cannot be tied down to definite claims about observations to
be made at a definite time and place. Hence there is no explicit observation to be
made in falsification. Astronomy, in comparison, makes explicit, specific
predictions about what will occur in the sky on such-and-such a date, in such-
and-such a place. If the prediction fails, then we know that the element of
astronomical theory which made the prediction is deficient, maybe even false.
Cosmology is a borderline case: since observations of cosmological significance
are so rare and hard-won—Hubble's observation of the red shift was one of the
first solid ones—it is very difficult, not to mention brave, to tie one's
cosmological theory to Popper's falsificationist principle as a guarantee of
scientific acceptability. But this is exactly what Bondi did.
Much later Bondi was to make explicit his debt to Popper:
    I think the person from whom we had most help on the philosophical side
    was Popper. His analysis of science encouraged one to be imaginative,
    and encouraged one to go for something that was very rigid and therefore
    empirically disprovable. (Bondi 1990, p. 194)

8. 8. 3. But It's Milne In the End
Yet Bondi's major philosophical debt was to Milne. According to Bondi, Milne's
theory was through and through deductive, which was reason enough for some
of his colleagues to condemn it:
   The aim of this discipline [= kinematic relativity] is to deduce as much as
   possible merely from the cosmological principle and the basic properties
   of space, time and the propagation of light. The beauty of this, as indeed
   of any deductive theory, rests on the rigour of the arguments and the small
   number of the axioms required...When the theory was first developed it

   Physics and Philosophy                                           Musa Akrami

   met with great hostility and was criticized very severely, often unjustly,
   and sometimes frivolously. (Bondi 1960), p. 123)
In addition to his admiration of Milne's H-D methodology, Bondi has high praise
as well for Milne's operationalism, particularly its use in defining distance:
   Imperfect as Milne's definition of distance may be, it is very much better
   than the ‘rigid ruler’ one used in most other theories…Milne's definition
   of distance, by no means perfect as it is, is probably the best yet devised.
   (Bondi 1960, p. 126-9)
In the end, Bondi sums up Milne's contributions with no uncertain praise:
    The foregoing brief description will have indicated the remarkable success
    of kinematic relativity in attempting to use the cosmological principle not
    only for the construction of the substratum but as chief guide in
    formulating ordinary physics. In this respect it differs greatly from all
    other cosmologies which either rely on a conventionally obtained body of
    physics or have not yet succeeded in drawing conclusions of local interest
    from the cosmological principle. (Bondi 1960, p. 136)

8. 8. 4. Return of the Cosmological Principle
Here Bondi speaks of Milne's cosmological principle. According to Milne's
principle, every observer in the universe should get the same world picture, that
is, should make precisely the same observations of the universe at the same
moment as any other observer. (Milne 1934b) Uniformity over spatial slices is
guaranted by Milne's invoking of the principle. Yet Milne's universe evolves, it
changes its form over time. Hence it has no temporal uniformity. Bondi felt that
this raised the possibility that physics itself might change over time. Because of
this risk, Bondi generalized Milne's cosmological principle into what he called
the perfect cosmological principle [=PCP]. According to this principle, all
observers at all places and at all times will look out upon the same unchanging,
unevolving, universe. Such a universe is a universe in a steady-state—hence the
Clearly, PCP is a daring, indeed heroic, interpretation of a methodological
necessity. Forty years after the fact, Bondi described the “philosophical attitude”
which underlay his “implausible” PCP:
   But the essential point of the philosophy was and is that if the universe
   was evolving and changing, then there is no reason to trust what we call
   the laws of physics, established by experiments performed here and now,
   to have permanent validity. (Bondi 1990, p. 192)
Hence, or so Bondi's argument goes, since there is reason not to trust the laws of
physics if the universe is evolving, let us presume that the universe is not

      Physics and Philosophy                                           Musa Akrami

   evolving and changing; that is, let us presume PCP. Although the principle (and
   the theory which results from it—steady state cosmology) is, as McVittie
   remarked, “much more restrictive than general relativity”; (McVittie 1990, p.
   45) it is this very restrictiveness which satisfies Bondi's Popperian wishes:
      For the correct argument has always been that the steady state model was
      the one that could be disproved most easily by observation, Therefore, it
      should take precedence over other less disprovable ones until it has been
      disproved. (Bondi and Kilmister 1959, p. 55-6)
   In another place, Bondi makes a similar point: “Comparison with observation
   becomes then possible and renders the PCP liable to observational disproof. This
   possibility of a clear-cut disproof establishes the scientific status of PCP.”
   (Bondi 1957, p. 198) Comments such as this make clear Bondi's committment to
   a Popperian addition to the basic deductive methodology he inherited from

   8. 8.5. A Popperian Conclusion
   In the end, the philosophical purity of Bondi's steady state theory served him,
   and cosmology, well. Of course, the usual suspect, Dingle, and others of his ilk,
   such as McVittie in particular, were outraged, and loudly, at Bondi's extension
   of Milne's methods. A passage from Dingle's R.A.S. Presidential Address
   suffices to show the tenor of the debate's declining days:
      Even idle speculation may not be quite valueless if it is recognized for
      what it is. If the new cosmologists would observe this proviso, calling a
      spade a spade and not a perfect agricultural principle, one's only cause for
      regret would be that such great talents were spent for so little profit.
      (Dingle 1953, p. 404)
   But PCP and the theory which it engendered were exactly as described:
   eminently falsifiable. No matter the extent of Dingle et al's disdain, Steady State
   theory stayed right out in front, ready for whatever empirical observations might
   be slung at it. As Bondi said “Show me some fossils from an evolving universe,
   and I'll give it up.” In 1965, the fossils arrived, courtesy of the observations of
   the 3° K remnant microwave radiation.
   And Bondi, true to his philosophy, gave it up.

 Bondi, H., 1957, “Some Philosophical Problems in Cosmology”, In
  British Philosophy in the Mid-Century. Edited by C. A. Mace. London:
  George Allen and Unwin.

      Physics and Philosophy                                       Musa Akrami

 Bondi, H., 1960, Cosmology, 2 ed. Cambridge: Cambridge University
 Bondi, H., 1990, “The Cosmological Scene 1945-1952”, In Modern
  Cosmology in Retrospect. Edited by B. Bertotti, et al. Cambridge:
  Cambridge University Press.
 Crowther, J. G. 1970, Fifty Years with Science, London: Barrie & Jenkins.
 Dingle, H. 1931, The Evolution of the Universe, London: Nature.
 Dingle, H., 1937, “Modern Aristotelianism,” Nature (London) 139: 784-
 Dingle, H., 1938, “Science and the Unobservable,” Nature (London) 141:
 Eddington, A. S., 1932, The Expanding Universe, Ann Arbor: Ann Arbor
  Paperbacks-U.Mich Press.
 Eddington, A. S. 1939, The Philosophy of Physical Science, New York:
  Macmillan ..
 McVittie, G. C., 1933a, “The Mass-particle in an Expanding Universe,”
  Mon.Not.R.astron.Soc. 93: 325-339.
 McVittie, G. C., 1933b, “Milne's Theory of the Expansion of the
  Universe,” Nature (London) 131: 533-534.
 McVittie, G. C., 1934, “The Spiral Nebulae and the Expansion of the
  Universe,” Phys.Soc.Reports (Lond.) 1: 24-29.
 McVittie, G.C., 1939, “Observation and Theory in Cosmology,”
  Proc.Phys.Soc.Lond 51: 529-537.
 McVittie, G. C. 1990, Interview, 21 Mar 78, In Interviews with
  Astrophysicists, Edited by American Institute of Physics, New York:
  American Institute of Physics.
 Milne, E. A., 1929, The Aims of Mathematical Physics, Oxford: Oxford
  University Press.
 Milne, E. A., 1933, “World-structure and the Expansion of the Universe,”
  Z.Astrophysik 6: 1-35.
 Milne, E. A., 1934a, “Some Points in the Philosophy of Physics: Time,
  Evolution and Creation,” Philos. 9: 19-38.
 Milne, E. A., 1934b, “World-models and the World-picture,”
  Observatory, 57: 24-27.
 Milne, E. A. 1935, Relativity Gravitation and World-Structure. Oxford:
  Clarendon Press.
 Milne, E. A., 1943, “The Fundamental Concepts of Natural Philosophy,”
  ProcRoySoc(Edin) 63: 10-24.
 Robertson, H. P., 1933a, “On E.A. Milne's Theory of World Structure,”
  Z.Astrophysik 7: 152-162.

      Physics and Philosophy                                      Musa Akrami

 Robertson, H. P., 1933b, “Relativistic Cosmology,” Rev.Mod.Phys. 5: 62-
 Robertson, H. P., 1935, “Kinematics and World-structure,” Ap.J. 82: 284-
 Robertson, H. P., 1936, “Review of Milne's Relativity Gravitation and
  World-Structure,” Ap.J. 83: 61-66.
 Temple, G., 1939, “Relativistic Cosmology,” PhysSoc.(London), 51: 465-
 Walker, A. G., 1934, “The Principle of Least Action in Milne's
  Kinematical Relativity,” Proc.Roy.Soc.(Lond.) 147A: 478-490.
 Walker, A. G., 1935, “On the formal comparison of Milne's kinematical
  system with the systems of general relativity,” Mon.Not.R.Astr.Soc. 95:
 Whittaker, E. T., 1935, “Review of Relativity Gravitation and World-
  Structure,” Observ. 58: 179-188.

   Physics and Philosophy                                           Musa Akrami

Chapter 9. The Origin of the
Universe and Contemporary
Cosmology and Philosophy
9. 1. Introduction
9. 2. Two Approaches in Cosmology
9. 3. Dichotomy of Laws and Initial Conditions
9. 4. In the Search of a New Type of Laws
9. 5. World Without Borders
9. 6. Creative Conceptions of the Universe
9.7. Creation from "Nothing
9. 8. Creation out of a "vacuum "
9. 9. Conceptions of the Universe which is Infinite in Time

Introductory remark
ABSTRACT: Since    the 1970s both in physics and cosmology, there has been a
controversy on the subject of the ‘beginning of the universe.’ This indicates that
this intriguing problem has reached scientific consideration and, perhaps, a
solution. The aim of this paper is to try to answer the question as to whether the
origin of the world has slipped out of the hands of philosophers (and
theologians), and passed in its entirety into the realm of science, and whether
science is able to solve this problem by itself. While presenting the main views in
this dispute, I try to show also that metaphysics, philosophy of nature and
epistemology provide important premises, proposals and methods that are
indispensable for a solution. These premises concern such issues as the
extremely subtle problem of the sense and existence of ‘nothing,’ the problem of
extrapolation of local physics onto the large-scale areas of the universe, the
epistemological status of cosmological principles, as well as problems of the
origins of the laws of nature. This last issue is entangled in the difficult problem
of the ‘rationality of the world’ and the problem of overcoming the dichotomy of
laws and preconditions, according to which the conditions and laws are
independent of each other.

By Tan Such, University of Poznan (Poland)

   Physics and Philosophy                                           Musa Akrami

9. 1. Introduction
One of the determinants of scientific rationality is the condition that science
undertakes only those problems whose solution is within the range of
possibilities of research methods which science currently applies or is able to
apply. Simply speaking, scientists are attracted by solvable problems. If this is
really so then the fact of widespread discussions since the 70s among physicists
and cosmologists on the subject of "the beginnings of the Universe" seem to be
an obvious sign that also this unusually intriguing problem has matured to its
scientific solution .
The purpose of my paper is to attempt to answer the question whether the
problem of the origin of the world currently evades philosophers (and
theologians) and passes completely to the realm of science (i.e. physics,
astronomy and cosmology), or whether science by itself is not able to solve this
problem. In the latter case one would have to acknowledge that metaphysics, the
philosophy of nature and epistemology, provides important premisses,
assumptions and methods indispensable for this solution .

9. 2. Two Approaches in Cosmology
The task cosmology has to perform is to explain the structure of the Universe as
it is observed. Contemporary cosmologists carry out this task by means of two,
to some extent contradictory, approaches. One wants to explain the structure of
the Universe observed through what the Universe was at the very beginning; the
other, on the other hand, tries to show its present structure as an inevitable
consequence of past physical and chemical processes, irrespective of what was
at the beginning. A permissible possibility here is that the Universe is so
constructed that no observable traces of its quantum origin remain. The Theory
of the Big Bang in its classical, purely relativistic interpretation, is an example
of the former approach. However, its inflational development which refers to the
physics of high energies and to quantum mechanics is the fullest expression of
the latter approach. Irrespective of how the Universe began (and whether it
began at all) that which we observe at present on a cosmological scale is the
result of an extremely short period of inflation in which, due to the unparallelled
intensity of extension at an exponential rate, it was transformed from a
microobject (with respect to its spatial dimensions) into a macroobject .
Obviously to solve the problem of the origin of the world, of fundamental
importance is the former approach which assumes that further evolution of the
Universe did not preclude the significance of its initial states for what we
observe now on a large scale .

   Physics and Philosophy                                           Musa Akrami

It does not mean that the prevalence of inflational models in modern relativist
and quantum cosmology renders cosmology incapable of dealing with questions
of the origin of the Universe. It is only in recent years that scientists have
concentrated on the former approach. There has been a search for fundamental
laws which would determine the initial conditions of the Universe .

9. 3. Dichotomy of Laws and Initial Conditions
In classical physics (and in general, in the modern approach to explanations of
phenomena) a principle of dichotomy of laws and of initial conditions.
According to this principle initial conditions (understood as conditions in which
laws may be applied) are totally independent of the laws of nature, in the sense
that from the point of view of laws their distribution is completely random .
Quantum mechanics seems to be the first theory which began to threaten this
dichotomy. According to Heisenberg's principle of indeterminacy initial
conditions of a mechanical system (i.e. position and velocity) are canonically
joined and as such cannot at the same time be determined with optional
precision. This imposes certain restrictions on the distribution of these
conditions and leads as is well known, to the undermining of the so-called
Laplace determinism which respected the principle of dichotomy .

In modern cosmological considerations concerning the earliest stages of the
Universe the problem of dichotomy of laws and conditions is given first-rate
significance. As it is the problem of the beginnings of the Universe may not be
solved in any way without shaking this dichotomy .

9. 4. In the Search of a New Type of Laws
In reference to the initial state of the Universe one should consider critically the
view that initial conditions are independent of the laws of nature. One might
assume that the Universe is exceptional in the sense that it is the only
nomologically coherent possibility. This means that the initial conditions are
also exceptional and through this become a law of Nature themselves ("a
superlaw"). Another possibility is that the universe is genetically unlimited, i.e.
is a Universe "without boundaries ."
This kind of approach leads to the search for a new type of laws. These would
not be the laws which determine a permissible change of the state of the world
between one moment and another, but laws which rule very initial conditions .
The traditional view, based on the dichotomy of laws and conditions as applied
to the Universe was often associated with the view that theologians deal with

   Physics and Philosophy                                             Musa Akrami

initial conditions and physicists deal with the laws of evolution. However,
contemporary cosmologists try to establish whether there are any laws of initial
conditions which would overcome randomness of their distribution. Studies
divide into two directions .

9. 5. World Without Borders
The first one, which is more radical, is the Hartle-Hawking conception of the
world without borders. A suspicion that time and space are not universal
characteristics of the physical reality, sometimes formulated in microphysics,
have been strengthened in this conception but only as far as time is concerned,
and transformed into an assumption that in Planck's era given extreme densities
under which quantum effect dominate time loses its properties which
differentiate it from space. First of all it stops being anisotropic, stops running in
a given direction. It means that the initial quantum state is actually a timeless
state and that there had been nothing "before" the beginning of the Universe
since "then" there was no time. As a result, in Planck's era the Universe behaves
as a four-dimensional hypersphere (surface of a ball). In this manner "the
condition of not occurring of a border" makes it possible to avoid the singularity
of the initial state. On the other hand, the ordinary character of time as
qualitatively different from space begins to crystallize in the first moments
following Planck's era. Therefore, we can see how the question on the beginning
of the Universe leads to the question of the nature of time itself .
Conception of time which becomes space — to be more exact still another
(fourth) dimension of space — is one of the most innovative ideas of modern
cosmology. The condition of non-occurring of the border shifts the whole
"responsibility" for the origin of the Universe onto the laws ruling the Universe
(and possibly onto their source, e.g. in the form of a Lawgiver). In this way the
question of dychotomy of laws and conditions is settled through total subjection
of initial conditions to initial laws, even at the cost of liquidating initial
conditions as such.
The solution for this dychotomy assumes another form in the other direction of
studies .

9. 6. Creative Conceptions of the Universe
This is a direction which contains various conceptions of the creation of the
Universe (1) out of "nothing" or (2) out of a "vacuum". However, at least one of
these conceptions solves the problem of dichotomy in a similar manner to the
conception of the lack of borders. This is a view that our Universe is exceptional

   Physics and Philosophy                                            Musa Akrami

in the sense that it is the only (logically or nomologically) cohesive possibility.
This leads to the conclusion that also the initial conditions could not have been
different from what they were. In this interpretation the role of conditions is as if
reduced to the role of laws, so that the conditions themselves become law (or
laws) of nature. (Let us notice that in this respect at the extreme end of
cosmological views there is a conception of a multitude of universes, according
to which there is an infinite number of worlds in which all possible conditions
are realized. This conception does not, therefore, undermine the classical
dychotomy of laws and conditions).
However, a vast majority of conceptions of creation assume that our Universe, in
which conditions arose for the existence of "a conscious observer", due to its
insignificant a priori probability is — from the point of view of laws which we
know — only one of many possible universes. Therefore, even if the initial
conditions are not totally independent of laws still the latter do not determine
them unequivocally. In the conceptions discussed the problem of the description
of initial conditions is reduced to giving characteristics of from what the
Universe arose .
From the point of view of philosophy what is significant is the division of
creative conceptions into those which assume that the Universe arose from
"nothingness" in the strong ontological meaning of the word and those which
lead to the conclusion that it was originated from a certain "poorer" physical
reality, usually called "a vacuum" or space-time. Both kinds of conceptions
usually refer to quantum mechanics or the future quantum theory of gravitation
which is to combine quantum mechanics with the general theory of relativity .

9.7. Creation from "Nothing "
Supranatural conceptions of creation out of "nothing" which refer to God are
well-known to us in European philosophy and Christian theology. In cosmology
the first conception of creation out of nothing appeared and was promulgated
already on the grounds of the relativist theory of the Big Bang, especially after
1970 when Penrose and Hawking proved their famous theorem on singularities.
It could be seen from these theorems that if there is a sufficient amount of matter
in the Universe and gravitation always and everywhere attracts, then the
extension of all light rays back in time, to infinity is impossible. This meant that
(at least some) time lines break at the moment of the Big Bang, or in the primary
cosmological singularity .
It could be interpreted as the rise of matter, time and space out of "nothing",
therefore, as "a beginning of the world and at the same time the beginning of
time". In this interpretation the world does not arise in time, but together with
time (which recalls St. Augustine's conception). However, since the general

   Physics and Philosophy                                          Musa Akrami

theory of relativity could not give any "mechanism" of transition from "the state
of nothingness" to "the state of existence" of the Universe, further conceptions
of creation out of "nothing" began to adduce quantum mechanics. This theory
describes at least two processes which may compete for the name of "creative
processes" which rouse the interest of cosmologists. These are phenomena of
"quantum tunnelling" and of "quantum fluctuation" which occur due to quantum
effects; consequently are impossible from the point of view of classical physics .
In the conceptions of creation out of "nothing" the former phenomenon is mostly
used. "Tunnelling" in its common quantum interpretation is overcoming certain
energetic potentials by microobjects whose energy resources are lower than the
necessary minimal energy if the process is to be interpreted in the light of the
unexceptional laws of classical physics .
In quantum cosmology the "tunnelling out of nothing" is discussed. When an
analogy with the effect of quantum tunnelling is made a mathematical
description of the process in which the Universe together with time and space
emerges out of nothingness, described in the language of mathematics by an
empty set. One cannot speak here about tunnelling in the strict sense of the
word, since such a claim would assume the existence of two different physical
states. In the meantime, the process postulating the creation out of nothingness
reveals that one cannot determine any earlier states of the emerging Universe
since no prior external time exists, previous in relation to the time which appears
together with the world .
If we apply Schrödinger's equation defining the wave function in ordinary
quantum mechanics for the whole Universe so that it also takes gravitation into
account (the space-time curvature) then the Wheeler-De Witt equation is
obtained which is called "the wave function of the Universe" U. In this way the
function T [x1, t1 ---> x2, t2] gives the probability of finding the Universe in
state x2 at the t2 moment, if at the previous moment t1 it was in the x1 state.
One of the possibilities consists in this that, according to functions U and T the
Universe tunnels to the state of existence out of nothing with a definite
probability. In other words, there is a certain probability of transition which has
such a form in which there are no previous initial states. According to this
scenario there is a certain probability of a spontaneous appearance of the
Universe of a definite type together with a definite time and space, created out of
nothing .
However, there is a fundamental question: Can nothingness (total nothingness in
the strong ontological sense) exist at all from the point of view of the laws of
physics? This doubt does not relate to the conception of creation out of a

   Physics and Philosophy                                           Musa Akrami

9. 8. Creation out of a "vacuum "
A well-known fundamental metaphysical question is: "Why is there rather
something than nothing?" which led great philosophers of various times
(Aristotle, Leibniz, Heidegger) to grapple with the basic philosophical problems.
It assumes the sensibleness of the concept of "nothingness ."
The question of the sensibleness of this concept is conspicuous in quantum
mechanics and in the quantum theory of the field, extended around quantum
electrodynamics. Sometimes a conclusion is drawn from Heisenberg's principle
of uncertainty that a "vacuum" (in the sense of something devoid of any
substrate or any physical properties) is impossible since its existence would
allow exact establishing of the value of the canonically joined values, e.g.,
position and velocity .
The quantum field theory (and attempts at creating of the quantum theory of
gravitation made on these grounds) interpret vacuum not as a nothingness, but as
an extremely active arena which through "fluctuation of a vacuum" constantly
creates virtual particles of all possible kinds. Vacuum in this interpretation has
not much in common with the philosophical concept of "nothingness", but
constitutes a kind of active time and space endowed with various physical
properties (which are usually divided into topological, metrical and properties of
symmetry). On the other hand, the dynamic character of the vacuum (time and
space) signifies that it is also apportioned with energy .
Conceptions of the creation of the Universe out of "vaccum" assume that it
arises in the process of "fluctuation of vacuum", and therefore it is created not
out of nothing, but out of a certain physical reality, poor in properties and called
a "vacuum ."
Some of the conceptions of this type, e.g. J. Wheeler's conception, impoverish
even more this initial reality of which the Universe was to emerge. They assume,
for instance, that time as such is a complex structure which consists of simpler
elements. Assuming that these elements "went into the composition" of time at
the moment of the rise of the Universe we obtain a conception according to
which time is created together with the Universe, but it is created not out of
nothing, but is preceded by certain elements of physical reality (this brings to
mind the conception of "the world without borders" where time in Planck's era
also loses some of its characteristics or, in other words, becomes impoverished).
Following this line of thinking one could imagine that our Universe was not
formed in one act of creation, but in a number of such acts, e.g. first out of
nothing (in the literal sense) elements of time and space had been created
(pregeometry) which then formed space-time ("vacuum"), and then out of
vacuum the Universe was created (which in the course of further development

   Physics and Philosophy                                           Musa Akrami

may be enriched with new essential ontological characteristics and so on without

9. 9. Conceptions of the Universe which is
Infinite in Time
Not all conceptions which deal with the origin of the Universe negate its
eternity; it is not negated by (1) A. Linde's conception of a chaotic inflation, (2)
the conception according to which the Universe suddenly starts an expansion
from the solid state in which it rested for an infinite period of time in the past,
(3) the conception which assumes that the Universe was smaller and smaller in
the past, however, never achieving zero dimensions and some others .
VIII. Cosmology and Philosophy
Let us go back now to the main problem of my paper: Has the beginning of the
Universe become a strictly scientfific question, i.e. such that science is able to
solve it itself?
A partial answer to this question can be given by consideration of the cognitive
status of these conceptions which assume the creation of the Universe out of
"nothing ."
So, the concept of nothingness itself and the assumption that nothingness is
possible, is a philosophical concept and a philosophical assumption, which goes
much beyond that which can be established by scientific research as such. The
latter reaches at most the concept of a vacuum which, as can be seen, is by no
means identical with the concept of nothing (in the philosophical sense). That
which is understood as vacuum in physics and cosmology is apportioned with
essential physical properties, and deserves rather the name of space or space-
time than that of nothing .
The fact that in these sciences at least several concepts of vaccum are used
("absolute vacuum", "relative vacuum"; "false vacuum", "true vacuum" etc.),
and that actually this concept is relativized to the concrete physical theories does
not change anything (e.g. the absolute vacuum is not nothingness in the
philosophical sense either). Similarly, the theses on the creation of the Universe
out of "nothingness", on "tunnelling out of nothingness", "fluctuation of
nothingness" and the like are not purely scientific theses. These kind of theses
and conceptions which they contain must assume as a basis much more than that
which corresponds to the philosophical (and also the everyday) understanding of
the concept of nothingness. If one omits energy, mass and even geometry
(chronogeometric properties) as characteristics not of nothingness, but of the
active (dynamic) space-time then one should recognize that "at the very
beginning" there must be laws of nature, according to which "nothingness

   Physics and Philosophy                                           Musa Akrami

creates the world", which also assumes the existence of something that can be
called the world of logic and mathematics. In this sense explanation of the origin
of the Universe cannot do without an assumption of some structure of
rationality .
Perhaps this assumption may not lead by itself to theology, but seems to lead
inevitably to philosophy. Perhaps physics is able to explain both the origin, the
order and content of the physical Universe, but not of the laws of physics
themselves. There must exist laws of quantum mechanics if quantum processes
are to lead to the rise of the Universe. From this point of view, open to critical
analysis is S. Hawking's conviction in which elimination of all questions about
the so-called boundary of time and space, which has its own place in his
conception, signifies as if automatic exclusion of problems which as a rule led to
religious and philosophical comments. From the philosophical point of view the
conception of the non-existence of borders shifts the problem of the source of
initial conditions to the question of the origin of physical laws, according to
which the Universe does not have borders .
Another reason which indicates an inevitable involvement of the question of the
beginning of the Universe in philosophy is that cosmology as an empirical
science is entitled to make statements on the structure and evolution of the
observable part of the Universe, but not on the Universe as a whole. In turn,
constraints on our scientific knowledge about the Universe to its observable part
(called the horizontal Universe) mean that we are not able to check scientifically
the correctness of a rule for initial conditions (or their lack) for the whole
Universe. After all we observe results of evolution of only some part (indeed a
very small one, which is confirmed by conceptions of inflation) of the initial
state .
However, it can be seen from this that extrapolations of local physics onto the
whole observable Universe cannot do without cosmological principles, about
which we know are basically of a philosophical character. Still extrapolations of
this kind conducted in cosmology are insufficient to make their conclusion
pertaining to the Universe, understood as the whole physical Universe .
One more reason of the inevitability of philosophy in cosmological
considerations is that the outcome of cosmological statements, also those that are
essential for the solution of the question of origin of the Universe, may be
interpreted differently, and that in the process of this interpretation an important
role is played by philosophical assumptions, both ontological and
epistemological (as well as those which are not connected with cosmological
principles). Great significance of interpretation in cosmology is emphasized by
circumstances that while macroscopic physical theories such as classical
mechanics — due to their relative "closeness" to experiment — have the so-
called natural interpretation (which generally does not rouse any doubts)

   Physics and Philosophy                                           Musa Akrami

microphysics and cosmology theories may be interpreted in many different
ways. Proof of this are numerous and extremely different interpretations of
quantum mechanics on the one hand, and the multitude of interpretations of the
shift to the red in galactic spectra, the multiaspectual dispute over the nature and
distance of quasars or different interpretations of the initial singularity, on the
other hand .
Hawking's criticism of metaphysics seems to be a little bit outdated because it
combines in itself elements of positivist philosophy of cognition with the
conception of God, shared by Clark in the 18th century, filling in the gaps in
natural science .
In connection with the occurrence in cosmology of numerous, and at the same
time significant, philosophical and methodological assumptions which cannot be
verified empirically without which it could not function as a science, cosmology
may be considered as "science not only of the Universe in its largest scale, but
also about assumptions which one should form in order to make such a science

       Physics and Philosophy                                           Musa Akrami

    Chapter 10. Cosmology and some
    Philosophical Questions
    Cosmology has evolved from an essentially religious and mythical description of
    the supernaturalistic origins and nature of the universe to an essentially
    naturalistic description. These cosmological descriptions originated from man's
    attempt to answer several fundamental questions about the universe:
   Why is there a universe?
   Is the universe finite or infinite?
   If finite then how big?
   Did the universe always exist or did it have a beginning?
   If the universe had a beginning then how did it come into being?
   When did it come into being?
   Where did it come into being?
   What exists in the universe?
   How do the contents of the universe behave and interact?
    Ancient cosmologies and even cosmologies emerging through the age of
    enlightenment were closely intertwined with religious belief. Only within the
    last half-century or so has a specialized science of cosmology emerged without
    making explicit mention of God or deities. In these modern cosmologies
    immediate human concerns often appear to dwindle to insignificance in the scale
    of cosmic time and space. Before the twentieth century it often seemed that any
    serious non-mythical investigation of the ordered universe led to a Mover or a
    Designer who could be assimilated to the being whom men and women
    worshiped as God.
    The following are brief summaries of the major cosmologies influencing western
    thought. The progressive development toward modern scientific cosmologies
    can be detected in each subsequent cosmology.
    Plato's Cosmology (428/427-348/347 B.C.) - Plato's account takes the form of a
    creation story, in the tradition of Greek mythologists. It is narrated by a
    philosopher named Timaeus of Locris (apparently a fictional character modeled
    on several of the Pre-Socratics). In this account, the whole of nature is initiated
    by a creator divinity, called the "Demiurge" (the Geek word for 'craftsman'),
    who seeks, to the best degree possible, to imitate through physical copies the
    ideally perfect structures of true being (i.e., the Ideas, or 'paradigms'). In this
    way he institutes the visible cosmos, that is, the ordered domain of things that
    are susceptible of process and change (e.g., birth, growth, alteration, and

    By Larry House

   Physics and Philosophy                                            Musa Akrami

dissolution - the realm of 'becoming,' genesis). The Demiurge himself only
assembles the supreme model of the cosmos, the 'world soul', and then delegates
his divine subordinates to fit out the detailed structures of the parts of the
cosmos. It follows that the whole cosmic system is pervaded with analogical
structures, most notably, the human form, which becomes a copy of the whole -
a microcosm, as it were - by virtue of the activity of these divine surrogates. All
phenomena of nature can be described as an interplay between the two forces of
reason and necessity. He represents reason as constituting the world soul. The
material medium (four elements of earth, air, water and fire) is introduced as the
'receptacle' representing the domain of necessity. It is unclear whether Plato
intended his cosmology as a literally true account of a created cosmos or a
metaphysical fiction. Aristotle insisted that Plato must be held to his literal work,
whereas Plato's immediate disciples favored a metaphorical reading. Division of
opinion has continued to the present day.
Aristotle's Cosmology (384-322 B.C.) - Aristotle's cosmology was to dominate
thought in the Western World for more than 2,000 years and its overthrow is
arguably the major achievement of Renaissance science. Aristotle's views on the
organization and structure of the universe are presented in De caelo. This work
contains some of the basic considerations of motion. All locomotion is either
straight, circular, or a combination of the two; and all bodies are either simple
(i.e., composed of a single element, such as fire or earth) or are compounds. The
element fire and bodies composed of it have a natural movement upward: bodies
composed of earth have a natural movement downward (i.e., toward the center
of the universe which is the earth). Circular movement is natural to some
substances other than the four elements and the circular movement is considered
more divine than these four elements (since circular motion is believed to be
prior to straight movement). Aristotle views the universe as two-spheres where
the changing region is up to the sphere of the moon, the earth is in the center
surrounded by water, and air and fire are at the top, beyond which the heavenly
bodies are in circular motion and in a realm without change. There is a separate
set of physical laws for each of the two regions, since they are composed of
different types of matter. Aristotle argues that the universe is not infinite because
the universe moves in a circle (as we can see with our eyes if we watch the
stars). If the universe were infinite, it would be moving though an infinite
distance in a finite time, which is impossible. This is an argument employing the
method of reductio ad absurdum (i.e., showing that the premise leads to an
absurd conclusion thus proving the opposite premise must be true). Aristotle
claimed also that there was only one world. He demonstrated this conclusion
also using a reductio ad absurdum argument. If there were more than one world,
each world with a center as the natural place for earthy material to move to and a
circumference for fire to move to, then the earth could move toward any of the

   Physics and Philosophy                                            Musa Akrami

centers and fire toward any of the circumferences. Chaos would ensue. Since we
observe order instead of chaos then there must be only one world. Aristotle also
showed that the heavens rotate and that the earth is spherical, stationary and in
the center of the heavenly sphere. In his arguments that the earth is spherical
(based on the circular shadow during eclipse and that different stars are seen
from different parts of the earth), Aristotle's use of observation is in stark
contrast to Plato's rejection of the evidence of the senses. This is seen by some
historians as a turning point in science, marking the beginning of extensive
empirical investigations. However, Aristotle's cosmology has a number of
teleological and animistic qualities that distinguish it from the modern
mechanical explanations. While bringing to Greek science a new emphasis on
the value of observation, Aristotle still differs in important ways from modern
scientific practice. For example his observations are used more to persuade his
readers of the truth of his conclusions than as an aid in arriving at his
conclusions. Also Aristotle does not conduct critical experiments with which to
test his conclusions.
Kant's Cosmology (1724-1804) - Kant provided the first model of a scientific,
albeit highly speculative and qualitative, cosmology. His cosmology was
thoroughly mechanistic and materialistic, but it makes clear that every
cosmology must begin with the perception of a 'systematic constitution,' that
could be viewed as evidence of some sort of 'grand design'. Although most of
Kant's main tenets were mistaken, his work was of unprecedented scope, made
detailed use of physical theory, and contained a number of fundamental insights.
Kant's cosmological explanation takes the form of showing how the 'systematic
constitution' arose, by way of Newton's laws of motion and the law of universal
gravitation, from an original chaos. The chaos consists of atoms or particles of
matter spread throughout an infinite space. According to Kant, the original chaos
was unstable: the denser particles begin at once to attract the more tenuous. This
is the explanation of the origin of motion and the formation of bodies, eventually
of the planets. To prevent the universe from becoming one big massive ball Kant
claims nature has still other forces in store which especially evidence themselves
when 'matter is diluted into fine particles, whereby they repulse one another and
through their conflict with [the force of] attraction produce that motion which
is, so to speak, and enduring life of nature. Through this repulsive force, which
reveals itself in the elasticity of vapors in the strongly smelling bodies and in the
expansion of all spirituous matter and which is an indisputable phenomenon of
nature, the elements sinking toward their points of attraction become directed
side-wise in all sorts of ways and the perpendicular fall issues in circular
motions which surround the center of sinking.' Lateral motion thus results when
attractive and repulsive forces between any two bodies are equal and the one
body, following the path of least resistance, begins to orbit about the other. As

   Physics and Philosophy                                            Musa Akrami

this summary indicates Kant's cosmology was largely qualitative. For example,
he nowhere provides a law, similar to that for attraction, by which the force of
repulsion can be determined. It is also important to note that while Kant's
cosmology was naturalistic he never gave up the attempt to reconcile teleology
and mechanism. In his Universal Natural History he claimed, that the very
perfection of the mechanism in terms of which the development of the universe
could be explained was at the same time the guarantee that it existed for a
purpose and was not simply the product of accident and chance.
Modern Cosmology - Modern relativistic cosmology emerged in the 20th
century. A science in a technical sense can emerge only after its philosophical
foundations have been clearly and distinctly laid. Nevertheless, cosmology, like
preceding scientific disciplines, seems to have developed its philosophical
foundation by a largely unconscious process. The philosophical foundation of a
science involves three essential stances; metaphysical, epistemological, and
methodological. These are outlined in Table 1. We define what it means to be
"scientific" as consisting of some choice of a combination of positions held
within each categorical stance: Metaphysics + Epistemology + Methodology.
Without this foundation we do not have a basis for stating 'what it is to be
scientific'. The choice of the specific position under each categorical stance is
independent of the specific position selected in the other categories. In other
words the individual positions held within the metaphysical, epistemological,
and methodological triad are mutually independent choices that are selected
without reference to the position held in each of the other categorical stances.
       Table 1. Philosophical Basis For What It Means to Be Scientific
                                             Operationalism - Only those entities
                                             that can be simply and directly
                                             observed are to be counted as real. The
                                             entities involved are those that may be
Metaphysical Stances This stance             defined by some sort of operation with
poses the question; "What sorts of           various physical instruments or
entities, among those referred to by         equipment.
scientific statements, are to be             Explanatory Realism - This position
understood as actual existents?"             adopts as an existence criterion
                                             something like "If a theoretical entity e
                                             must be hypothesized in order to
                                             explain observable phenomenon p, then
                                             e exists."
Epistemological Stances In this stance Empiricism - Only information from
the question is asked; "What are the   observational and experimental results
legitimate sources of scientific       are acceptable as a source for

   Physics and Philosophy                                              Musa Akrami

knowledge?"                                   cosmological theorizing. Scientific
                                              knowledge is founded in sensory
                                              Rationalism - It is permissible for
                                              cosmologists to originate their
                                              theoretical efforts in very general ideas
                                              about what the universe should be like.
                                              Hypothetico-deductivism (H-D'ism) -
                                              Hypotheses are generated on the basis
                                              of general ideas about the universe, and
                                              then the consequences of these
Methodological Stances The question           hypotheses are deduced with the hope
related to this stance is; "What are the      that at least some of the consequences
acceptable procedures for constructing        involve observational possibilities.
a scientific theory?"                         Inductivism - Logical induction is used
                                              to produce generalizations and
                                              extrapolations based on solid
                                              observational and experimental
One of the relatively popular choices among several scientific fields is:
Operationalism + Rationalism + H-D'ism. Another choice that has been
identified is: Operationalism + Empiricism + Inductivism. Perhaps the most
typical position of a physical scientist is: Realism + Empiricism + Inductivism.
In the case of modern relativistic cosmology it was Operationalism +
Rationalism + H-D'ism that ended up providing the philosophical model. The
main point is that within science itself there are inconsistencies between what it
means to be scientific from one discipline to the next. This is important because
understanding the philosophical basis for a scientific interpretation of nature is
an essential first step for a rational critique of the conflict between scientific
cosmology and biblical cosmology.

   Physics and Philosophy                                           Musa Akrami

Chapter11. The Beginning of the
Universe [Philosophical and Theological
   1. Scientific Cosmology
   2. Quantum Cosmology and Inflating Universes
   3. A Philosophical Evaluation of Quantum Cosmologies
   4. Philosophical Issues
   5. The Question of a Philosophical Cosmology or 6. [A Religious
      Cosmology: the Case of] A Christian Cosmology
   6. Something from Nothing
   7. Christian Spirituality and the New Cosmology


1. Scientific Cosmology
The noted scientific cosmologist, P. James E. Peebles, summed up the current
state of this field by saying that at its heart is the solidly established big bang
theory. But Peebles immediately cautioned, "That the universe is expanding and
cooling is the essence of the big bang theory. You will notice I have said nothing
about an "explosion" – the big bang theory describes how our universe is
evolving, not how it began."1 To the big bang, he tells us, scientists are trying to
add the theory of inflation, that is, that early in its life the universe expanded
rapidly. There is also strong evidence that most of the mass of the universe
cannot be accounted for by the things we see, but there must be some sort of
unknown dark matter. Further, it appears that something, some dark energy or
quintessence, is making the universe accelerate.

It is remarkable not only how quickly this field is changing today, but how our
picture of the universe has been transformed in less than a century. When
Einstein was writing his theory of general relativity in 1916 the prevailing
feeling that the universe was static was so strong that when his equations
indicated that the universe should be expanding, or contracting, he introduced a

By James Arraj

   Physics and Philosophy                                             Musa Akrami

cosmological constant to produce a universe at rest. Not only was there a
consensus that the universe was static, but it was also equated with our own

By 1929, however, the picture was changing. Edwin Hubble was discovering
other galaxies, and found that the farther away they were, the more the light
from them was shifted towards the red end of the spectrum, indicating that they
were moving away and the universe was therefore expanding. And physicists
like Alexander Friedmann and George Lemaître and others had uncovered
Einstein’s apparent mistake. In 1965, two Bell Laboratory scientists, Arno
Penzias and Robert Wilson, while trying to eliminate radio interference,
discovered cosmic background microwave radiation left over from the big bang.

Now we are faced with a universe so big and so old that it defies our
imaginations to grasp it. It appears to have begun 15 billion years ago. Our
galaxy, alone, has some 100 billion stars, and it is just one of perhaps a 100
billion galaxies, and this immense universe is expanding at an ever increasing

This is an awe-inspiring picture, but what does it say about the origin of the
universe? Let’s imagine that the scientific cosmologists have been creating an
ever more detailed and vivid movie of the structure and movement of the
universe, and this film, when it is played backwards, makes the universe appear
as if it is coming together and beginning in an intensely hot and dense state. But
the real question is whether this movie takes us back to the absolute beginning,
or very origin of the universe. It doesn’t appear to do so because the basic laws
of nature, as described by Einstein’s relativity, break down as we approach this
beginning. It is as if the film runs out and just before we reach the beginning we
are dazzled with a blinding white light. And we are faced with the very difficult
question: can science find a way to talk about the very beginning of the universe,
or is this simply outside its scope?

The scientists, themselves, are divided about the matter. The physicist Charles
Townes writes: "I do not understand how the scientific approach alone, as
separated from a religious approach, can explain an origin of all things. It is true
that physicists hope to look behind the ‘big bang,’ and possibly to explain the
origin of our universe as, for example, a type of fluctuation. But then, of what is
it a fluctuation and how did this in turn begin to exist? In my view, the question
of origin seems always left unanswered if we explore from a scientific view
alone."2 But other scientists are less reluctant to put science to the task and to try
to develop a scientific theory of the beginning of the universe. Let’s look at
some of these attempts.

   Physics and Philosophy                                            Musa Akrami

2. Quantum Cosmology and Inflating Universes
Since relativity appears to break down as we approach the beginning of the
universe, scientific cosmologists have turned to the other great pillar of modern
physics, quantum theory, in order to overcome this limitation, and to create a
quantum cosmology that can answer the question of the origin of the universe.
Let’s try to get a general sense of this quantum cosmology, not in the scientific
particulars of this or that theory, but rather, how scientists present these theories
with philosophical and religious overtones.

In 1983, James Hartle and Stephen Hawking proposed that a cosmic wave
function be applied to the entire universe similar to the wave function that
quantum mechanics had applied to elementary particles. "According to this
approach, the usual distinction between future and past breaks down in the very
early universe; the time direction takes on the properties of a spatial direction.
Just as there is no edge to space, there is no identifiable beginning to time."3

Hawking writes elsewhere: "the quantum theory of gravity has opened up a new
possibility, in which there would be no boundary to space-time and so there
would be no need to specify the behavior at the boundary. There would be no
singularities at which the laws of science broke down and no edge of space-time
at which one would have to appeal to God or some new law to set the boundary
conditions for space-time. One could say: "The boundary condition of the
universe is that it has no boundary." The universe would be completely self-
contained and not affected by anything outside itself. It would neither be created
nor destroyed. It would just BE."4

And a little later he adds: "So long as the universe had a beginning, we could
suppose it had a creator. But if the universe is really completely self-contained,
having no boundary or edge, it would have neither beginning nor end: it would
simply be. What place, then, for a creator?"5

The Russian cosmologist, Alexander Vilenkin, now at Tufts University, has his
own version of the beginning based on the aspect of quantum mechanics in
which a particle can appear and disappear in a vacuum like outer space. An
account of this theory which appeared in Discover magazine gives us the flavor
of how these theories of the beginning of the universe are reported in the popular
scientific press not only uncritically, but with a certain sense of awe:

   Physics and Philosophy                                           Musa Akrami

"If a particle can pop into existence from nothing, why not a whole universe?
Vilenkin wondered. If space can be thought of as an energy field with an
average value of zero, why not think of pre-creation nothingness as a sort of
space-time field whose average value is zero? Rather than a virtual particle
popping into existence, a whole universe, along with matter and energy and
space and time and everything else, pops into existence from nothing. Once he
started to think about the universe in this way, he raised the possibility of not
just one universe but many. Proto-universes could be popping into existence all
the time… The pre-universal nothingness he described was the purest form of
nothingness imaginable. Since matter and energy create time and space,
Vilenkin’s nothingness had neither. There was no countdown to the Big Bang,
because time did not yet exist. In a stroke, he reduced creation from a
metaphysical event to a physical one. What had seemed unknowable was
suddenly reduced to a set of equations."6

More recently, Vilenkin, together with Jaume Garriga of the University of
Barcelona, developed a "many worlds in one" theory in which our universe
contains an infinite number of other universes, or O-regions, where alternate
histories play themselves out. There is one, for example, where Elvis Presley is
still alive. Alan Guth, himself a noted cosmologist, thinks that this idea has
profound philosophical implications. "We already know that our planet is merely
a tiny speck in a vast cosmos," Guth told UPI, "but now we are being told that
we do not even hold a unique copyright of our own identities. Instead, each of us
is actually only a single copy of an infinite number of beings that are completely
identical to ourselves."7 Elsewhere Vilenkin said that he created this theory as a
"metaphysical diversion." "Physicists usually want to make predictions and see
if their theory is correct. This paper was not of that kind, although, in principle,
we could travel to one of those other parts of the universe, although we won’t be
able to do that anytime soon," he says. "To a large degree, eternal inflation is not
accessible to observation."8 He doesn’t plan to explore the matter further, he tells
us. It was a "metaphysical exercise."

Vilenkin’s compatriot, Andrei Linde, now at Stanford University, has proposed
an inflationary universe which he hopes will address some of cosmology’s
outstanding questions including the biggest question of them all, "the very
existence of the big bang." 9 He describes an "eternally existing, self-reproducing
inflationary universe"10 in which quantum fluctuations in a scalar field are
looked at as waves. These waves freeze and decrease the field in some parts of
the universe and increase it in others. These increasing fields are soon bigger
than the other parts of the universe: "In essence, one inflationary universe
sprouts other inflationary bubbles, which in turn produce other inflationary
bubbles. This process, which I have called eternal inflation, keeps going as a

   Physics and Philosophy                                           Musa Akrami

chain reaction, producing a fractal-like pattern of universes. In this scenario the
universe as a whole is immortal. Each particular part of the universe may stem
from a singularity somewhere in the past, and it may end up in a singularity
somewhere in the future. There is, however, no end for the evolution of the
entire universe.

"The situation with the very beginning is less certain. There is a chance that all
parts of the universe were created simultaneously in an initial, big bang
singularity. The necessity of this assumption, however, is no longer obvious.
Furthermore, the total number of inflationary bubbles on our "cosmic tree"
grows exponentially in time. Therefore, most bubbles (including our own part of
the universe) grow indefinitely far away from the trunk of this tree. Although
this scenario makes the existence of the initial big bang almost irrelevant, for all
practical purposes, one can consider the moment of formation of each
inflationary bubble as a new "big bang." From this perspective, inflation is not a
part of the big bang theory, as we thought 15 years ago. On the contrary, the big
bang is a part of the inflationary model."11

When a reporter from Discover magazine went to visit Alan Guth, the originator
of the idea of an inflationary early universe, at the Massachusetts Institute of
Technology, the reporter rhapsodized, "Now that inflation theory is approaching
dogma, it is bringing science to the brink of answering one of the largest
questions of all: Why is there something rather than nothing?" 12 And Guth
certainly didn’t discourage this type of approach. "It’s not a coincidence," he
said, "that the Bible starts with Genesis… Most people really want to know
where we came from and where everything around us came from. I like to
strongly push the scientific answer. We have evidence. We no longer have to
rely on stories we were told when we were young." 13 We are told that at the
beginning of the universe there was nothing, a pure vacuum with no space or
matter, a vacuum which is subject to quantum uncertainties so that things can
come out of it and vanish back into it. And what came out of it was a false
vacuum, a particular kind of matter which has never been observed. From this
false vacuum, one billionth the size of a proton, the universe emerged and the
stuff in it "out of nowhere."14

Along similar lines, the Copenhagen interpretation of quantum theory had long
proposed that subatomic particles were in more than one state at a time in a sort
of superimposition of possible states, and somehow these possibilities had to
collapse to give us the one world we see around us. This led to the question of
what caused this collapse, and it was proposed that it was the interaction of these
superimposed states with an observer. This, in turn, led to the famous paradox of
Schrِ inger’s cat sealed inside a container. The cat was conceived of as both

   Physics and Philosophy                                          Musa Akrami

alive and dead until we looked inside, and then it was either alive or dead. But
there was another solution proposed by Hugh Everett in 1957. In his
interpretation the possible states do not collapse, but the universe somehow
divides, and accommodates each possibility in a new world. This many worlds,
or multiverse, view is still seriously proposed by some cosmologists like Bryce
DeWitt and David Deutsch, and it is even claimed that it is the majority view
among scientific cosmologists. We have to be clear about what this many
universe theory is actually saying. It means that each time we do something, or
each time something, no matter how small, changes in the universe, a new
universe is created, and therefore millions and billions of universes are being
created at every moment. Deutsch says: "I don’t think there are any
interpretations of quantum theory other than many worlds… The others deny

It would be misleading if citing these remarks of the scientific cosmologists on
the origin of the universe left us with the impression that metaphysical style
reflections occupied the forefront of the attention and energy of the majority of
today’s cosmologists. They no more do so than do esoteric interpretations of
quantum theory. Alan Guth, some of whose philosophical forays we have
already seen, illustrates this situation with the structure of his book, The
Inflationary Universe. It starts and ends with musings about the beginning of the
universe, but the bulk of the book deals with the physics about and underlying
the theory of the inflationary universe. In short, thoughts about the beginning of
the universe are the speculative icing on the cake.

But it is certainly worth looking at Guth’s beginning and ending pages to help us
sum up what some of the cosmologists have been saying. He recalls the initial
paper of Edward Tryon who first suggested that the universe might be a vacuum
fluctuation, "essentially from nothing at all," as Guth puts it.16 Part of the
reasoning that undergird this assertion was that although the mass of the
universe represented a large amount of positive energy, it was canceled out by
gravity which was represented as negative energy, leaving the universe at zero
so that its creation would not be a violation of the laws of the conservation of

Physicists objected to Tryon’s theory because the empty space from which the
universe was supposed to have come was still something. So Alexander Vilenkin
suggested that it would be better to start with "literally nothing," which was not
matter, space or time, but a total empty geometry of absolute nothingness from
which the universe made the transition to a non-empty state by quantum

   Physics and Philosophy                                           Musa Akrami

3. A Philosophical Evaluation of Quantum
What can we make of these fascinating but rather bizarre-sounding theories? Are
we really on the brink of a scientific explanation for the absolute beginning, or
origin, of the universe? Let’s take a more critical look at what is going on. First
of all, from the scientific side of things, these are highly speculative and
controversial theories, and they rest on problematic foundations since there is as
yet no theory that embraces both quantum mechanics and relativity, and thus
there is no well-substantiated theory of quantum gravity. Christopher Isham has
spelled out some of these difficulties in his "Quantum Theories of the Creation
of the Universe."18 And added to these technical difficulties, he finds general
conceptual problems including various difficulties with the Copenhagen and
many worlds interpretations of quantum theory: "These are so severe," he writes,
"that a number of professional physicists believe that the entire quantum
cosmology program may be fundamentally misguided."19

But the philosophical problems these theories face are just as severe. Timothy
Ferris, for example, suggests that quantum cosmologists look at three
fundamental problems: that of a first cause, that of something coming from
nothing, and the issue of infinite regress. In essence, he is asking that scientific
cosmology address properly philosophical questions, and in doing so he is
simply following in the footsteps of the scientific cosmologists we have been
listening to. Let’s see how successful his own attempts are to deal with these
philosophical issues.

"There can be no effect without a cause."20 This he calls a noble and venerable
argument, but finds that it is now more problematical. Quantum physics have
shown us that there are, indeed, events without causes, i.e., radioactive decay, or
vacuum fluctuations. "So strict causation may break down both in quantum
physics and in considering the origin of the universe." 21

"You can’t get something from – or for – nothing."22 This philosophical
challenge, he feels, can be overcome, as well, if we imagine that matter and
energy in the universe are positive, and the force of gravity is negative, as we
saw, so that the total energy of the universe is zero so we are not really getting
something from nothing.

   Physics and Philosophy                                           Musa Akrami

In the final philosophical challenge we are told the universe must have
originated from another system which, in turn, had to have an origin, and so "we
are caught in infinite regress."23 But if the very early universe was a quantum
space-time foam there would be no arrow of time, and so the issue would be
meaningless. The problem of logical regress in contrast to this kind of temporal
regress, he admits, is harder to overcome. "Certainly it is very difficult to
imagine a theory in which the universe originates out of absolutely nothing. 24
Even if we say it comes from some kind of scalar field, we are left asking where
the field came from. Ferris’ questions are good ones, but his answers are less
than satisfactory.

It is natural for scientists to want to pursue the story of the universe as far back
to its beginning as they can, and it is also natural for them as men and women to
want to know its ultimate origin. The real problem arises when scientific
cosmologists give their theories a philosophical or ontological meaning, and act
as if science possesses the only genuine way to know about these matters.

Stephen Hawking, for example, writing about his approach to how one can
understand the universe, says: "There is a real problem here. The people who
ought to study and argue such questions, the philosophers, have mostly not had
enough mathematical background to keep up with modern developments in
theoretical physics."25 The implication is clear. Philosophers need to be
theoretical physicists because physicists are the people who can really address
the question.

His former wife, Jane, comments: "There’s one aspect of his thought that I find
increasingly upsetting and difficult to live with. It’s the feeling that, because
everything is reduced to a rational, mathematical formula, that must be the truth.
He is delving into realms that really do matter to thinking people and in a way
that can have a very disturbing effect on people — and he’s not competent."26
And later she adds: "I pronounce my view that there are different ways of
approaching it (religion), and the mathematical way is only one way,… and he
just smiles."27

Another example of this same kind of mentality comes from the physicist Frank
Tipler in his book The Physics of Immortality: "Either theology is pure nonsense,
a subject with no content, or else theology must ultimately become a branch of
physics. The reason is simple. The universe is defined to be the totality of all
that exists, the totality of reality. Thus, by definition, if God exists, He/She is
either the universe or part of it. The goal of physics is understanding the ultimate
nature of reality. If God is real, physicists will eventually find Him/Her." 28 This

   Physics and Philosophy                                               Musa Akrami

is an amazing assertion that crumbles as soon as we reject the gratuitous premise
that the universe is identical with all that exists.

4. Philosophical Issues
Let’s pursue these philosophical issues further by looking at two interconnected
questions: the interpretation of quantum theory, and the epistemological type of
modern physics. From the very beginning of the creation of quantum theory
scientists have been divided about what kind of interpretation to give it. The
mathematical formalism of quantum mechanics works extremely well, but there
is no universally accepted understanding of what it means. The Copenhagen
interpretation has shed an aura of quantum weirdness over the whole field with
its paradoxes like Schrِ inger’s cat, which is both alive and dead until we look,
and particles which go through both slits of our apparatus until we decide to
measure them. And it has become somewhat of a truism to imagine that quantum
theory has demonstrated that causality does not hold sway in the microworld. In
actual fact there is no reason to believe that this is true, or that quantum theory,
itself, demands quantum weirdness. That is not to say that quantum theory is not
surpassingly strange in its own way. It appears that nonlocality, i.e., the
instantaneous interaction of distant particles, is an intrinsic part of it. But there is
no reason to believe that something like radioactive decay takes place without a
cause, or that we need an observer to collapse the superimposed states in order
to decide whether the cat is alive or dead. I have looked at these issues in some
detail in The Mystery of Matter. Unfortunately, this kind of reasoning that has
always existed in quantum theory is now being applied to the universe as a
whole, and we will have to look at how much sense it makes to imagine particles
popping out of nothing, still less the universe itself.

The epistemological type of modern physics simply means that it has its own
distinctive way of knowing things. It measures things and submits these
measurements to the formal rule of mathematics, and in the best of cases, makes
predictions that can be confirmed or disconfirmed by further measurements. It
has its own distinctive way of grasping things in a web of measurements and
mathematics that gives us a genuine knowledge of the world around us, but a
knowledge that is somewhat indirect in the sense that the physicist does not fully
understand just what he or she is capturing with this net of physico-mathematical

The physicist faces two temptations. The first is to imagine that physics is the
only way to know things. We have seen the remarks of Hawking and Tipler that

   Physics and Philosophy                                             Musa Akrami

end up strongly leaving that impression. If we accept them in an absolute and
literal way, then all we would have would be physics. Art and poetry,
philosophy and theology, literature and history, would all be reduced to wishful
thinking. Even if we don’t go to this extreme, any philosophical understanding
of cosmology would be ruled impossible.

William Craig in an interesting article called, "Design and the Cosmological
Argument," writes: "Remarkably, Hawking has recently stated explicitly that he
interprets the Hartle-Hawking model nonrealistically. He confesses, "I’m a
positivist… I don’t demand that a theory correspond to reality because I don’t
know what it is." Still more extreme, "I take the positivist viewpoint that a
physical theory is just a mathematical model and that it is meaningless to ask
whether it corresponds to reality." In assessing the worth of a theory, "All I’m
concerned with is that the theory should predict the results of measurements." 29

Some physicists even seem to go further and imagine that physics has given
them a privileged seat from which to discern a lack of meaning in the universe.
Steven Weinberg, for example, was flying over the U.S. and saw a beautiful
sunset and reacted like this: "It is very hard to realize that this all is just a tiny
part of an overwhelmingly hostile universe. It is even harder to realize that this
present universe has evolved from an unspeakably unfamiliar early condition,
and faces a future extinction of endless cold or intolerable heat. The more the
universe seems comprehensible, the more it also seems pointless." 30

To his mind, religion is an obvious "adversary" of science because it "teaches
that we are actors playing a part set up by God. I don’t agree with that."31

The second temptation is more subtle. What are we to make of the mathematical
results that the physicists have come up with to explain the origin of the
universe? First, we need to ask about what measurements they are based on, and
what predictions they make. In short, they have to undergo genuine scientific
scrutiny. But even if the starting point of these statements in the form of
measurements are anchored in reality, we still need to ask whether there is a
point-to-point correspondence between this or that mathematical symbol found
in the equations of these scientific cosmologists and the universe, itself. This is a
more philosophical question that does not directly interest the physicist. Kip
Thorne, echoing some of the remarks of Hawking we just saw, writes: "Is
spacetime really curved? Isn’t it conceivable that spacetime is actually flat?
What is the real, genuine truth? … To a physicist like me this is an uninteresting
question because it has no physical consequences."32

   Physics and Philosophy                                         Musa Akrami

But it is a critical one from a philosophical perspective. Hawking, for example,
will use a number of mathematical techniques including imaginary numbers to
create his no boundary view of the universe. But it is quite another matter to
discover what, if anything, these imaginary numbers tell us about the actual
universe around us.33 Or we may say that the wave function applies to the
universe as a whole, and points to the existence of a multitude of universes. But
this kind of physical assertion cannot be demonstrated by the mathematics alone,
and there is no physical evidence for more than one universe.

This problem of how to go from mathematical symbols to the actually existing
things around us has become much more acute since the creation of quantum
theory. Physics, itself, has over the last century become more mathematical, and
this trend shows itself in a particularly acute form when we come to quantum
cosmology. If before mathematics served the measurements we made of the
world around us in order to try to come to some sort of understanding of this
world, now the mathematics seems to take the lead and impose a certain view on
the universe rather than let it speak to us. Clearly it speaks in some way to us
through mathematics, but not mathematical symbol by symbol.

What can we conclude from these two points? Quantum theory and the quantum
cosmologies built on them come to us freighted with all sorts of baggage that
cannot be uncritically accepted. And the mathematical constructs of the
scientific cosmologists can’t be directly transposed into a view of how the
universe really is in itself.

5. The Question of a Philosophical Cosmology or
Something from Nothing
The central question of the origin of the universe is whether something can come
from nothing. But this is a very philosophical, or even metaphysical issue and
brings with it the question of whether science is equipped in virtue of its own
methods to deal with it, and whether there can be a philosophical cosmology at
whose heart this question would be found.

First some clarifications are necessary. We have to clearly distinguish the
different "nothings" that are being talked about. There is what we could call a
philosophical nothing which is the absence of all being or existence, an absolute
nothingness. Then there is a scientific nothing, a vacuum like outer space, or
some sort of quantum vacuum that fluctuates, or a primordial scaler field, etc.

   Physics and Philosophy                                           Musa Akrami

But from a philosophical point of view these things are not nothing, but
something. Unfortunately, however, scientific cosmologists and their
commentators sometimes slide from one kind of nothing to another, and don’t
even notice they are doing so.

What we are going to be talking about here is absolute nothingness, and from
that perspective the various scientific nothings are somethings which, in turn,
need to have their origin explained, and even an infinite series of inflating
universes giving birth to each other may obscure, but does not answer the
question of an absolute beginning.

The quantum cosmologists theorize that the universe, or universes, have popped
out of nothing, but, as we have just indicated, this nothing is really something,
and even if we could demonstrate particles popping out of a vacuum, the
vacuum, itself, has a certain existence, and is far from being the nothingness that
philosophy talks about, and is even conceived of by physicists as being
supremely full.

And even a more fundamental aspect of this problem is whether science is
capable of talking about this absolute nothingness at all. If absolute nothingness
simply does not exist in any way, then it cannot be measured, or observed, and
therefore it does not fall under the scope of scientific inquiry. But if science
can’t deal with absolute nothingness, is there a discipline that can? The
questions we saw Timothy Ferris asking, and attempting to answer, are not
really scientific questions, but philosophical ones. Here we arrive at the issue of
whether there can be a philosophical cosmology which would address the
question of the origin of the universe, itself, and even have a distinctive view of
matter, space and time. A philosophical cosmology would not be an alternative
science. It would not be able to tell us about quasars or black holes, or the
acceleration of the universe, but it would have to address the magnificent and
startling fact that the universe exists, and it would have to ask about its origins.

In today’s world where we hear so much about scientific cosmology, the very
idea of a philosophical cosmology is difficult to imagine, and may even appear
ridiculous. The very words cosmology and cosmologists are reserved for the
physicists, and the word metaphysics conjures images of new age
pronouncements, and even sometimes the remarks of the scientific cosmologists,
themselves. But a genuine philosophical or metaphysical cosmology could exist
in harmony with today’s scientific cosmology. It would not compete with
science, but complement it, and have its own distinctive way to look at the

   Physics and Philosophy                                           Musa Akrami

Let’s outline some of the features it would have and how it would proceed. It
could take the most basic findings of scientific cosmology as its starting point.
We live in an immensely large universe which appears to have begun some 15
billion years ago, and is still expanding. Such a view delivers to philosophical
cosmologists two undeniable facts, facts that were already accessible to us, but
which science now presents in a more detailed and dramatic way. First, the
universe exists. And secondly, it exists in a distinctive way. Let’s look at this
second fact first. Scientific cosmologists insist that if the fundamental physical
constants of the universe were different, our universe, itself, would be very
different. It is not my intent here to examine where they go with these sorts of
arguments in terms of the purpose and design of the universe. We will look at
those issues later. All I am saying is that we find the universe existing in one
way, but it could conceivably have existed in another. We live in a particular
kind of universe.

The first fact, that the universe exists, appears at first glance to be an obvious
assertion of no particular value to us. It is what science implicitly accepts, and
then goes on to examine how it exists. But for a philosophical cosmologist it is
not an unexamined premise, but a mystery that it must try to fathom. An
immensely large and beautiful universe exists, but why does it exist rather than
not exist? Existence is not a brute fact. It is the most fundamental and wonderful
of facts.

So a philosophical cosmology is founded on two undeniable facts: the universe
exists, and it exists in a distinctive way. These facts could be rephrased in a
more general way by saying that things exist, and different kinds of things exist.
We can accept that we are surrounded by many different existing things. The sun
exists and warms us. And the moon exists and circles the earth. And the sun is
not the moon. The sun has a certain kind of existence, and the moon a different
kind. But the next step in the creation of a philosophical cosmology is much
harder. Neither the sun nor the moon represents the totality of what it means to
exist. Indeed, our universe, itself, is a distinctive kind of universe, and is only
one of many possible universes, so our universe cannot be equated with the
fullness of existence. The things around us, and the universe as a whole,
therefore, are partial reflections, or refractions, of Existence, itself.

There is another line of reasoning that leads to the same conclusion. Everything
we experience changes. The stars have their own life cycles, as does the universe
as a whole. But to change means that something becomes something that it was
not before. Things become more or less, or cease existing altogether. Things
have a more or less precarious grip on existence, and they modify each other’s
existence. But what does this imply? It means that what they are is not the same

   Physics and Philosophy                                          Musa Akrami

as that they are. The sun came into existence, but we can imagine a time when it
is no more. It does not have to always exist.

The kind of philosophical cosmology that I am outlining categorically denies
that something can come from absolutely nothing. In scientific cosmologies we
have things coming from nothing that are really somethings, that is, fields,
vacuums, etc. Or we have something coming from nothing based on certain
kinds of interpretations of quantum theory that are not intrinsically connected
with its mathematical formalism, but are philosophical interpretations of it. And
we have some rather bald assertions on the part of some scientific cosmologists
and their popularizers about something from nothing, but all in all, I can see no
real scientific evidence that something emerges from absolutely nothing.

Something from nothing defies common sense, and by common sense I mean
the deep pre-philosophical sources of the working of our intelligence that we
rightly rely upon in our daily lives. I don’t expect my banker, for example, to be
content when I explain that my overdrawn account will be remedied by money
popping into it from absolutely nowhere. Nor do I expect a parking spot to
miraculously pop out of nowhere in Berkeley or Cambridge. The scientific
cosmologists don’t expect these things to happen, either, so why should we
expect it to happen in the case of a single proton, or an entire universe?
Something existing is not the same as it not existing. If we deny this, then all
hope of reasonable discourse disappears. Then why does scientific cosmology
sometimes have a predilection for a universe popping out of nothing? First of all
it is for the reasons we have just seen, that is, that their nothings are really
somethings, because of particular interpretations of quantum theory, and so
forth. But there may be another reason, as well. When faced with the question of
the origins of the universe there are two possible options. We can say it came
from nothing, or we can say that it came from something, a something when
posed leads to all sorts of philosophical and religious questions. It would be
entirely reasonable for scientific cosmologists, precisely as cosmologists, not to
deal with these philosophical and religious issues. But the distinction between a
person and his or her profession are usually not drawn that clearly, and so we
sometimes have scientific cosmologists attempting to slam the door on these
kinds of philosophical and religious questions. Some of them even appear at
times to go out of their way to oppose science to philosophy and religion. The
end result is to have the universe popping out of nothing where this nothing is
not some conclusion arrived at by science, but is equivalent to saying that there
is no role for philosophy or religion in cosmology, or in life, itself.

The other fundamental option is to develop a philosophical cosmology in which
effects have causes, and something is not nothing, and the universe had an

   Physics and Philosophy                                           Musa Akrami

absolute beginning. It came from something. This something, however, cannot
be a something like the things around us with their fragile hold on existence. It
must be conceived as the source or foundation or fountain of Existence. If we go
in this direction, a very different view of the universe begins to emerge. We
begin to see the universe as a beautiful iridescent rainbow floating on a sea of
Existence. The limited existence of the things around us rests on unlimited
Existence. The universe as a specific kind of universe is a reflection of the
fullness of Existence. By way of analogy we can liken this fullness to the
vacuum of the quantum theorists from which particles appear and disappear.
This vacuum, instead of being empty, is supremely full. It is nothing only in the
sense that it is not like the usual matter and energy we encounter, but rather,
some deeper and richer matrix from which they emerge. If we translate this
image into a properly philosophical arena, we can say that the universe truly and
marvelously exists as the partial expression of a deeper and richer ocean of
Existence from which it has come.

The universe, for example, not only originates from this ocean of Existence, but
continually rests upon it and unfolds and evolves in relationship to this dynamic
ground, this immense ontological field of Existence. If the universe is a partial
and limited reflection of Existence, itself, it is contingent. It does not have to
exist. Therefore we would be mistaken to conceive the universe as some sort of
necessary emanation from Existence itself, for if it were, it would somehow
share in the intrinsic nature of Existence and not have the limited contingent
existence that we experience.

Further, while this universe could have been made out of the matter of a
previous universe, ultimately this contingent matter must have been made
without any such matter, that is, without the use of some contingent pre-existing
material. It has to flow directly from Existence, itself, because only Existence
has the power to make things exist. Once existing things are created, they enter
into causal relationships with each other, that is, relationships of giving and
receiving existence.

Existence and the things it creates are never static. Existence makes something
to be in a certain distinctive way, and this very distinctive kind of existence acts
in a distinctive fashion. This kind of action could be called a law of nature.
These laws are not imposed from without, but are simply the expression of the
particular kind of existence that things have. A proton, for example, has certain
essential qualities, not because those qualities are decreed by some outside
agency, but because they flow from the very being that makes the proton to be
what it is. My point here is not to try to set out in detail such a philosophical
cosmology, but simply to indicate that it exists.

   Physics and Philosophy                                            Musa Akrami

6. [A Religious Cosmology: the Case of] A Christian
Now let’s turn to the kind of cosmology that exists within Christianity. When we
think of the Christian doctrine of the origin of the universe, we first usually think
of Genesis, but while it certainly finds one of its foundations there, we need to
avoid two misunderstandings from the outset.

The first is that of the creationists who imagine that the Scriptures were written
by God dictating its words into the ears of its human authors, and thus every
word must be literally true in some eternal, immutable, and even scientific sense.
Thus if Genesis speaks about the universe created in six days then it must be so
because God certainly knows his science. Therefore their job is to find the
science to back up what he said, and sometimes they can be quite ingenious in
attempting to do so. But they are driven, not by their love of science, but their
love of God, and the result is that they end up opposing not only the anti-
religious biases of some scientists, but science itself, by twisting what it has
discovered to fit into their understanding of Genesis which, in turn, is motivated
by their particular view of biblical inspiration.

Ironically the creationists and their arch foes the scientists who imagine that
their science justifies their disdain of philosophy and religion are really mirror
images of each other, for neither can peacefully and intelligently embrace both
science and religion. Most Christians do not hold to the narrow view of the
creationists about how the Bible is inspired, and don’t look to Genesis for a
scientific account of the origin of the universe. But this does not stop them from
appreciating the central message of Genesis which clearly and graphically
portrays God as the creator of the universe. And many Christians have a genuine
interest and appreciation of modern science either as scientists, themselves, or as
well-educated people in other fields.

The second difficulty in reading Genesis is similar to the first, but is more subtle.
We would be putting an interpretive strain on Genesis if we wanted to find in it
in some explicit way a philosophical cosmology. According to some
commentators, for example, it might not even be possible to find in the first
verses of Genesis a clear enunciation of the doctrine of the creation of the
universe out of nothing. Bruce Vawter, who is of this opinion, renders its first
verses like this: "In the beginning, when God created the heavens and the earth,
the earth was a formless wasteland…"34 And he suggests that the priestly author

   Physics and Philosophy                                            Musa Akrami

could very well have been saying that God’s creation of the world is a process of
organization of the unformed chaos. Questions like where this unformed
wasteland came from would not have entered the author’s mind. If the priestly
author was not writing science, he was not writing metaphysics, either. He is
trying to describe the saving works of God, so creation has to be seen in the
same line as the exodus and all the rest of God’s saving deeds. There is no
contradiction between this kind of approach and the philosophical cosmology we
have begun to become acquainted with. Indeed, later in the book of Machabees,
it appears that the doctrine of creation out of nothing is more clearly articulated,
but we need not, and should not, read into the biblical texts a fully developed
Christian doctrine of creation, for it only slowly evolved in the Scriptures and in
the writings of the Fathers and theologians of the Church. While a Christian
doctrine of creation has much in common with a philosophical cosmology, or
better said, is compatible with such a cosmology, indeed, this philosophical
cosmology grew up in a Christian context, a philosophical cosmology is the fruit
of human reason, and not of faith. The Christian doctrine of creation could be
called a theological cosmology, and has quite a different tone to it. There the
God of creation is certainly Existence, itself, but much more to the point, the
God of creation is the God of Genesis and Exodus, and all the saving deeds in
the Old and New Testaments. In short, God as the Creator is a personal, loving
God who spoke through Jesus and who watches over the birds of the air and the
lilies of the fields. So Christians affirm their belief by saying, "I believe in God,
the Father Almighty, Creator of heaven and earth…" A distillation of the long
development of the Christian doctrine of creation can be found in these kinds of
definitive statements and could be summed up as follows:

God is conceived as a loving Father who is the Creator of everything out of
absolute nothingness. There is no prior matter or field of energy out of which
God makes things.

God’s creative act is free. Things do not necessarily emerge or emanate from
God’s nature, but God decides what to create.

God is the Creator of everything, and everything that God creates is good.

God is not completed or perfected by creating the universe. God acts not out of
need, but freely out of love. God created the universe and everything in it
because God wanted us to have a chance to enjoy it, and each other, and God.

We are thus confronted with three distinctive kinds of cosmologies: a scientific
one, a philosophical one, and a Christian one, which has much in common with
that of Judaism and Islam. They all talk about the same universe, but in different

   Physics and Philosophy                                           Musa Akrami

ways. We could say that each of them with its own way of knowing cuts a
certain intelligible cross-section of the universe out and examines it. A Christian
cosmology, using faith illuminated by reason, sees the universe in the light of a
personal God who created it out of love. A philosophical cosmology sees the
universe in relationship to Existence, itself, and a scientific cosmology looks at
the universe as observable and measurable.

These three approaches do not contradict each other. It is entirely possible to
hold all three of them simultaneously, and to do so gives us an even richer sense
of what the universe is like. Science, philosophical reasoning and faith are not at
odds here. The challenge is to understand the distinctive way of knowing of each
one. This theme of their distinctive ways of knowing is something we are going
to encounter over and over again. To conclude, let’s look at a case study of what
happens when Christians rush to build their theologies and spiritualities upon
science’s latest findings without first scrutinizing what these findings really

7. Christian Spirituality and the New Cosmology
If the creationists fend off science to protect religion, other Christians are much
more open to it, but this openness is not without its challenges. They can
imagine, for example, that the kind of scientific speculation we have been seeing
about quantum theory and the origin of the universe is scientific fact and be
over-hasty in trying to build a philosophy, theology, or spirituality upon it. Or
seeing the unfortunate resistance to science by Christianity, they not only try to
redress the balance, but by way of reaction go too far and appear to leave some
essential aspects of Christianity behind.

"The quantum theory in physics pushes both the scientific imagination and the
religious fascination to new frontiers unknown by previous generations," a
recent book cover tells us, and goes on to cite its author to the effect: "Theology
has no choice but to submit to it, but in the very process it becomes one of the
most exciting fields of exploration today, meriting the title of Quantum
Theology."35 A well-respected journal echoes this sentiment and introduces an
article: "We no longer experience the world as Plato and Aristotle did. The new
physics has seen to that. And its new epistemology leads to a new theology –
one from which fresh truths emerge."36 If a new theology is, indeed, emerging
from the new cosmology, can we go a step further and say that we are on the
threshold of discovering a new spirituality, a Quantum spirituality?

   Physics and Philosophy                                              Musa Akrami

Christian spirituality, aided by the work of people like Matthew Fox, Thomas
Berry and others, has rediscovered a deeper sense of the beauty and wonder of
creation, and the magnificent scientific discoveries of this century tell us of the
explosive beginning of an evolving universe which is filled with a myriad of
galaxies and vast beyond imagining. Ecologically sensitive spiritualities are
helping us see the challenges presented by the dark side of human technology
which has wrought such havoc upon the earth. The importance of these insights
can hardly be overestimated. And if that is what those quantum quotations we
just saw had in mind, we could, in fact, conclude that we are on the brink of an
age of Quantum spirituality, that is, a spirituality receptive to modern science
and sensitive to its ecological responsibilities.

But this vitally important message appears to carry along with it some disturbing
tendencies. At first glance, some of these tendencies appear to be merely a
question of style, or a certain oversimplification for the sake of pedagogy.
Thomas Berry, for example, will call himself a geologian instead of a
theologian, and Matthew Fox will tell us that on one side we have a
fall/redemption spirituality, and on the other, a creation-centered one. The
fall/redemption spirituality has Augustine as its champion, while the creation
spirituality has Jesus and Teilhard. The fall/redemption spirituality urges us to
control our passions, and talks about original sin, while the creation-centered
spirituality is in favor of ecstasy and original blessing. 37

It would certainly be ungracious to complain too much about this kind of
oversimplification if that, indeed, was all it was. But it can give us pause and
make us ask an important question: Just what is the relationship between this
new kind of cosmologically inspired spirituality with Christian theology and
spirituality on the one hand, and with the findings of modern science on the

Let’s look at the first part of this question. Just how does this new style of
spirituality relate to Christian spirituality? Obviously, it is critical of some of the
tendencies of the past, as Matthew Fox’s dichotomies indicate. There can be no
objection to that. Christian spirituality is always in need of renewal. But
legitimate criticism in this kind of cosmologically inspired spirituality has a
tendency to grow to the point of rupture.

We are told, for example, that Thomas Berry "offers a comprehensive
interpretation of the universe, one that goes beyond both science and theology in
and of themselves."38 If we are not immediately sure of what that means, a little
later we read: "For Thomas Berry the universe is primary. He enters with no
distracting agendas drawn from conciliar documents. He does not attempt to see

   Physics and Philosophy                                           Musa Akrami

the universe as a gloss on the Bible. From his point of view, to attempt to cram
this stupendous universe into categories of thought fit for scriptural studies or
systematic theology is to lose the very magnificence that stuns us in the first
place."39 Theology and science are somehow being superseded by a higher
synthesis, and if theology is being surpassed, so is what we have known up until
now as Christian spirituality. The old Christian spirituality was built on faulty
cosmological foundations, we are told, and now must be reconstructed on the
basis of the new cosmology. "The insights of all thinkers previous to our time
are, to varying degrees, conditioned by spatial cosmologies, all of which have
been surpassed. Thomas Berry’s insistence is that until we begin our thinking in
this time-developmental universe, we condemn all our thoughts to conceptual
frameworks in the midst of collapse. How convincing are theologies that are
framed by worldviews no longer regarded as real?"40

We are left with the rather chilling impression that we are not simply renewing
Christian spirituality, but well on the way to replacing it, and this impression is
reinforced, on occasion, by Berry, himself. We are in need of a new story, he
tells us, and the universe is the primary revelation, or primary expression of that
story. But then, are we to conclude that Christian revelation is somehow a
secondary revelation? "I sometimes think that we worry too much about Jesus
Christ. We have a great literature on the Scriptures, we have a great literature on
Jesus, but we have no literature on the natural work and the Christ-universe
equation. I suggest we might give up the Bible for a while, put it on the shelf for
perhaps twenty years. Then we might have a more adequate approach to it. We
need to experience the divine revelation presented to us in the natural world.
Excessive concern with the historical Christ is presently just not that helpful." 41
Am I reading too much into these kinds of statements? I certainly hope so. But
the language used is a bit too intemperate, and so it makes dialogue with
classical Christian theology and spirituality more difficult.

The fundamental issue of whether a cosmologically inspired spirituality is being
presented as a way to renew or even expand our Christian vision, or as a
replacement for it cannot be sidestepped. Let’s look at a more egregious
example. In the past, writes Diarmuid O’Murchu, "only those who believed in
God (as described by formal religion) could be theologians. Quantum theology
seeks to dismantle this exclusivity and open up the theological exploration to
everybody, to all who are prepared to engage with their lived experience of the
universe as a quantum reality."42 Is the next step a quantum spirituality in which
we no longer have the need to believe in God? What we have here, I think, is a
quantum theology that does not seem to hesitate to substitute itself for Christian
theology and spirituality as we have known them. "God is first and foremost a
propensity and power for relatedness, and the divine imprint is nowhere more

   Physics and Philosophy                                         Musa Akrami

apparent than in nature’s own fundamental desire (exemplified in the quarks) to
relate – interdependently and interconnectedly. Questions arise which become
immensely disturbing for orthodox theologians. "Does God, then, have no
independent existence?" "Is God somehow dependent on evolution?" These
questions arise from a certain mode of patriarchal consciousness, characteristic
of our mechanistic age, needing certainty, precision, and authoritative clarity.
They are valid questions, but of no real interest to a quantum theologian."43

Once God has disappeared into some evolutionary process, then historical
Christianity is bound to soon follow. The story, we are told, is more important
than the facts: "Whether or not there was an empty tomb, whether or not
anybody actually saw the Risen Jesus, is not of primary significance. If through
modern archaeological research we were to rediscover the remains of Jesus, thus
establishing that he never rose physically from the grave, that discovery would
not undermine the faith of a genuine believer. It would create immense doubt
and confusion for millions who follow a dogmatic creed rather than a spirituality
of the heart. (It could also be a catalyst for a profound conversion experience.)

Theologians in general and guardians of orthodox religion will find the above
comments quite disturbing; some will consider them to be blatantly heretical." 44
Frankly, I do find them "quite disturbing." This kind of Quantum theology and
whatever kind of Quantum spirituality that could be erected on it has lost its
moorings in genuine Christian faith.

As Robert Brungs writes in a review of O’Murchu’s book, "Unfortunately
O’Murchu’s agendum is much more directed to a new spirituality, one that
replaces religion altogether. He says: "Spirituality is inherent to the human
condition – also to planetary and cosmic growth; in my estimation, religion is
not. Spirituality has an enduring quality, coterminous with human evolution;
religion serves a transitory and temporary purpose." And "as a human species
we are outgrowing our need for formal religion." With such ease he wipes out
Judaism, Christianity, and Islam."45

But aren’t these cosmologically inspired theologies and spiritualities resting on
the firm foundation of the new cosmology? Don’t they have the impressive
weight of modern scientific discoveries behind them? This brings us to the
second part of our central question. What is the relationship between these
spiritualities and modern science? We need to immediately make a distinction
between the basic discoveries of the sciences and their interpretation. We are on
solid ground when our spirituality is inspired by an expanding and evolving
universe, or the insights of ecologists on the web of life that nourishes us and
how that web is being torn apart by our thoughtlessness. But it is quite another

   Physics and Philosophy                                          Musa Akrami

matter when we are dealing with the interpretation of scientific discoveries
either by the scientists, themselves, or by those who would like to use them to
create a new theology and spirituality.

We have looked at some of the things that the scientific cosmologists have been
saying. But what are we to make of them? Are we faced with a genuine solution
to the question of the creation of the universe which, because it just popped into
existence from nothing, has eliminated the need for a Creator? Are we to build a
cosmological spirituality based on this? Of course not. William Craig notes that,
"It is sobering to note… how eagerly and uncritically these theories have been
adopted by popular science writers, even long after their demise (among the
physicists). For example, referring to the quantum vacuum as "the originating
power (which) gave birth to the universe," Brian Swimme and Thomas Berry of
the so-called Center for the Story of the Universe substitute for the Genesis story
what amounts to a scientific mythology for our time: "In the beginning was a
flashing forth of evanescent beings," particles that dissolve back "into the same
night that had given them forth, into non-existence, absorbed back into that
abyss, that originating and annihilating power that is the marrow of the

O’Murchu, following Swimme’s, "being itself arises out of a field of fecund
emptiness," comments, "The ground of the universe then is empty fullness, a
fecund nothingness," and "fecund emptiness is the source of everything that
exists." It predates the big bang, or compared with the traditional doctrine of
creation from nothing, "does little to open us up to the wonder of the quantum
vacuum."47 This way of proceeding is to put science, philosophy and religion
into a blender where they lose their distinctive natures and then can be made to
say just about anything we would like.

The need for an explanation for the origin of the universe still confronts us, and
we don’t need to run about frantically trying to fathom the theological and
spiritual implications of the universe popping into existence from nothing. The
nothing of the physicist is the vacuum of empty space, not the nothing of the
metaphysician, as we saw. The sure findings of physics must be carefully
distinguished from this kind of speculation, and even these sure findings have to
be subjected to a careful philosophical scrutiny before we can determine exactly
what they mean and how they can be used in theology and spirituality.

Another example is in order which illustrates the unfortunate consequences of an
over-hasty attempt to build a new theology and spirituality on the basis of the
new physics. Here we are directly confronted with the "facts" of quantum
physics and their supposed theological and spiritual implications. Heisenberg’s

   Physics and Philosophy                                           Musa Akrami

uncertainty principle states that you cannot measure both the velocity and
position of an electron at the same time. This, in turn, indicates that the electron
is "intrinsically indeterminate,"48 and sometimes mysteriously manifests itself as
a particle, and at other times as a wave. And this indeterminacy, we are told,
leads to a revolution in epistemology that bears fruit in all sorts of new
theological truths.

These strange qualities of the electron help us understand the origin of
consciousness, and if we are bold enough, they lead to revolutionary theological
conclusions. "Divine revelation," for example, "in an indeterminate universe can
neither be complete nor closed."49 "There is no distortion of human nature that
leads to wickedness. We are not a "fallen race" in any sense of "original sin." 50
"We need not wonder why the early Christian church in a static universe yearned
to divinize Jesus literally, but in our time we can recognize the greater
opportunity for the incarnation of all self-reflective creatures, while renewing
the human role of Jesus."51

These conclusions would certainly be revolutionary if they could be shown to be
the direct consequence of the indubitable findings of quantum physics. But they
cannot be. It has become almost commonplace to be told of the indeterminacy of
the microworld in which causality has failed, and to be confronted with the
supposedly strange wave/particle nature of the electron. But, to repeat again,
while quantum theory has produced superb experimental results, physicists from
its very inception have disagreed about what it means. There is no unanimity
among them today that says that some sort of intrinsic indeterminacy reigns in
the microworld, or that it is demonstrated by the wave/particle nature of the
electron. Therefore, it is premature, to say the least, to erect philosophical and
theological structures on such shaky foundations. What is needed is the
development of a deeper philosophical understanding of quantum theory, and
even then it is hard to imagine that it would have much to say about
consciousness, still less revelation, original sin and the historical Jesus.

"I happen to think that the religious conservatives are wrong in what they
believe," writes Steven Weinberg, no fan of religion as we saw, "but at least they
have not forgotten what it means to believe something. The religious liberals
seem to me to be not even wrong.

"Very strange, that the existence and nature of God and grace and sin and
heaven and hell are not important! I would guess that people do not find the
theology of their own supposed religion important, because they cannot bring
themselves to admit that they do not believe in any of it."52

   Physics and Philosophy                                          Musa Akrami

But Weinberg’s remarks leave out two other kinds of participants in the dialogue
between science and religion. One is a small but vocal number of high-profile
scientists who seem to take a certain almost adolescent glee in claiming that
science is irreducibly opposed to Christianity. The other category which I hope
is far larger than all the previous ones is made up of both Christians and
scientists who actually believe that science and Christianity can live in harmony.

What are the results of Experiment 1? There is nothing in the genuine findings
of modern cosmology that makes it more difficult, still less impossible, for
Christians to believe in God as the Creator of the universe. Indeed, cosmology,
itself, seems to point in the direction of the universe having a beginning.

   1. Scientific American, Jan. 2001, p. 54.
   2. Ferris, The Whole Shebang, p. 245-246.
   3. Scientific American, Jan. 1999, p. 68.
   4. Hawking, A Brief History, p. 136.
   5. Ibid., p. 140-141.
   6. Discover, Feb. 1996, p. 71.
   7. UPI, March 25, 2001.
   8. In the Tufts newsletter on web.
   9. Scientific American, Nov. 1994, p. 48.
   10.Ibid., p. 54.
   11.Ibid., p. 54-55.
   12.Discover, April 2002, p. 34.
   13.Ibid., p. 35.
   14.Ibid., p. 36.
   15.Discover, Sept. 2001, p. 41.
   16.Guth, The Inflationary Universe, p.13.
   17.Ibid., p. 275.
   18.Isham, "Quantum Theories of the Creation of the Universe," p. 77ff.
   19.Ibid., p. 78.
   20.Ferris, The Whole Shebang, p. 246.
   21.Ibid., p. 247.
   22.Ibid., p. 247.
   23.Ibid., p. 248.
   24.Ibid., p. 249.
   25.Hawking, Black Holes and Baby Universes, Ch. 6.

  Physics and Philosophy                                        Musa Akrami

   26.Hawking, A Life, p. 168.
   27.Ibid., p. 170.
   28.Frank Tipler, The Physics of Immortality.
   29.William Craig, "Design and the Cosmological Argument," p. 349.
   30.Steven Weinberg, The First Three Minutes, p. 154.
   31.Steven Weinberg interview, Discover, May 2002, p. 18.
   32.Thorne, Black Holes and Time Warps.
   33.Deltete, "Hawking on God and Creation."
   34.Vawter, On Genesis, p. 37.
   35.Diarmuid O’Murchu, Quantum Theology.
   36.James N. Studer, "Consciousness and Reality: Our Entry into Creation," p.
   37.Matthew Fox, Original Blessing, p. 316.
   38.Brian Swimme, "Science: A Partner in Creating the Vision," p. 84.
   39.Ibid., p. 85.
   40.Ibid., p. 87.
   41.Thomas Berry, C.P. "Dialogue with Thomas Clarke, S.J.," in Befriending
      the Earth.
   42.O’Murchu, Quantum Theology, p. 49.
   43.Ibid., p. 83.
   44.Ibid., p. 114.
   45.Brungs, a review of Quantum Theology, p. 440.
   46.William Craig, "Design and the Cosmological Argument," p. 345.
   47.O’Murchu, Evolutionary Faith, p. 44.
   48.Studer, "Consciousness and Reality," p. 16.
   49.Ibid., p. 27.
   50.Ibid., p. 29.
   51.Ibid., pp. 27-28.
   52.As cited in Karl Schmitz-Moormann’s Theology of Creation in an
      Evolutionary World.

Berry, Thomas. 1987. Thomas Berry & and the New Cosmology, edited by Anne
Lonergan. Mystic, CT: Twenty-Third Publications.

_____ 1988. The Dream of the Earth. Sierra Club Nature and Natural
Philosophy Library.

Berry, Thomas, C.P. in Dialogue with Thomas Clarke, S.J. 1991. Befriending
the Earth. Mystic, CT: Twenty-Third Publications.

   Physics and Philosophy                                        Musa Akrami

Brungs, Robert, SJ. 1997. A Review of Quantum Theology by Diarmuid
O’Murchu. Review for Religious, July-Aug. 1997, p. 440.

Craig, William Lane. 1998. "Design & the Cosmological Argument" in
Dembski, William A., Editor. Mere Creation: Science, Faith & Intelligent
Design. Downers Grove, IL: InterVarsity Press.

Davies, Paul. 1990. "What Caused the Big Bang? in Physical Cosmology and
Philosophy by John Leslie. NY: Macmillan Publishing Co.

Deltete, Robert, "Hawking on God and Creation" in Zygon, Dec., 1993, pp. 485-

Ferris, Timothy. 1998. The Whole Shebang. Phoenix.

Folger, Tim. 2001. "Quantum Shmantum" in Discover, Sept. 2001, p. 37-43.

Fox, Matthew. Original Blessing, Bear & Company, 1983, p. 316.

Freedman, David. "The Mediocre Universe" in Discover, February 1996, pp. 65-

Guth, Alan. 1997. The Inflationary Universe: The Quest for a New Theory of
Cosmic Origins. Reading, MA: Helix Books, Addison-Wesley.

Hawking, Stephen. 1988. A Brief History of Time.

_____ 1993. Black Holes and Baby Universes. NY: Bantam.

"How Did the Universe Begin?" in Scientific American. Jan. 2000. p. 68.

Isham, C.J. 1993. "Quantum Theories of the Creation of the Universe" in
Quantum Cosmology and the Laws of Nature. Berkeley, CA: The Center for
Theology and the Natural Sciences.

Lemley, Brad. 2002. "Guth’s Grand Guess" in Discover, April 2002, p. 32-9.

Linde, Andrei. 1994. "The Self-Reproducing Inflationary Universe" in Scientific
American, Nov. 1994, p. 48-55.

O’Murchu, Diarmuid. 1997. Quantum Theology. Crossroad Publications.

   Physics and Philosophy                                       Musa Akrami

_____ 2002. Evolutionary Faith: Rediscovering God in Our Great Story.
Maryknoll, NY: Orbis Books.

Peebles, P. James E. 2001. "Making Sense of Modern Cosmology" in Scientific
American. Jan. 2001, p. 54-5.

Sachs, Mendel. 2000. "Will the 21st Century See a Paradigm Shift in Physics
from the Quantum Theory to General Relativity?" in Revue Internationale de
Philosophie 2/2000, p. 351-368.

Sarna, Nahum M. 1983. "Understanding Creation in Genesis" in Is God a
Creationist?, edited by Roland Mushat Frye. NY: Charles Scribner’s Sons.

Schmitz-Moormann, Karl. 1997. Theology of Creation in an Evolutionary
World. Cleveland, OH: The Pilgrim Press.

Studer, James N. "Consciousness and Reality: Our Entry into Creation" in Cross
Currents. Spring 1998, p. 15.

Swimme, Brian. 1987. "Science: A Partner in Creating the Vision" in Thomas
Berry & and the New Cosmology, edited by Anne Lonergan, Twenty-Third

_____ 1996. The Hidden Heart of the Cosmos. Maryknoll, NY: Orbis Books.

Tipler, Frank. 1994. The Physics of Immortality.

Toolan, David. 2001. At Home in the Cosmos. Maryknoll, NY: Orbis Books.

Tryon, Edward P. 1990. "Is the Universe a Vacuum Fluctuation?" in Physical
Cosmology and Philosophy by John Leslie. NY: Macmillan Publishing Co.

Vawter, Bruce. 1977. On Genesis: A New Reading. Garden City, NY:
Doubleday & Co., Inc.

_____ 1983. "Creationism: Creative Misuse of the Bible" in Is God a
Creationist?, edited by Roland Mushat Frye. NY: Charles Scribner’s Sons.

Weinberg, Steven. 1993. The First Three Minutes: A Modern View of the Origin
of the Universe. BasicBooks.

   _____ 2002. Interview in Discover, May 2002, p. 18.

   Physics and Philosophy                                           Musa Akrami

Chapter12. Philosophy of space and
1. Absolutism vs. Relationalism
2. Conventionalism
3. The structure of spacetime
    3.1. Invariance vs. Covariance
    3.2. Historical Frameworks
    3.3. Holes
4. The direction of time
    4.1. The Causation solution
    4.2. The Thermodynamics solution
    4.3. The Laws Solution
5. The flow of time
6. Dualities
7. Quantum gravity
8. References

          Introductory remaks
          Philosophy of Space and Time is a branch of philosophy
          which deals with issues surrounding the ontology,
          epistemology and character of space and time. While this type
          of study has been central to philosophy from its inception, the
          philosophy of space and time, an inspiration for, and central to
          early analytic philosophy, focusses the subject into a number of
          basic issues.

1. Absolutism vs. Relationalism
The debate between whether space and time are real objects themselves, i.e
absolute, or merely orderings upon real objects, i.e. relational, began with a
debate between Isaac Newton, through his spokesman Samuel Clarke, and
Gottfried Leibniz in the famous Leibniz-Clarke Correspondence.

From Wikipedia, the Free Encyclopedia

   Physics and Philosophy                                                Musa Akrami

Arguing against the absolutist position, Leibniz offers a number of thought
experiments aiming to show that assuming the existence of facts such as
absolute location and velocity will lead to contradiction. These arguments trade
heavily on two principles central to Leibniz's philosophy: the Principle of
Sufficient Reason and the Identity of indiscernibles.

For example, Leibniz asks us to imagine two universes situated in absolute
space. The only difference between them is that the second is placed five feet to
the left of the first, a possibility available if such a thing as absolute space exists.
Such a situation, however, is not possible according to Leibniz, for if it were: a)
where a universe was positioned in absolute space would have no sufficient
reason, as it might very well have been anywhere else, hence contradicting the
Principle of Sufficient Reason, and b) there could exist two distinct universes
that were in all ways indiscernible, hence contradicting the Identity of

Standing out in Clarke's, and Newton's, response to Leibniz arguments is the
bucket argument. In this response, Clarke argues for the necessity of the
existence of absolute space to account for phenomena like rotation and
acceleration that cannot be accounted for on a purely relationalist account.
Since, Clarke argues, the curvature of the water in the rotating bucket can only
be explained by stating that the bucket is rotating, and that the relational facts
about the bucket are the same for the stationary and rotating bucket, then the
bucket must be rotating in relation to some third thing, namely absolute space.

Stepping into this debate in the 19th century is Ernst Mach. Not denying the
existence of phenomena like that seen in the bucket argument, he still denied the
absolutist conclusion by offering a different answer as to what the bucket was
rotating in relation to: the fixed stars. Mach argues that thought experiments like
the bucket argument are problematic because we cannot reason as to what would
happen in a universe with only a bucket and otherwise empty. A bucket rotating
on the earth is different relationally from one at rest, e.g. in its relation to the tree
from which the rope is hanging. While the surrounding matter of the tree, the
earth and the universe in general would seem inconsequential, Mach argues to
the contrary pioneering Mach's principle.

Perhaps the most famous relationalist is Albert Einstein who saw his General
Theory of Relativity as vindicating Mach's intuition that the fixed stars play a
part in which motions are inertial and which aren't, by offering a rigorous
scientific formulization.

   Physics and Philosophy                                            Musa Akrami

Contemporary philosophy, however, is not quite as unanimous about the import
of the GTR on the absolutism/relationalism debate. One popular line of thinking
believes that the results are mixed. While the GTR offers the relationalist
success, by placing views in which there are absolute facts about position,
velocity and acceleration in a compromised position, so too is classic
relationalism compromised by the existence of solutions to the equations of the
GTR in which the universe is empty of matter.

2. Conventionalism
The position of conventionalism states that there is no fact of the matter as to the
geometry of space and time, but that it is decided by convention. The first
proponent of such a view, Henri Poincare, reacting to the creation of the new
non-euclidean geometry, argued that which geometry applied to a space was
decided by convention, since different geometries will describe a set of objects
equally well, based on considerations from his sphere-world.

This view was developed and updated to include considerations from relativistic
physics by Hans Reichenbach. Reichenbach's conventionalism, applying to
space and time, focusses around the idea of coordinative definition.

Coordinative definition has two major features. The first has to do with
coordinating units of length with certain physical objects. This is motivated by
the fact that we can never directly apprehend length. Instead we must choose
some physical object, say the Standard Metre at the Bureau International des
Poids et Mesures (International Bureau of Weights and Measures), or the
wavelength of cadmium to stand in as our unit of length. The second feature
deals with separated objects. Although we can, presumably, directly test the
equality of length of two measuring rods when they are next to one another, we
can not find out as much for two rods distant from one another. Even supposing
that two rods, whenever brought near to one another are seen to be equal in
length, we are not justified in stating that they are always equal in length. This
impossibility undermines our ability to decide the equality of length of two
distant objects. Sameness of length, to the contrary, must be set by definition.

Such a use of coordinative definition is in effect, on Reichenbach's
conventionalism, in the GTR where light is assumed, i.e. not discovered, to mark
out equal distances in equal times. After this setting of coordinative definition,
however, the geometry of spacetime is set.

   Physics and Philosophy                                            Musa Akrami

As in the absolutism/relationalism debate, contemporary philosophy is still in
disagreement as to the correctness of the conventionalist doctrine. While
conventionalism still holds many proponents, cutting criticisms concerning the
coherence of Reichenbach's doctrine of coordinative definition have led many to
see the conventionalist view as untenable.

3. The structure of spacetime
Building from a mix of insights from the historical debates of absolutism and
conventionalism as well as reflecting on the import of the technical apparatus of
the General Theory of Relativity details as to the structure of spacetime have
made up a large proportion of discussion within the philosophy of space and
time, as well as the philosophy of physics. The following is a short list of topics.

3.1. Invariance vs. Covariance
Bringing to bear the lessons of the absolutism/relationalism debate with the
powerful mathematical tools invented in the 19th and 20th century, Michael
Friedman draws a distinction between invariance upon mathematical
transformation and covariance upon transformation.

Invariance, or symmetry, applies to objects, i.e. the symmetry group of a space-
time theory designates what features of objects are invariant, or absolute, and
which are dynamical, or variable.

Covariance applies to formulations of theories, i.e. the covariance group
(mathematics) designates in which range of coordinate systems the laws of
physics hold.

This distinction can be illustrated by revisiting Leibniz's thought experiment, in
which the universe is shifted over five feet. In this example the position of an
object is seen not to be a property of that object, i.e. location is not invariant.
Similarly, the covariance group for classical mechanics will be any coordinate
systems that are obtained from one another by shifts in position as well as other
translations allowed by a Galilean transformation

In the classical case, the invariance, or symmetry, group and the covariance
group coincide, but, interestingly enough, they part ways in relativistic physics.
The symmetry group of the GTR includes all differentiable transformations, i.e.
all properties of an object are dynamical, in other words there are no absolute

   Physics and Philosophy                                            Musa Akrami

objects. The formulations of the GTR, unlike that of classical mechanics, do not
share a standard, i.e. there is no single formulation paired with transformations.
As such the covariance group of the GTR is just the covariance group of every

3.2. Historical Frameworks
A further application of the modern mathematical methods, in league with the
idea of invariance and covariance groups, is to try to interpret historical views of
space and time in modern, mathematical language.

In these translations, a theory of space and time is seen as a manifold paired with
vector spaces, the more vector spaces the more facts there are about objects in
that theory. The historical development of spacetime theories is generally seen to
start from a position where many facts about objects or incorporated in that
theory, and as history progresses, more and more structure is removed.

For example, Aristotle's theory of space and time holds that not only is there
such a thing as absolute position, but that there are special places in space, such
as a center to the universe, a sphere of fire, etc. Newtonian spacetime has
absolute position, but not special positions. Galilean spacetime has absolute
acceleration, but not absolute position or velocity. And so on.

3.3. Holes
With the GTR, the traditional debate between absolutism and relationalism has
been shifted to the question as to whether or not spacetime is a substance, since
the GTR largely rules out the existence of, e.g., absolute positions. One powerful
argument against spacetime substantivalism, offered by John Earman is known
as the "hole argument".

This is a technical mathematical argument but can be paraphrased as follows:

Define a function d as the identity function over all elements over the manifold
M, excepting a small neighbourhood (topology) H belonging to M. Over H d
comes to differ from identity by a smooth function.

With use of this function d we can construct two mathematical models, where
the second is generated by applying d to proper elements of the first, such that
the two models are identical prior to the time t=0, where t is a time function
created by a foliation of spacetime, but differ after t=0.

   Physics and Philosophy                                            Musa Akrami

These considerations show that, since substantivalism allows the construction of
holes, that the universe must, on that view, be indeterministic. Which, Earman
argues, is a case against substantivalism, as the case between determinism or
indeterminism should be a question of physics, not of our commitment to

4. The direction of time
The problem of the direction of time arises directly from two contradictory facts.
Firstly, the laws of nature, i.e. our fundamental physics, are time-reversal
invariant. In other words, the laws of physics are such that anything that can
happen moving forward through time is just as possible moving backwards in
time. Or, put in another way, through the eyes of physics, there will be no
distinction, in terms of possibility, between what happens in a movie if the film
is run forward, or if the film is run backwards. The second fact is that our
experience of time, at the macroscopic level, is not time-reversal invariant.
Glasses fall and break all the time, but shards of glass do not put themselves
back together and fly up on tables. We have memories of the past, and none of
the future. We feel we can't change the past but can affect the future.

4.1. The Causation solution
One of the two major families of solution to this problem takes a more
metaphysical tack. In this view the existence of a direction of time can be traced
to an asymmetry of causation. We know more about the past because the
elements of the past are causes for the effect that is our perception. We feel we
can't affect the past and can affect the future because we can't affect the past and
can affect the future. And so on.

Traditionally, there are seen to be two major difficulties with this view. The
most important is the difficulty of defining causation in such a way that the
temporal priority of the cause over the effect is not so merely by stipulation. If
that is the case, our use of causation in constructing a temporal ordering will be
circular. The second difficulty, doesn't challenge the views consistency, but its
explanatory power. While the causation account, if successful may account for
some temporally asymmetric phenomena like perception and action, it does not
account for many other time asymmetric phenomena, like the breaking glass
described above.

   Physics and Philosophy                                           Musa Akrami

4.2. The Thermodynamics solution
The second major family of solution to this problem, and by far the one that has
generated the most literature, finds the existence of the direction of time as
relating to the nature of thermodynamics.

The answer from classical thermodynamics states that while our basic physical
theory is, in fact, time-reversal symmetric, thermodynamics is not. In particular,
the second law of thermodynamics states that the net entropy of a closed system
never decreases, and this explains why we often see glass breaking, but not
coming back together.

While this would seem a satisfactory answer, unfortunately it was not meant to
last. With the invention of statistical mechanics things get more complicated. On
one hand, statistical mechanics is far superior to classical thermodynamics, in
that it can be shown that thermodynamic behavior, glass breaking, can be
explained by the fundamental laws of physics, paired with a statistical postulate.
On the other hand, however, statistical mechanics, unlike classical
thermodynamics, is time-reversal symmetric. The second law of
thermodynamics, as it arises in statistical mechanics merely states that it is
overwhelmingly likely that net entropy will decrease, it is not an absolute law.

Current thermodynamic solutions to the problem of the direction of time aim to
find some further fact, or feature of the laws of nature to account for this

4.3. The Laws Solution
A third type of solution to the problem of the direction of time, although much
less represented, argues that the laws are not time-reversal symmetric. For
example, certain processes in quantum mechanics, relating to the weak nuclear
force, are deemed as not time-reversible, keeping in mind that when dealing with
quantum mechanics time-reversibility is comprised by a more complex

Most commentators find this type of solution insufficient because a) the types of
phenomena in QM that are time-reversal symmetric are too few to account for
the uniformity of time-reversal assymmetry at the macroscopic level and b) there
is no guarantee that QM is the final or correct description of physical processes.

   Physics and Philosophy                                            Musa Akrami

One recent proponent of the laws solution is Tim Maudlin who argues that, in
addition to quantum mechanical phenomena, our basic spacetime physics, i.e.
the General Theory of Relativity, is time-reversal asymmetric. This argument is
based upon a denial of the types of definitions, often quite complicated, that
allow us to find time-reversal symmetries, arguing that these definitions
themselves are the cause of there appearing to be a problem of the direction of

5. The flow of time
The problem of the flow of time, as it has been treated in analytic philosophy,
owes its beginning to a paper written by J. M. E. McTaggart. In this paper
McTaggart introduces two temporal series that are central to our understanding
of time. The first series, which means to account for our intuitions about
temporal becoming, or the moving Now, is called the A-series. The A-series
orders events according to their being in the past, present or future, simpliciter
and in comparison to each other. The B-series, which does not worry at about
the "when" of the present moment, orders all events as earlier than, and later

McTaggart, in his paper The Unreality of Time, argues that time is unreal since
a) the A-series is inconsistent and b) the B-series alone cannot account for the
nature of time as the A-series describes an essential feature of it.

Building from this framework, two camps of solution have been offered. The
first, the A-theorist solution, takes becoming as the central feature of time, and
tries to construct the B-series from the A-series by offering an account of how
B-facts come to be out of A-facts. The second camp, the B-theorist solution,
takes as decisive McTaggart's arguments against the A-series and tries to
contruct the A-series out of the B-series, for example, by temporal indexicals.

6. Dualities
Quantum field theory models have shown it is possible for theories in two
different spacetime backgrounds, like AdS/CFT or T-duality, to be equivalent.

  Physics and Philosophy                                       Musa Akrami

7. Quantum gravity
Quantum gravity calls into question many previously held assumptions about

      Albert, David (2000) Time and Chance. Harvard
      Earman, John (1989). World Enough and Space-Time. MIT
      Friedman, Michael (1983) Foundations of Space-Time Theories.
      Grunbaum, Adolf (1974) Philosophical Problems of Space and Time, 2nd
       Ed. Boston Studies in the Philosophy of Science. Vol XII. D. Reidel
      Horwich, Paul (1987) Asymmetries in Time. MIT Press
      Mellor, D.H. (1998) Real Time II. Routledge
      Reichenbach, Hans (1958) The Philosophy of Space and Time. Dover
      ---(1991) The Direction of Time. University of California
      Sklar, Lawrence (1976) Space, Time, and Spacetime. University of

   Physics and Philosophy                                            Musa Akrami

   Chapter13. [Philosophy of]Time

          1. What should a philosophical theory of time do ?
          2. How is time related to mind ?
          3. What is time ?
          4.What does science require of time ?
          5. What sort of time travel is possible ?
          6. Is the relational theory of time preferable to the absolute
          theory ?
          7. Does time flow ?
          8. What gives time its direction or "arrow ?"
                a. What needs to be explained?
                b. Explanations or theories of the arrow
                c. Multiple arrows
                d. Reversing time
          9. Is only the present real ?
          11. Are there essentially tensed facts ?
          11. What is temporal logic, the symbolic logic of time ?

              12. Supplement of frequently asked questions
                 References and Further Reading

By Bradley Dawden

    Physics and Philosophy                                           Musa Akrami

Introductory remark
Time has been studied by philosophers and scientists for 2,500 years, and thanks
to this attention it is much better understood today. Nevertheless, many issues
remain to be resolved: what time actually is ;whether time exists when nothing is
changing; what sort of time travel is possible, why the time dimension has an
arrow but a space dimension does not; whether the future is real; how to analyze
the metaphor of time's "flow"; whether there was a time before the Big Bang;
whether tensed or tenseless concepts are semantically basic; what is the proper
formalism or logic that captures the special role that time plays in reasoning; and
what are the neural mechanisms that account for our experience of time .

 Of these issues, the general public is interested mostly in time travel .Einstein's
 special theory of relativity implies that you can travel into someone else's future
 by high speed travel in space. Travel into the past is more controversial, but
 doesn't appear to be inconsistent with relativity theory .Several physicists have
 produced novel suggestions on how to create time machines that exploit regions
 of space-time that curve back onto themselves ,either naturally or by human

 Philosophers of time are deeply divided on the question on what sort of
 ontological differences there are among the present, past and future .Presentists
 argue that necessarily only present objects and present experiences are real; and
 we conscious beings recognize this in the special "vividness" of our present
 experience. The growing-universe theory is that the past and present are both
 real, but the future is not yet real. The most popular view is that there are no
 significant ontological differences among present, past and future. This view is
 called "eternalism" or "the block universe theory ".

 This raises the issue of tenseless versus tensed theories of time. The block
 universe theory implies a tenseless theory. In the earliest version of this theory,
 it is declared that tensed terminology (such as "will win" within the sentence
 "The Lakers will win the basketball game") is not semantically basic ,but instead
 is analyzable into tenseless terms (such as "does win at time t" and" happens
 before" and "is simultaneous with"). Once all tenseless facts are fixed, all tensed
 facts are thereby fixed. In later versions of the tenseless theory, the claim is not

   Physics and Philosophy                                            Musa Akrami

made that tensed terminology is removable or reducible ,but only that the truth
conditions of tensed remarks can be handled with tenseless facts. On the other
hand, advocates of a tensed theory of time say that tenseless terminology is not
semantically basic but can be analyzed in tensed terms, and tensed facts are
needed. For example, a tensed theory might imply that the world involves
irreducible tensed properties such as presentness or now-ness or being-in-the-
present, and no adequate account of the present tensed fact that it's now
midnight can be given without these tensed properties .So, the philosophical
debate is over whether tensed concepts have semantical priority over untensed
concepts, and whether tensed facts have ontological priority over untensed facts .

This article explores to some extent what is now known about time, but it
focuses upon what is controversial and unresolved, by addressing the questions
set forth in the table of contets of this article.

1. What should a philosophical theory of time do ?
Ideally we would like a philosophical theory of time to provide a definition of
the term "time." Can we begin the search for a theory of time by starting with a
short definition of time? Perhaps, but there are two considerations that must be
faced. First, the definition will not be able to define time in terms of more
primitive, yet familiar, notions. Second, succinct definitions of time are rarely
helpful unless they are backed up with a more elaborate and systematic
treatment of time. The brief definitions that stand alone are either trivial( Time is
the collection of instants) or too imprecise (Time is the dimension of causality)
or circular (Time is what keeps everything from happening all at once) or simply
cryptic (Time is the flow of events past the stationary I). When philosophers ask ,
"What is time ,"?they normally are asking for a philosophical theory designed to
answer many of the philosophical questions about time such as whether the past-
present-future distinction is objective and how we should understand the flow of
time. A succinct definition of time will be adequate only insofar as it is backed
up by this more elaborate theory.

Although there are theories of how to solve a specific problem about time, it is
always better to knit together solutions to several problems. Ideally, the goal is
to produce a theory of time that will solve in a systematic way the constellation
of problems involving time. What are those problems ?

   Physics and Philosophy                                           Musa Akrami

One is to clarify the relationship between time and the mind .It is easy to
confuse time itself and the perception of time. Does time exist for beings that
have no minds?

We have many intuitions about time. Some of these may reflect deep insights
into the nature of time, and others may be faulty ideas inherited from our
predecessors. It is not obvious which is which. How should a philosophical
theory of time treat our intuitions about time? For one example, if our intuition
is that time flows smoothly, but science implies otherwise, then which view
should get priority ?

A philosophical theory of time should reveal what physical science presupposes
and implies about time, and a later section of this article examines this topic.
Most all philosophers of time claim that philosophical theories should be
consistent with physical science, or, if not ,then they must accept the heavy
burden of proof to justify the inconsistency .

A philosophical theory of time should describe the relationship between instants
and events. Does the instant that we label as "11:01 AM" for a certain date exist
independently of the events that occur then? In other words, can time exist if no
event is happening? This question raises the thorny metaphysical issue of
absolute vs. relational theories of time.

A theory of time should address the question of time's apparent direction. If the
projectionist in the movie theater (cinema) shows a film of cream being added
into black coffee but runs the film backwards, we in the audience can
immediately tell that events couldn't have occurred this way. We recognize the
arrow of time because we know about the one-directional processes in nature.
This arrow becomes less and less apparent to us viewers as the film subject gets
smaller and smaller and the time interval gets shorter and shorter until finally we
are viewing processes that could just as easily go the other way, at which point
the arrow of time has disappeared. Philosophers disagree about the explanation
of the arrow. Could it be a consequence of the laws of science? The arrow
appears to be very basic for understanding nature ,yet it is odd that asymmetries
in time don't appear in most of the basic dynamical laws of physics.
Philosophers also wonder what life would be like in some far off corner of the
universe if the arrow of time were reversed there .Would our counterparts walk
backwards up steps while remembering the future?

Another philosophical problem about time concerns the two questions, "What is
the present moment and why does it move into the past?" How long does the
present last? Present events seem to flow by, receding ever farther into the past.

   Physics and Philosophy                                             Musa Akrami

Many philosophers are suspicious of this notion of the flow of time or the march
of time. They doubt whether it is a property of time as opposed to being some
feature of human perception. Assuming time does flow, is the flow regular?
With some theories time, we can make sense of Friday seconds lasting much
longer than Thursday seconds, as the flow of Friday time slows to a crawl.

Some philosophers are suspicions about whether the future or past are somehow
as real as the present, the feature that is referred to by the word" now ".But some
argue that, if the future were real, then it would be fixed now, and we would not
have the freedom to affect that future ,so it can't be real.

For a last example of a philosophical issue regarding time, is time a fundamental
feature of nature, or does it emerge from more basic features--in analogy to the
way the smoothness of water flow emerges from the complicated behavior of the
underlying atoms ?

A full theory of time should address this constellation of philosophical issues
about time. Narrower theories of time will focus on resolving a few members of
this constellation, but the long-range goal is to knit together these theories into a
full, systematic theory of time.

2. How is time related to mind ?
Physical time is public time, the time that clocks are designed to measure .
Psychological time is private time. It is best understood as being consciousness
of physical time. Psychological time passes slowly for someone who is waiting
anxiously for the water to boil on the stove, and it passes swiftly for someone
enjoying a book and paying no attention to the water on the stove. Psychological
time is completely transcended in the mental state called " nirvana." Meanwhile,
the clock by the stove is measuring physical time and is not affected by
consciousness. When a physicist defines speed to be the rate of change of
position with respect to time, the term "time" refers to physical time. Physical
time is more basic for helping us understand our shared experiences in the
world, and so it is more useful than psychological time for doing science. But it
is vitally important for understanding many human thought processes. We even
have a sense of the passage of time during our sleep, and we awake knowing
we've slept for one night, not one year. But if we've been under a general
anesthetic and wake up, we have no sense of how long we've been unconscious.
Psychological time almost stopped.

   Physics and Philosophy                                            Musa Akrami

On the standard view of human history, first there was time, then came the
sensation of time, then the idea of time, and finally the word "time." Having the
idea or concept was dependent on the evolution of conscious organisms. Any
organism's sense of time is subjective, but is the time that is sensed also
subjective, a mind-dependent phenomenon? If it were subjective in the way
judgments of good food or good music are subjective, then it would be
miraculous that everyone can so easily agree on the ordering of public events in
time .First, Einstein was born, then he went to school, then he died. Everybody
agrees that it happened in this order: birth, school, death. No other order .The
agreement on time order for so many phenomena suggests time is an objective
phenomenon not dependent on being consciously experienced. But maybe it is
not. Maybe time is really subjective because all minds think alike about time
order. If so, our concept of time would be intersubjective, though not arbitrarily

If there were no minds, would time be absent, too? Aristotle raised the
metaphysical question: "Whether, if soul (mind) did not exist, time would exist
or not, is a question that may fairly be asked; for if there cannot be some one to
count there cannot be anything that can be counted [ "...Physics ,chapter 14]. He
doesn't answer his own question because, he says rather profoundly, it depends
on whether time is the conscious numbering of movement or instead is just the
capability of movement's being numbered were consciousness to exist.
Aristotle's distinction foreshadows the modern distinction between
psychological time and physical time.

St. Augustine ,adopting a subjective view of time, said time is nothing in reality
but exists only in the mind's apprehension of that reality. Henry of Ghent and
Giles of Rome both said time exists in reality as a mind-independent continuum,
but is distinguished into earlier and later parts only by the mind. In the 11th
century, the Persian philosopher Avicenna doubted the existence of physical
time, arguing that time exists only in the mind due to memory and expectation.
In the 13th century, Duns Scotus disagreed with all these philosophers and
recognized both physical and psychological time.

At the end of the 18th century ,Kant suggested a subtle relationship between
time and mind--that our mind structures our perceptions so that we know a priori
that time is like a mathematical line. Time is, on this theory, a form of conscious

The controversy in metaphysics between idealism and realism is that, for the
idealist, nothing exists independently of the mind. If this controversy is settled in

   Physics and Philosophy                                           Musa Akrami

favor of idealism, then time, too, would have that subjective feature--physical
time as well as psychological time.

Another philosophical issue involving time and mind is how to account for our
"feeling" that time passes, that it flows? Philosophers disagree about whether
this flow is an objective feature of reality or is, instead, entirely a feature of
human perception. This is an issue even if it is agreed that time itself is
objective. Section 7 below is devoted to the topic of the flow of time .Within
the field of cognitive science, one wants to know what are the neural
mechanisms that account for our experience of time, but so far very little
progress has been made on this fascinating topic .

3. What is time ?
A wide variety of short answers have been given to the question "What is
time?" Some are backed up by more elaborate theories of time, and some are
not .The success of that backup theory is what supports the answer. For
example, the most popular answer to "What is time?" is that it is a certain system
of relations among instantaneous events. This is the answer offered by some
philosophers, for example, Adolf Grünbaum, who want to apply the
contemporary mathematical theory of continuity to physical processes. How do
we tell whether this is the correct answer? To be convinced, we need to be told
what the relevant terms mean, such as "certain system of relations;" we need to
be presented with a theory of time implying that time is this system of relations ;
and we need to be shown how that theory adequately addresses the many
features mentioned above that are required for a successful theory of time.
Another answer to the question "What is time?" is that time is the form of
becoming. To assess this answer, from Alfred North Whitehead, we need to be
told what the term "form of becoming" means; we need to be presented with a
detailed theory of time implying that time is the form of becoming; and we need
to investigate how it addresses those many features required for a successful
theory of time. The metaphysical attitude being expressed here is that problem
solving is a guide to what exists. It is analogous to the attitude in the philosophy
of mathematics that declares zero to exist because zero is so useful in providing
us with solutions to the numerical equation x + b = c in the special case when b

If physical time ,psychological time, and biological time are three different kinds
of time, then three answers are required to the question "What is time?" and
some commentary is required regarding their relationships, such as whether one

   Physics and Philosophy                                           Musa Akrami

is the most fundamental. Many philosophers of science argue that physical time
is the most fundamental of the three even though psychological time is
discovered first by each of us as we grow out of our childhood, and even though
psychological time was discovered first as we human beings evolved from our
animal ancestors. The remainder of this article will focus on physical time.

One way to answer the question "What is time?" is to declare that it is whatever
the time variable t is denoting in the best-confirmed and most fundamental
theories of current science. Then one can inspect those theories noting what
science requires of time--for example, that any duration be a linear continuum of
instants--and in this way know all there is to know. A later section of this article
is devoted to revealing what science requires time to be .Many philosophers
complain that this approach to the answer is methodologically suspect because
the nature of physical time can be revealed only with a philosophical theory of
time that addresses the many philosophical issues that scientists don't concern
themselves with .

Some philosophers, notably Zeno and McTaggart, answer the question, "What is
time?" by replying that it is nothing because it doesn't exist. In a similar vein,
the early 20th century English philosopher F. H. Bradley argues, "Time, like
space, has most evidently proved not to be real, but a contradictory
appearance....The problem of change defies solution." However, most
philosophers agree that time does exist. They just can't agree on what it is.
Physicists are convinced of the objective existence of time by the argument at
the end of the section Why are some standard clocks better than others ?in the
Supplement of Frequently Asked Questions that accompanies this article.

Whatever time is, it is not "time." One has four letters; the other does not.
However, it can be helpful to learn not only the reference of the word " time" but
also its sense or meaning. Should the proper answer to the question" What is
time?" produce a definition of the word? Definitely not--if the definition must
be some analysis that provides a simple paraphrase in all its occurrences. There
are just too many varied occurrences of the word: time out ,behind the times, in
the nick of time, and so forth .

But how about a definition that is more realistic? Might it be helpful to explore
the grammar of the term "time" in either ordinary language or the physics
literature? Most philosophers today would agree with Prior who remarked that,
"there are genuine metaphysical problems, but I think you have to talk about
grammar at least a little bit in order to solve most of them." However, do we
learn enough about what time is when we learn about the grammatical intricacies
of the word? Ordinary-language philosophers are especially interested in time

   Physics and Philosophy                                          Musa Akrami

talk, in what Wittgenstein called the" language game" of discourse about time,
but most philosophers of time who are trying to answer our question are not
especially interested in confining their attention to conceptual analysis. Most
want to uncover important features about time itself .

That was Aristotle's goal when he asked, "What is time "?Aristotle provided an
early ,careful answer to our question by remarking that time is the "number of
movement in respect of the before and after, and is continuous.... In respect of
size there is no minimum; for every line is divided ad infinitum .Hence it is so
with time" [Physics ,chapter 11]. Occasionally Aristotle spoke as if time were
motion, but in these passages [especially in Physics ,chapter 14], he asserts that
time, though linked to motion, is neither the circular motion of the heavens
(Plato's view) nor any other motion .Because motion is the paradigm example of
change [it's a change of place over time], Aristotle agreed that time is "some
aspect of change" [Physics ,chapter 11]. Although Aristotle did say "time is the
measure of change" [Physics ,chapter 12], he believed time is not something by
which we count change but rather some aspect of change that is countable.
Aristotle envisioned an intimate connection between time and change that is
now referred to as the relational theory of time; he believed that time relates
different states of substances, and that "there is no time apart from change "....
[Physics ,chapter 11]. Nevertheless he was very clear" that time is not change
[itself]" because a change "may be faster or slower ,but not time…" [Physics ,
chapter 10], that is, because a change can have a property that time cannot have.

René Descartes had a very different answer to "What is time?" He argued that a
material body has the property of spatial extension but no inherent capacity for
temporal endurance ,and that God by his continual action recreates the body at
each successive instant. Time, therefore, is a divine process of re-creation .

In the 17th century, the English physicist Isaac Barrow rejected Aristotle's
linkage between time and change by saying that time is something which exists
independently of motion or change and which existed even before God created
the matter in the universe. Barrow's student, Isaac Newton, agreed. Newton
argued very specifically that time and space are an infinitely large container for
all events, and that the container exists with or without the events. Space and
time are not material substances, he added, but are like substances, in not being
dependent on matter or motions or anything else except God .

Gottfried Leibniz objected. He argued that time is not an entity existing
independently of actual events. He insisted that Newton had underemphasized
the fact that time necessarily involves an ordering of any pair of non-

   Physics and Philosophy                                           Musa Akrami

simultaneous events. This is why time "needs" events, so to speak. Leibniz
added that this overall order is time .

In the 18th century, Immanuel Kant said time and space are forms that the mind
projects upon the external things-in-themselves. He spoke of our mind
structuring our perceptions so that space always has a Euclidean geometry, and
time has the structure of the mathematical line. Kant's idea that time is a form of
apprehending phenomena is probably best taken as suggesting that we have no
direct perception of time but only the ability to experience things and events in
time. Some historians distinguish perceptual space from physical space and say
that Kant was right about perceptual space. It's difficult, though, to get a clear
concept of perceptual space. If physical space and perceptual space are the same
thing, then Kant is claiming we know a priori that physical space is Euclidean.
With the discovery of non-Euclidean geometries in the 1820s, and with
increased doubt about the reliability of Kant's method of transcendental proof,
the view that truths about space and time are apriori truths began to lose favor.

In 1924, Hans Reichenbach defined time order in terms of possible cause. Event
A happens before event B if A could have caused B but B couldn't have caused
A. This was the first causal theory of time .Its usefulness depends on a
clarification of the notorious notions of causality and possibility without
producing a circular explanation that presupposes an understanding of time
order. Reichenbach's idea was that causal order can be explained in terms of the
"fork asymmetry". The asymmetry is due to the fact that outgoing processes
from a common center tend to be correlated with one another, but incoming
processes to a common center are uncorrelated. [Do you remember tossing a
rock into a still pond? Imagine what the initial conditions at the edge of a pond
must be like to produce correlated, incoming, concentric water waves that would
expel the rock and leave the water surface smooth.] Some philosophers argue
that temporal asymmetry, but not temporal priority, can be analyzed in terms of
causation. But even if Reichenbach were correct that temporal priority can be
analyzed in terms of causation, the question remains whether time itself can be
analyzed in those terms .

The usefulness of the causal theory also depends on a refutation of David
Hume's view that causation is simply a matter of constant conjunction [that is ,
always being together]. For Hume ,there is nothing metaphysically deep about
causes preceding their effects; it's just a matter of convention that we use the
terms "cause" and "effect" to distinguish the earlier and later members of a pair
of events which are related by constant conjunction.

   Physics and Philosophy                                            Musa Akrami

During history, a variety of answers have been given to the question of whether
time is like a line or, instead, like a circle. The concept of linear time first
appeared in the writings of the Hebrews and the Zoroastrian Iranians .The
Roman writer Seneca also advocated linear time. Plato and and most other
Greeks and Romans believed time to be motion and believed cosmic motion was
cyclical, but this wasn't envisioned as requiring any detailed endless repetition
such as the multiple rebirths of Socrates. However, the Pythagoreans and some
Stoic philosophers did adopt this drastic position .

With circular time, you can be assured that after your death you will be reborn.
The future will become the past. If time is like this, then the question arises as
to whether there would be an endless number of times when each state of the
world reoccurred, or whether, accepting Leibniz's Principle of the Identity of
Indiscernibles, each supposedly repeating state of the world would occur just
once because each state would be not be discernible from the repeated state .

Islamic and Christian theologians adopted the Jewish-Zoroastrian notion that
time is linear with the universe being created at a definite moment in the past .
Augustine insisted that human experience is a one-way journey from Genesis to
Judgment, regardless of any recurring patterns or cycles in nature. In the
Medieval period ,Thomas Aquinas agreed .Nevertheless, it was not until 1602
that the concept of linear time was clearly formulated--by the English
philosopher Francis Bacon. In 1687, Newton advocated linear time when he
represented time mathematically by using a line rather than a circle. The concept
of linear time was promoted by Barrow, Leibniz, Locke and Kant. In 19th
century Europe, the idea of linear time became dominant in both science and
philosophy. However, in the twentieth century ,Gödel and others discovered
solutions to the equations of Einstein's general theory of relativity that allowed
closed loops of proper time .These causal loops or closed curves in spacetime
allow you to go forward continuously in time until you arrive back into your
past. You might even meet your younger self. If so, we should revise our
definition of" person." The logic of the term "time" that is embedded in our time
talk does not rule out a nonlinear structure for time, but there is no reason to
believe (physical) time is actually like this or that anything has gone back in
time .

Is time finite or infinite? For example, did time have a beginning? By invoking
the radical notion that God is "outside of time," St. Augustine claimed, "Time
itself being part of God's creation, there was simply no before "!In the 20th
century, scientists agreed with St. Augustine that the amount of past time in
finite, less than 14 billion years; but in the 21st century, cosmologists are tilting
toward the opposite answer .

   Physics and Philosophy                                          Musa Akrami

Is time infinitely divisible or instead composed of discrete moments? This is an
open question with many physicists betting on discrete moments but having no
experimental evidence in support of their theories .

Is time an emergent entity? Sound emerges from molecules in the sense that,
although a single molecule can have no sound, a very large group of molecules
can make a sound. Does time emerge from more basic entities ?There are two
camps that are divided on this question. One says that both space and time
emerge from some micro-substrate, although there is no agreed upon theory of
what the substrate is. The second camp says that space emerges but time does
not. In 2004, after winning the Nobel Prize in physics, David Gross expressed
the views of this second camp 9

Everyone in string theory is convinced...that spacetime is doomed. But we don't
know what it's replaced by. We have enormous amount of evidence that space is
doomed. We even have examples, mathematically well-defined examples, where
space is an emergent concept.... But in my opinion the tough problem that has
not yet been faced up to at all is, "How do we imagine a dynamical theory of
physics in which time is emergent?" ...All the examples we have do not have an
emergent time. They have emergent space but not time. It is very hard for me to
imagine a formulation of physics without time as a primary concept because
physics is typically thought of as predicting the future given the past. We have
unitary time evolution. How could we have a theory of physics where we start
with something in which time is never mentioned?

4. What does science require of time ?
The general theory of relativity and quantum mechanics are the two most
fundamental theories of physics, not counting theories of quantum gravity .
According to both these fundamental theories ,spacetime is, loosely speaking, a
collection of points called "spacetime locations" where the universe's physical
events occur. Spacetime is four-dimensional and a continuum ,with time being a
distinguished, one-dimensional sub-space of this continuum .That is what time
is. Any interval of time, that is, any duration, is a linear continuum of instants,
so a duration has a structure like an interval of real numbers .

But this first response to the question "What does science require of time "?is
too simple. There are complications. There is an important difference between
the universe's cosmic time and a clock's proper time ;and an important difference
between proper time and a reference frame's coordinate time. Not all spacetimes

   Physics and Philosophy                                            Musa Akrami

can have coordinate systems. And what do we mean by the term "universe"
when it is used within the theory of the multiverse of quantum gravity? This
section is devoted to explaining and elaborating on what has been said in these
first two paragraphs.

Aristotle, Leibniz, Newton, and everyone else before Einstein, believed there
was a frame-independent duration between two events. If the time interval
between two lightning flashes is 100 seconds on someone's clock, then the
interval also is 100 seconds on your clock, even if you are flying by at an
incredible speed, assuming your clock isn't faulty. Einstein rejected this piece of
common sense in his 1905 special theory of relativity when he declared that the
time interval between two events depends on the observer's reference frame .As
Einstein expressed it, "Every reference-body has its own particular time; unless
we are told the reference-body to which the statement of time refers, there is no
meaning in a statement of the time of an event." Each reference frame, or
reference-body, divides spacetime differently into its time part and its space part .

In 1908, the mathematician Hermann Minkowski had an original idea in
metaphysics regarding space and time. He was the first person to realize that
spacetime is more fundamental than time or space alone. As he put it,
"Henceforth space by itself, and time by itself, are doomed to fade away into
mere shadows, and only a kind of union of the two will preserve an independent
reality." The metaphysical assumption behind Minkowski's remark is that what
is "independently real" is what does not vary from one reference frame to
another. It's their "union," what we now call "spacetime," that doesn't vary. It
follows that the division of events into the past ones, the present ones, and the
future ones is also not "independently real". However, space and time are not
completely equivalent even in relativity because time is a "distinguished "sub-
space of the 4-d spacetime continuum. Being distinguished implies that time
isn't just another 4th dimension of physical space; it's a special dimension unlike
the space dimensions, even when we confine our attention to a single reference

A coordinate system is a way of representing space and time using numbers to
represent spacetime points. Science confidently assigns numbers to times
because, in any reference frame, the happens-before order-relation on events is
faithfully reflected in the less-than order-relation on the time numbers (dates)
that we assign to events. In the fundamental theories such as relativity and
quantum mechanics, the values of the time variable t are real numbers, not
merely rational numbers. Each number designates an instant of time, and time is
a linear continuum of these instants ,similar to the mathematician's line segment.
Therefore, if these fundamental theories are correct, physical time is one-

   Physics and Philosophy                                             Musa Akrami

dimensional rather than two-dimensional, and continuous rather than discrete.
These features don't require time to be linear rather than circular because a
segment of a circle is also a linear continuum, but there is no evidence for
circular time, that is ,for causal loops or worldlines that are closed curves in
spacetime .

What about instants? A duration is an ordered set of instants, not a whole or
sum of instants. That is, instants are members of durations, not parts of them.
Any duration is infinitely divisible, and it endlessly divides into more intervals;
it never divides into instants. The parts of durations are just more durations.
The instant is not part of the duration; instead, the singleton set of an instant is a
subset of the duration. Instants are like real numbers in that they are boundaries
of durations. They are locations in time, but they are" in" time as members are
in sets, not as parts are in wholes .

Regarding the number of instants in a duration, time's being a linear continuum
implies there is a nondenumerable infinity of them. They are so densely packed
that between any two there is a third, and yet no instant has a next instant. There
is little doubt that the actual temporal structure of events can be embedded in the
real numbers, but how about the converse? That is, to what extent is it known
that the real numbers can be adequately embedded into the structure of the
instants? The problem is that, although time is not quantized in quantum theory,
for times shorter than about 10 43-seconds, the so-called Planck time, science has
no experimental grounds for the claim that between any two events there is a
third. Instead, the justification is that the assumption of continuity is convenient
and useful, and that there are no better theories available.

Because of quantum mechanical considerations, physicists agree that the general
theory of relativity must fail for durations shorter than the Planck time, but they
don't know just how it fails. Most importantly here, there is no agreement among
physicists as to whether the continuum feature of time will be adopted in the
future theory of quantum gravity that will be created to take account of both
gravitational and quantum phenomena. The string theory of quantum gravity
predicts that time is continuous, but the main alternative to string theory, loop
quantum gravity ,does not .

In 1922, the Russian physicist Alexander Friedmann predicted from general
relativity that the universe should be expanding. In 1927, the Belgian physicist
Georges Lemaitre suggested that galaxy movement could best be accounted for
by this expansion. And in 1929, the American astronomer Edwin Hubble made
careful observations of clusters of galaxies and confirmed that the universe is
undergoing a universal expansion. Atoms are not expanding; our solar system is

   Physics and Philosophy                                           Musa Akrami

not expanding; even the cluster of galaxies to which the Milky Way belongs is
not expanding. But most every galaxy cluster is moving away from the others .
It's as if the clusters are exploding away from each other, and in the future they
will be very much farther away from each other. Now, consider the past instead
of the future. At any earlier moment the universe was more compact .Projecting
to earlier and earlier times, and assuming that gravitation is the main force at
work, the astronomers now conclude that 13.7 billion years ago ( plus or minus
1%) the universe was in a state of nearly zero size and infinite density. Because
all substances cool when they expand, physicists believe the universe itself must
have been cooling down over the last 13.7 billion years ,and so it begin
expanding when it was extremely hot. The Big Bang theory is a theory of how
our universe evolved, how it expanded and cooled from this beginning. This
beginning process is called the "Big Bang." As far as we knew back in the 20th
century, the entire universe was created in the Big Bang, and time itself came
into existence "at that time". So, asking what happened before the Big Bang was
like asking what on earth is north of the North Pole. At least that's the best
response to this question assuming the classical theory of the Big Bang of the
20th century. With the appearance of the new theories of quantum gravity and
the multiverse in the 21st century, the question has been resurrected as
legitimate, as we shall see below.

In the literature in both physics and philosophy, descriptions of the Big Bang
often assume that a first event is also a first instant of time and that spacetime
did not exist outside the Big Bang. This intimate linking of a first event with a
first time is a philosophical move, not something demanded by the science. It is
not even clear that it's correct to call the Big Bang an event .The Big Bang event
is a singularity without space coordinates, but events normally must have space
coordinates. One response to this problem is to alter the definition of "event" to
allow the Big Bang to be an event. Another response, from James Hartle and
Stephen Hawking, is to consider the past cosmic time-interval to be open or
unbounded at t = 0 rather than closed or bounded at t = 0. Looking back to the
Big Bang is then like following the positive real numbers back to ever smaller
numbers without ever reaching a smallest positive one. If Hartle and Hawking
are correct that time is actually like this, then the universe had no beginning
event, but it has a finite amount of past time, and the term "the Big Bang" refers
not to any single event. But in order to simplify the discussion ahead, this article
will speak of "the" Big Bang event as if it were a single event. The Big Bang
theory in some form or other is accepted by the vast majority of astronomers, but
it is not as firmly accepted as is the theory of relativity .

There are serious difficulties in defending the Big Bang theory's implications
about the universe's beginning. They are based on the assumption that the

   Physics and Philosophy                                             Musa Akrami

universal expansion of clusters of galaxies can be projected all the way back.
Yet physicists agree that the projection must fail in the Planck era, that is, for all
times less than 10 43-seconds after "the" Big Bang. Therefore, current science
cannot speak with confidence about the nature of time within the Planck era. If a
theory of quantum gravity does get confirmed, it should provide information
about the Planck era, and it may even allow physicists to answer the question,
"What caused the Big Bang?" The scientifically radical, but theologically
popular, answer, "God caused the Big Bang, but He, himself, does not exist in
time" is a cryptic answer because it is not based on a well-justified and detailed
theory of who God is ,how He caused the Big Bang, and how He can exist but
not be in time. It is also difficult to understand St. Augustine's remark that "time
itself was made by God." On the other hand, for a person of faith, belief in God
as creator is usually stronger than belief in any scientific hypothesis or in any
epistemological desire for a scientific justification of the remark about God or in
the importance of satisfying any philosopher's demand for clarification .

Careful cosmological observations near the end of the 20th century and
beginning of the 21st have now convinced astrophysicists that the volume of
space is not finite, but is infinite and by-and-large flat. Its large scale geometry
is Euclidean, not Riemannian nor hyperbolic. Since 2000, we've come to
believe the Big Bang wasn't the beginning after all, and the universe was infinite
even when our Big Bang was initiating .This has fueled theories of the
multiverse with parallel universes much like our universe, except very far away
from ours. The key idea here is that if spacetime is infinite, then everything that
is possible is actual somewhere .Since there are different possible initial values
at the time of our Big Bang ,there must be different kinds of Big Bangs that have
taken place elsewhere at different times [before and after our Big Bang].
Ascending another level up the hierarchy of multiverses, if there are different
possible values for the physical constants and for the kinds of elementary
particles in our universe ,then there must be parallel universes far from us which
have all those possible values. To ascend yet again, if, according to quantum
mechanics, at any instant in a universe, there are alternative possibilities for
what event occurs next ,then there must be parallel universes in which all those
possibilities are actualities, though these universes won't be far away, but will be
truly parallel in the sense of being off in their own space. Finally, progressing
again up the hierarchy of speculation about multiverses, if there are various
logically possible alternatives for the laws of physics, then every such logically
possible universe is an actual universe, and we have something very similar to
the modal realism of the Princeton philosopher David Lewis. [See Tegmark
2003.] In some of these universes there is no time dimension.

   Physics and Philosophy                                              Musa Akrami

Relativity theory challenges a great many of our intuitive beliefs about time. The
theory is inconsistent with the common belief that the order in which two events
occur is independent of the observer's point of view. For events occurring at the
same place, relativity theory implies the order is absolute ( independent of the
frame), but for distant events occurring close enough in time to be in each other's
absolute elsewhere ,event A can occur before event B in one reference frame,
but after B in another frame, and simultaneously with B in yet another frame.

Science impacts our understanding of time in many other fundamental ways .
Relativity theory implies there is time dilation between one frame and another.
For example, the faster a clock moves, the slower it runs, relative to stationary
clocks. Time dilation shows itself when a speeding twin returns to find that his
(or her) earth-bound twin has aged more rapidly. This surprising dilation result
has caused some philosophers to question the consistency of relativity theory,
arguing that, if motion is relative, then from the perspective of the speeding
twin, the speeding twin should, instead, be the one who aged more rapidly. This
argument is called the twins paradox .Experts now are agreed that the mistake is
within the argument for the paradox ,not within relativity theory. As is shown in
more detail in the Supplement of Frequently Asked Questions, the argument
fails to notice the radically different relationships that each twin has to the rest of
the universe as a whole.

There are two kinds of time dilation. Special relativity's time dilation involves
speed; general relativity's involves acceleration and gravitational fields. Two
ideally synchronized clocks need not stay in synchrony if they undergo different
accelerations or different gravitational forces. This effect would be especially
apparent if one of the two clocks were to fall into a black hole .A black hole can
form when a star exhausts its nuclear fuel and contracts so compactly that the
gravitational force prevents anything from escaping the hole ,even light itself.
The envelope of no return surrounding the black hole is its event horizon. As a
clock falls toward a black hole, time slows on approach to the event horizon, and
it completely stops at the horizon (not just at the center of the hole)--relative to
time on a clock that remains safely back on earth.

General Relativity theory may have even more profound implications for time .
In 1949, the logician Kurt Gödel discovered radical solutions to Einstein's
equations, solutions in which there are closed timelike curves, so that as one
progresses forward in time along one of these curves one arrives back at one's
starting point. Gödel drew the conclusion that in such a universe, there cannot
be "an objective lapse of time." So, "whether or not an objective lapse of time
exists," that is, whether time really exists, depends " on the particular way in
which matter and its motion are arranged in the world." If matter is distributed

   Physics and Philosophy                                             Musa Akrami

so that there is Gödelian spacetime, then the universe has no time. Reinforcing
this conclusion, Stephen Hawking showed in 1969 that only if a general
relativistic spacetime fails to have closed timelike curves can it admit of a
partition into spacelike 3-d slices.

In Einstein's relativity theory, the focus is on proper time rather than a global,
coordinate time .Proper time along a worldline in 4-d spacetime is the time
elapsed by an object having that worldline, as shown on an ideal clock having
the same worldline .According to the relationist, what it is that is being
measured when we measure proper time? If the object being measured never
changes, then we aren't measuring change in the object. The standard answer is
that we are measuring the advancing phase of the quantum wave function, an
esoteric kind of change .

String theory may affect our understanding of time .String theory is the leading
theory attempting to unify quantum field theory with the general theory of
relativity, and most of its advocates believe it will require rejection of the 20th
century assumption that spacetime is ontologically fundamental. See above for
more details .

The Supplement to this article continues with the topic of what science requires
of time, and it provides background information about other topics discussed in
this article.

5. What sort of time travel is possible ?
The term "time travel" is a metaphor because the ordinary term "travel "implies
change in spatial location. The term "time travel" is meant to refer to certain
unusual changes in temporal "location." There are many phenomena that have
been taken by some people to be time travel but which are not now under serious
consideration by philosophers of time, but this section does not focus on them .

Travel to the future
Using the term "time travel" in the sense that is of interest today to philosophers
of time, there is travel to the past and travel to the future .According to relativity
theory, there are two ways to travel into another person's future. In the twins
paradox ,a person speeding away from his twin who remains on earth will, upon
reunion, have entered the earth-twin's future. For a second type of forward time
travel, if a twin goes to a stronger gravitational field by leaving the dinner table
and descending to the cellar for a bottle of wine and then returns, he (or she) will

   Physics and Philosophy                                           Musa Akrami

have entered the future of his twin who stayed at the dinner table. When
someone enters a relatively stronger gravitational field, the person's physical
time slows down relative to the time of those who didn't enter the stronger field.

Regarding the first way to time travel to the future, if you have a fast enough
spaceship, you can travel to the year 4,500 A.D. and see the future of earth. You
can affect that future, not just see it. This is a direct consequence of the time
dilation described in the theory of relativity. You can travel to someone else's
future, not your own. You're always in your own present .Unfortunately, once
you go to 4,500 A.D. (as judged in a frame of reference in which the earth is
considered stationary), you are stuck in the earth's future .You can not reverse
course in your spaceship and return to the 21st century on earth. You must live
with the consequence that all your friends have died centuries ago .

On this trip to 4,500 A.D., how much time would elapse on your own clock?
The answer depends on how fast your spaceship goes, what accelerations occur,
and what gravitational forces are acting. The faster your spaceship goes, the less
time it will take--actually take, not just appear to take. As you approach
infinitesimally close to the speed of light, the trip to 4,500 A.D. will take
essentially no time at all. That's from your own perspective though; observers
who remained stationary on earth and judged your flight from that perspective
will have observed you for thousands of years.

In science fiction movies, which almost always depict nonrelativistic time travel,
time travelers suddenly appear from out of the past, and other travelers suddenly
disappear from now and pop into the future. These phenomena have never been
observed, despite the literature in parapsychology. If they were reliably
observed, then we might very well consider accepting the hypothesis that
spacetime has an extra dimension allowing time travel. The discontinuous
worldline in ordinary 4-d spacetime could actually be a continuous trajectory in
-5d spacetime. How could we ever verify that the time traveler took one
trajectory in the higher dimension rather than another?

Travel to the past
Special relativity does not permit time travel to the past, assuming there are no
such things as tachyons, but general relativity seems to .

One of the major metaphysical assumptions made in the analysis of time travel
to the past is that the world is never logically contradictory. This is the heart of
the Grandfather Paradox. According to this paradox, you step into a time
machine, go back and kill your grandfather before he's met your grandmother, so

   Physics and Philosophy                                             Musa Akrami

you prevent your own birth. Therefore, you both exist and don't exist right now.
This result violates the law of noncontradiction, so we may conclude that we
erred in assuming the possibility of this sort of time travel .If time travel is going
to exist, it can't permit any change in what is known to have happened--
presuming that logic is more fundamental than metaphysics.

How about influencing history instead of changing it? That is allowed. The time
traveler helps make history what it was. For example, Joe Stalin, the dictator of
Russia, was 21 years old in 1900. Let's suppose time machines are invented in
2030. In that year, Sam decides to assume the identity of Stalin. He knows
Russian history, speaks fluent Russian, is 21 years old, and looks like Joe Stalin
did at 21. Sam enters the newly invented time machine, goes back to ,1911
secretly murders Stalin, then starts calling himself "Stalin". Sam never reveals
his past [as Sam], and he eventually becomes the dictator of Russia.

This possibility requires altering our normal assumptions about personal
identity. Because Stalin really died in 1953, Sam must die in 1953, many years
before he is born. To accept that the time travel occurred, we'd have to revise our
current notion of personal identity as well as our notion of what can be
remembered, assuming that Sam-Stalin remembers life before stepping into his
time machine.

Sam's worldline will be composed of discontinuous segments. The worldlines of
more continuous time travelers might be a loop, a closed timelike curve. Either
possibility implies backward causation. Some philosophers believe backward
causation can be ruled out by the definition of "cause," just as they can rule out
Monday ever immediately following Friday. Many other philosophers disagree
on the grounds that backward causation is improbable or nonexistent, but not
impossible .

Another implication of Sam's time travel is his apparent violation of the law of
conservation of matter by popping into existence in 1900. Must we also revise
that law? The modern version of the law of conservation of matter-energy is that
the conservation is statistical; matter is conserved on average. The shorter the
time span and the smaller the mass involved then the more likely that there can
be violations in conservation.

There are other significant implications involved with this sort of participatory
time traveling--traveling back in time to participate in what actually happened.
The future is oddly constrained by the time traveling. After Stalin's death, the
world's events must allow Sam at age 21 to enter the time machine. Nothing can
happen to prevent Sam getting to the machine. All his enemies somehow must

   Physics and Philosophy                                          Musa Akrami

botch their attempts to kill him. Attempted sabotage of the time machine must
also fail. Scientists viewing these attempts will be surprised that they are
continually yet inexplicably frustrated by unfavorable circumstances. Looking
back from the year 2030 it will appear as if the world conspired to ensure that a
predestined event occurred. It has been argued that because we've never seen the
world conspire with massive coincidences, this sort of time travel never occurs
even if it is logically and conceptually possible.

An additional argument against time travel of the kind that influences past
events but doesn't change them is that by now we should have seen all sorts of
time traveler tourists from the distant future. Nobody has ever seen one ,despite
some unreliable witnesses described in supermarket tabloids. Therefore ,time
travel most probably never occurs even if it could. The principal counter is that
there might be very good reasons why our time hasn't yet been visited .The
travelers might be uninterested in us. It might be very expensive to go to our
time. They might be here but be invisibly cloaked so as not to interfere with us.
Therefore, it is jumping to conclusions to be so pessimistic about the probability
of time travel.

Admittedly, though, no one has any practical and realistic plans for how to build
a time machine. The best plans use such phrases as "First, take a wormhole
and...." W .J. van Stockum found a solution to the equations of general relativity
that permits a physical object to travel at less than the speed of light and yet
arrive at its own past. The proper time line of the orbiting space traveler can
form a closed curve in spacetime. This travel requires orbiting around a very
rapidly spinning cylinder that is infinitely long. Since Stockum's initial work in
1937, Kurt Gödel in 1949 found another time travel possibility. Mathematical
physicists have subsequently described even more time machines, or at least
universes containing backward time travel, that are consistent with Einstein's
equations of general relativity. Stephen Hawking believes all these time
machines are ruled out by the laws of general relativity. General relativity theory
is so complex that it isn't always clear, even to the experts, what is and isn't
allowed by the theory. Other physicists accept that Einstein's equations do allow
time travel, but they rule out these solutions as being physically impossible or
improbable for other reasons, such as there being no infinitely long, rapidly
spinning cylinder available. Einstein himself died believing that time travel to
the past is impossible.

Probing the possibility of a contradiction in backwards time travel, John Earman
has described a rocket ship that carries a very special time machine. The time
machine is capable of firing a probe into the past. Suppose the ship is
programmed to fire the probe on a certain date unless a safety switch is on .

   Physics and Philosophy                                            Musa Akrami

Suppose the safety switch is programmed to be turned on if and only if the
"return" of the probe is detected by a sensing device on the ship. Does the probe
get launched? The way out of Earman's paradox seems to require us to accept
that (a) the universe conspires to keep people from building the probe or the
safety switch or the sensing device, or (b) time travel probes must go so far back
in time that they never make it back to the time when they were launched, or (c)
past time travel is impossible .

Feynman diagrams in particle physics were described by Feynman himself as
illustrating how a particle's moving forward in time is actually its antiparticle
moving backward in time. However, physicists don't take Feynman's suggestion
literally. As a leading particle theorist, Chris Quigg of Fermi National
Accelerator Laboratory, explained, "It's not that antiparticles in my laboratory
are actually moving backward in time. What's really meant by that is that if I
think of a particle moving from one place to another forward in time ,the
physical process is the same as it would be if we imagine running the film
backward and also changing the particle into an antiparticle".

In addition to time travel that changes the past and time travel that participates in
the past, consider a third kind, time travel that reaches the past of a different
universe. This idea appeals to an unusual interpretation of quantum mechanics,
the parallel universes interpretation. According to this interpretation, everything
that can happen does happen in some universe or other. There's a universe in
which the Nazis won World War II and Stalin was assassinated. There's another
universe in which the Nazis won World War II and Stalin escaped all
assassination attempts. On this theory of time travel, for you to travel back in
time and have lunch with President Abraham Lincoln is for you to stop existing
in the present universe as you enter the time machine and for you to appear
earlier in time in a parallel universe, one in which you in fact did have lunch
with Abraham Lincoln. This parallel worlds theory implies that we must change
our current view of what makes a person the same person through time [say,
bodily identity and continuity of consciousness through time in a single
universe] and accept some kind of trans-universe identity.

For more discussion of time travel, see the article " Time Travel "elsewhere in
this Encyclopedia.

   Physics and Philosophy                                           Musa Akrami

6. Is the relational theory of time preferable to the
absolute theory ?
Absolute theories say time exists independently of the spacetime relations
exhibited by physical events. Relational theories say it does not. Some absolute
theories describe spacetime as being like a container for events. The container
exists with or without events in it. Some other metaphors might help. Absolute
spacetime is like a painter's canvas. Take away the paint (spacetime events )
from the painting and you have the canvas left. Relational spacetime is like
citizenship. Take away the citizens, and you have no citizenship left.

The absolute theories imply that spacetime could exist even if there were no
physical objects and events in the universe, but relational theories imply that
spacetime is nothing but objects, their events, and the spatiotemporal
relationships among them. Everyone agrees time cannot be measured without
there being objects and changes, but the present issue is whether it exists without
objects and changes .

There are two senses of "absolute" that need to be distinguished. As we are
using the term, it means independent of the events. A second sense of
"absolute" means independent of observer or reference frame. Einstein's theory
implies there is no absolute time in this second sense. Aristotle accepted
absolute time in this second sense, but he rejected it in our sense. Aristotle took
the relationalist position that, "neither does time exist without change [ Physics,
218b]." However, the battle lines were most clearly drawn in the early 18 th
century when Leibniz argued for Aristotle's position against Newton, who had
protested that time exists regardless of whether anything changes .

Leibniz's principal argument against Newton is a reductio ad absurdum.
Suppose Newton's absolute space and time do exist. Then space would surely
be the same in every place and every direction and every time. But one could
then imagine a universe just like ours except with everything shifted five miles
east and five minutes earlier. But there'd be no reason why this universe doesn't
exist and ours does. Now we've arrived at a contradiction. If there's no reason,
then we have violated Leibniz's Principle of Sufficient Reason: that there is an
understandable reason for everything being the way it is. So, Newton's absolute
space and time do not exist. In short, the trouble with Newton's absolutism is
that it leads to too many unnecessary possibilities .

Suppose Newton were to use the same reasoning against Leibniz by saying that
Leibniz's relational space has the same problem. It doesn't exist because, if it

   Physics and Philosophy                                           Musa Akrami

did exist, then God could have re-oriented everything, but there'd be no reason
why He would prefer one orientation over another. Why doesn't this reductio ad
absurdum argument succeed? Well, in a relational space, either the two
situations would be discernible or they wouldn't. Suppose it is possible to
discern a difference between the first universe and the reoriented universe .Then
there must be some difference in the relationships among the objects in space,
and it's understandable that God could easily have willed the relationships of the
first universe rather than the reoriented universe. So ,there's no contradiction,
and Newton's argument would fail. On the other hand ,if there were no
detectable difference between the first and the reoriented universe, that is, if the
difference were indiscernible, then by Leibniz's Principle of the Identity of
Indiscernibles, there would just be one universe and not two, and once again
Newton's argument would fail to produce a contradiction .

So, Newton needed some other response to Leibniz. He offered this two-part
response: (1) Leibniz is correct to accept the Principle of Sufficient Reason
regarding the rational intelligibility of the universe. But there don't have to be
knowable reasons for humans ;God might have had His own sufficient reason
for creating the universe at a given place and time even though mere mortals
cannot comprehend His reasons. (2) The bucket thought-experiment shows that
acceleration relative to absolute space is detectable; thus absolute space is real.
Newton's second argument, the non-theological one, is generally considered to
be the more effective of the two. Partially fill a bucket with water. Notice that
there's no relative motion between the bucket and the water. Then spin the
bucket. After a minute the water will have the same angular velocity as the
bucket, and there will again be no relative motion between the bucket and the
water. What then accounts for the difference that in the first situation the water
surface is flat but in the latter case the water surface is concave? Because we
can disregard the rest of the environment, and because all the bucket to water
relations are the same, says Newton, the only explanation of the difference in
surface shape must be that in the first case there's no motion relative to space but
in the latter case there is. That is ,space is acting on the water surface when it
spins. Alternatively expressed ,the key idea is that the presence of centrifugal
force is a sign of rotation relative to absolute space. Leibniz's theory cannot
offer this absolutist explanation, but Leibniz could not otherwise account for the
result of the bucket experiment .

One hundred years later, Kant entered the arena on the side of Newton. In a
space containing only a single glove, Leibniz couldn't account for its being a
right glove versus a left glove because all the internal relationships would be the
same. However, we all know that there is a difference between a right and a left

   Physics and Philosophy                                             Musa Akrami

glove, so this difference is due to the glove's relationship to space itself. But if
there is a "space itself," then Newton is correct.

In 1969, Sydney Shoemaker presented an argument to convince us of the
understandability of time existing without change, as Newton's absolutism
requires. Divide space into three disjoint regions, called region 3, region 4 ,and
region 5. In region 3, change ceases every third year for one year. People in
regions 4 and 5 can verify this and convince the people in region 3 after they
come back to life at the end of their frozen year. Similarly, change ceases in
region 4 every fourth year for a year; and change ceases in region 5 every fifth
year. Every sixty years, that is, every 3 x 4 x 5 years, all three regions freeze
simultaneously for a year. In year sixty-one, everyone comes back to life, time
having marched on for a year with no change.

Newton's theory of time was dominant in the 18th and 19th centuries, but
Huygens ,Berkeley ,and Mach entered the arena on the side of Leibniz. In the
20th century ,Reichenbach and the early Einstein declared the special theory of
relativity to be a victory for the relational theory. However ,some philosophers
say Reichenbach and the early Einstein may have been overstating the amount of
metaphysics that can be extracted from the physics .Newton's own absolute
theory of space used the notion of a space-filling material aether at rest in
absolute space with distances and times being independent of reference frames,
and this is admittedly inconsistent with special relativity, but other absolute
theories are consistent with current science, and they have their own candidates
for the "container." The container metaphor may work for special relativity, but
general relativity requires that the curvature of spacetime be affected by the
distribution of matter, so today it is no longer plausible for an absolutist to assert
that the "container" is independent of what it contains.

Absolute theories were dominant in the 18th and 19th centuries, and the
relational theories were dominant in most of the 20th century, but at the end of
the century, absolute theories gained some ground and there is no convergence
of opinion on this prominent issue.

Absolute theories are called "substantival" or " substantial" if they require
spacetime to be a substance. In On the Gravity and Equilibrium of Fluids ,
Newton said space is neither a substance nor an attribute, but exists.
Substantivalists disagree among themselves about what it means to be a
substance. It does not usually mean that spacetime is a kind of stuff out of which
physical events are composed. What does it mean ?Absolutists have described
spacetime as "an antecedent arena for events" and" ontologically prior to events"
and "an irreducible object of predication" and " the substrata for properties" and

   Physics and Philosophy                                            Musa Akrami

"the domain of the intended models of the basic physical theories." All these
descriptions seem to be consistent with saying that our universe is one model of
General Relativity. Would they have to be consistent with saying that any
model of General Relativity could have been our universe? There are solutions
to the equations of General Relativity that describe a universe with spacetime
but with no matter or energy.

There can be no "empty" time, the relationist says. If events occur in a room
before 11:01 AM and after 11:01 AM, but not exactly at 11:01 AM, must the
relationist say there never was a time of 11:01 AM in the room? No relationist
wants to answer, "yes." One relationist response is to say 11:01 exists in the
room and everywhere else because somewhere outside the room something is
happening then, and somehow or other sense can be made of time in the room in
terms of these external events. Perhaps there will be an appeal to action at a
distance or action at both a spatial and temporal distance. A second response to
losing 11:01 AM would be to say possible events occur then in the room even if
actual events do not. A third response is to argue that quantum fields exist
everywhere so there is never a possibility of empty space anywhere.

If the relational theory were to consider spacetime points to be permanent
possibilities of the location of events, then the relationist theory would collapse
into substantivalism, and there would no longer be a difference between the two
theories, John Earman has argued. To the absolutist, a spacetime point is also
just a place where something could happen .

Hartry Field argues for the absolute theory by pointing out that modern physics
requires gravitational and electromagnetic fields that cover spacetime .They are
states of spacetime. These fields cannot be states of some Newtonian aether, but
there must be something to have the field properties. What else except
substantive spacetime points?

7. Does time flow ?
"It is as if we were floating on a river, carried by the current past the manifold of
events which is spread out timelessly on the bank," said Plato .Santayana offered
another metaphor: "The essence of nowness runs like fire along the fuse of
time." The philosopher's goal is to clarify the metaphor of time's flow or time's
passage. Everyone agrees that it "appears" to us to flow ,although few believe
that all conscious beings, say crocodiles, recognize the flow. Even if time does

   Physics and Philosophy                                             Musa Akrami

flow, there is the additional question of whether the flow can change. Can time's
flow be slower on Friday afternoon?

There have been three major theories of time's flow. The first, and most popular
among physicists, is that the flow is an illusion, the product of a faulty metaphor.
The second is that it is not an illusion but rather is subjective, being deeply
ingrained due to the nature of our minds. The third is that it is objective, a
feature of the mind-independent reality that is to be found in, say, today
scientific laws, or, if it has been missed there, then in future scientific laws. The
third theory is often called the "dynamic theory" of time, and a popular synonym
for the "flow of time" is "temporal becoming." Some dynamic theorists argue
that the boundary separating the future from the past is the moment at which that
which was undetermined becomes determined, and so " becoming" has the same
meaning as "becoming determined ".

Is the passage of time a feature of the world to be explained by noting how
events change ?Do events, as they cross the boundary of the present, lose their
property of being indeterminate, or lose their property of futurity [ McTaggart's
theory], or gain some other property, and doesn't this explain the flow of time ?

Many other philosophers object on the grounds that an event's "changing" from
being future to being present, or from indeterminate to determinate, is not a real
change in the event's essential, intrinsic properties, but only in its relationship to
the observer. For example, saying the death of Queen Anne is an event that
changes from present to past is much like saying her death changed because
someone changed their attitude from approving of her death to disapproving of
it. This extrinsic change in approval doesn't count as a real change in her death
and neither does the so-called change from present to past. So, it is concluded
by these philosophers that the notion of time's flow is a myth. Attacking the
notion of time's flow in this manner, Grünbaum said" 9Events simply are or
occur...but they do not 'advance' into a pre-existing frame called 'time.' ...time is
a system of relations between events, and as events are, so are their relations.
An event does not move and neither do any of its relations ".

Instead of arguing that events change their properties, some advocates of the
dynamic theory of time embrace the flow of time by saying that the flow is
reflected in the change over time of truth values of a sentence such as "It is now
raining." In response, critics suggest that the indexical sentence "It is now
raining" is not used to express a single proposition that is true at some times and
false at other times. It expresses a propositional function; that is ,it is used to
express different propositions on different occasions. The propositions that are
expressed at each particular time, such as "It is raining at midnight on Jan. 1,

   Physics and Philosophy                                            Musa Akrami

2000 in Chicago," do not change their truth values through time, but are
timelessly true; and so the flow of time cannot be explained in terms of them.
[For an explanation of the differences among sentences, statements,
propositions, and utterances, see the article Truth .The word "now" is called an
"indexical" because what it stands for depends on who says it, not just on its
meaning. Other indexical words are "I" and "you" and" here ]".

Recognizing this distinction between propositions and propositional functions,
some advocates of the flow of time ask us to re-consider the situation by
focusing on facts. "It is now raining" is a propositional function, they agree, and
"It is raining at midnight on Jan. 1, 2000 in Chicago "is not. Assuming it did
rain in Chicago then, this latter tenseless sentence can be used to express a
proposition that is true when uttered on Jan. 1, 2000 ,but is not true in 1950. The
tenseless fact did not exist in 1950, but it came into existence in 2000. This
coming into existence of facts, the actualization of new states of affairs, is time's
flow. What facts there are depends upon what time it is, and this is the key to the
flow of time .

Even if time were to flow, there is the additional question of whether the flow
can change. Can the flow on Friday be slower than the flow on Thursday? On a
relational theory it is difficult to make sense of this, but on a substantival theory
of time, the flow could slow down on Friday because fewer events happen then
than on Thursday .

8. What gives time its direction or "arrow ?"
a. What needs to be explained
Time's arrow is evident in the process of mixing cool cream into hot coffee .You
soon get lukewarm coffee, but you never notice the reverse--lukewarm coffee
unmixing into a cool part and a hot part. Such is the way this irreversible
thermodynamic process goes. You can predict what will happen when you upset
the equilibrium of a birthday party by pricking a balloon. Normally the air
inside the balloon rushes out; it doesn't stay inside while the outside air comes
in .The arrow of a physical process is the way it normally goes, the way it
normally unfolds through time. If a process normally goes one-way, we call it an
"irreversible process." The amalgamation of the universe's irreversible
processes produces the cosmic arrow of time, the master arrow. Usually this
arrow is what is meant when one speaks simply of "time's arrow".

   Physics and Philosophy                                          Musa Akrami

The goals of a theory of time's arrow are to understand why this arrow exists,
what it would be like for the arrow to reverse direction, what exactly is the
relationship between the direction of time and the direction of causation, and
what the relationships are among the various more specific arrows of time--the
various temporally asymmetric processes such as entropy increases [ the
thermodynamic arrow], causes preceding their effects [the causal arrow ,]our
knowing the past more easily than the future [the psychological arrow], and so

Actually, time is directional in two senses. In one sense, which is not the sense
meant by the phrase "the arrow of time," time is directed from the future to the
past. This is the sense in which any future event is temporally after any past
event. Because this is implied by the very definition of the terms "future" and
"past," to say "Time is directed from future to past "is to express a merely
conventional truth of little interest to the philosophical community.

However, time is directed in a second sense, one that isn't merely a matter of the
definition of the relevant terms but is about the particular ordering of events in
time. It is what distinguishes events ordered by the happens-before relation from
those ordered by its converse, the happens-after relation. It is still an open
question in philosophy and science as to what it is about events that gives them
this arrow .

Because physical processes do have an arrow you might think that an inspection
of the basic physical laws would readily reveal time's arrow. It won't. With some
apparently minor exceptions involving Higgs boson decay, all the basic laws of
fundamental processes are time symmetric. This means that if a certain process
is allowed by the equations, then that process reversed in time is also allowed ,
and either direction is as probable as the other .Maxwell's equations of
electromagnetism, for example, can be used to predict that television can exist,
but the equations don't tell us whether those signals arrive before or arrive after
they are transmitted. In other words, these basic laws of science are insensitive
to the arrow of time.

Let's suppose you could have a movie of a basic physical process such as two
electrons bouncing off each other. You can't actually create this movie because
the phenomenon is too small, but let's forget that fine point for a moment. If you
had such a movie, you could run it forwards or backwards, and both showings
would illustrate a possible process according to the basic laws of science, and
they would be equally probable processes. That is, you couldn't tell from just
looking at the movie whether you were looking at the original or at it being

   Physics and Philosophy                                           Musa Akrami

shown backwards in time. Time's arrow isn't revealed in this microscopic
process .

The reason why this result is so interesting to scientists and philosophers is that,
if you had a movie of the mixing of black coffee and white cream, then you
could tell which way is the right way to show the movie. The arrow of time that
was absent in the microscopic movie would be evident in the macroscopic
movie. This difference between microscopic movies and macroscopic movies is
odd because macroscopic processes are presumed to be composed of, and to be
explainable in terms of, more basic processes. Why does the arrow of time
appear in one movie but not the other? After all, either movie could be shown in
either direction and still be showing a physically possible process; it's not
impossible for brown coffee to un-mix into black coffee and white cream. The
disappearance of time's arrow in the movie of the microscopic process, does not
show that time itself fades away as you look at briefer and smaller processes;
this is because there are still events happening, and so time does exist there. The
principal question is why the arrow itself disappears.

b. Explanations or theories of the arrow
The first clue to answering this deep question was discovered in the mid-19th
century by the German physicist Rudolf Clausius. He discovered an early
version of the 2nd law of thermodynamics, which states that a closed system will
evolve to be more disordered, its useful energy converting to heat. That is ,

(a) 2nd Law: In a closed system, entropy increases .

Entropy is a measure of this disorder or of the conversion of useful to useless
energy. Physicists immediately realized that they could explain time's arrow as
entropy increase. The problem, though, was that the new kinetic theory of gases
for which the concept of entropy was defined was supposed to provide the
foundation for all gas behavior, yet this foundational theory is time symmetric.
That is, the theory is insensitive to the arrow of time, to the distinction between
past and future--because a moving molecule could just as well move in one
direction as in the reverse direction. How were the physicists to resolve this
apparent contradiction of having temporal asymmetry in processes that are
supposed to be explained via a temporally symmetric theory?

Ludwig Boltzmann had an answer in 1872. It's also an answer to why the arrow
of time emerges in the macroscopic movie but isn't evident in the microscopic
movie. Boltzmann was the first to show how an irreversible macroscopic
phenomenon may arise from reversible microscopic laws. He showed that

   Physics and Philosophy                                            Musa Akrami

irreversible macroscopic thermodynamic processes are irreversible because the
probability of their actually reversing is insignificant. To be more specific ,
consider a container with hot gas in one half and cold gas in the other half .The
gases mix and reach a common, lukewarm temperature. That is, they come to an
equilibrium temperature. By applying the kinetic theory of gases to molecules
obeying Newton's mechanics, Boltzmann discovered an important statistical
asymmetry: there are more lukewarm microstates of the set of the gas'
constituent molecules than there are microstates with separated hot and cold
regions, so the system changes toward a common equilibrium temperature
because it evolves in the "direction" of what is most probable. To express the
point somewhat more precisely, let A be the set of microstates of an isolated
container in which the left half of the container contains very hot gas and the
right half of the container contains very cold gas, and there is no barrier
separating the left half from the right. Let B be the microstates with lukewarm
gas in both halves. Assume all the microstates are equally probable a priori .
Boltzmann pointed out that the number of B states is dramatically larger than the
number of A states, so the probability that one of the A states will soon evolve
into one of the B states is almost one whereas the probability that a B state will
soon evolve into an A state is almost zero. That is why the process of heat flow
in an isolated gas is irreversible.

How does this explain the 2nd law of thermodynamics? Boltzmann redefined
both the concept of entropy and the 2nd law. He redefined entropy as how
probable a state is. Then he deduced a revised 2nd law 9

(b) 2nd Law: In a closed system, entropy is likely to increase .

Although his actual proof was shown to depend on some probability theory and
not merely on Newton's laws of motion, his treatment of entropy as being
basically a statistical concept was broadly accepted, as was his claim that time's
arrow is to be explained in terms of entropy increase .

Boltzmann's achievement soon had to confront two other obstacles, one from
Henri Poincaré and one from Josef Loschmidt. A dynamic system is a system
defined by the values of the positions and velocities of all the system's particles--
such as the places and speeds of the atoms in a cup of coffee. Poincaré's
recurrence theorem in statistical mechanics says every isolated dynamical
system will eventually return to a state as close to the initial state as we might
wish. Wait long enough, and the lukewarm coffee will separate into hot coffee
and cool cream. In other words, strictly speaking, there are no irreversible
processes. So, there is a contradiction between Poincaré's theorem and
Boltzmann's proof. The second law implies that entropy probably increases, but

   Physics and Philosophy                                         Musa Akrami

Poincaré's theorem implies that, given a long period of time, entropy remains the
same .

Nietzsche concluded that these Poincaré cycles rob human life of any ultimate
moral progress. If a person demonstrates moral progress, the universe will
eventually return to a state in which the person hasn't made this progress .
Nietzsche concluded that the theorem implies that "God is dead".

To avoid the Poincaré problem, the second law needs another revision 9

(c) 2nd Law: In a closed system, entropy is likely to increase for any period
of time short compared to the Poincaré period for that system.

The problem raised by Poincaré is less of a problem for Boltzmann's treatment
of time's arrow than is the Loschmidt Problem. Loschmidt pointed out that
Boltzmann's statistical mechanics predicts for any point in time that not only
should entropy be higher in the future but also it should be higher in the past.
However, we know that it was not higher in the past. Here is a graph
representing this knowledge .

   Physics and Philosophy                                           Musa Akrami

The conclusion to be drawn from this is that entropy increase is only part of the
story of time's arrow .

Loschmidt and Einstein suggested that the low entropy in the past must be
explained by what the initial conditions happened to be like at the beginning of
the universe. Among cosmologists, this plus the 2nd Law is now the generally
accepted answer to the origin of time's arrow. Yet this answer leads naturally to
the request for an explanation of the initial configuration of our universe .Is this
temporally asymmetric initial boundary condition simply a brute fact ?Are there
no laws to explain the fact?

The Swiss physicist Walther Ritz and, more recently, Penrose and Prigogine ,say
we must not yet have found the true laws (or invented the best laws )underlying
nature's behavior. We need to keep looking for basic, time asymmetrical laws in
order to account for time's arrow.

Even if physicists agree someday on the initial conditions of the universe and on
the laws of the universe, and thereby explain the entropy of the early universe
and the cause of the cosmic arrow of time, there is no good reason to believe this
theory would be a theory of everything. That theory wouldn't enable the
prediction of your birth. The theory presumably would be a quantum
mechanical theory. The probabilistic nature of quantum theory prevents the
prediction of even the date that a radioactive uranium atom will fission into
fragments, and it surely would prevent the prediction of your birth.

c. Multiple arrows
Consider the difference between time's arrow and time's arrows .For a process
to be classified as an arrow of time, it must work differently or not at all if time
were reversed. The direction of entropy change is the thermodynamic arrow.
Here are some suggestions for additional arrows9

a. There are records of the past but not of the future .

b. It is easier to know the past than to know the future.

c. Light and radio waves spread out from, but never converge into, a point.

d. The universe expands rather than shrinks.

e. Causes precede their effects.

   Physics and Philosophy                                               Musa Akrami

f. We see black holes but never white holes.

g. Conscious actions affect the future but not the past.

h. B meson decay, neutral kaon decay, and Higgs boson decay are each different
in a time reversed world.

i. Quantum mechanical measurement collapses the wave function.

j. Possibilities decrease as time goes on.

Most physicists suspect all these arrows are linked so that we can't have some
arrows reversing while others do not. The linkage may require as yet
undiscovered laws. But could all the arrows reverse? That is, could the cosmic
arrow of time have gone the other way? Most physicists suspect that the answer
is "Yes, if the initial conditions of the universe at the Big Bang had been
different ".

d. Reversing time
Philosophers have gone on to ask interesting questions about different scenarios
involving the reversal of time's arrow. Suppose the cosmic arrow of time were
someday to reverse in a distant, populated region far away from earth. Imagine
what life would be like for the time reversed people. Their past would be our
future. Would they become pre-cognitive and able to remember( what we call)
the future? [Probably yes, but since their brain processes would be reversed,
their experience wouldn't be different from ours.] If Aristotle is correct that the
future, unlike the past, is undetermined or open, then their future would be open,
too. But it's our past. What do we conclude from this puzzle--that our past is
undetermined and open? Would it imply that our past could change? And there
are other questions. If the arrow of time reversed in some region, wouldn't
people in that region grow younger? Surely someone can't become unborn. Or
can they? Consider communication between the two regions .Could the
message cross the border, or would it dissolve there? If a film were sent across
the border to us, should we play it in the ordinary way or in reverse?

If the cosmic arrow of time were to reverse, it would be possible for our past to
be re-created. This re-occurrence of the past is different than the re-living of
past events via time travel .With time travel ,the past is re-visited, but it is not re-
created in reverse order .

   Physics and Philosophy                                            Musa Akrami

9. Is only the present real ?
Have past objects, such as Socrates, slipped out of existence? Philosophers are
divided on this question. More generally, there is no agreement about the reality
of the past and future. The presentist viewpoint maintains that the past and the
future are not real, and that only the present is real .Advocates of a growing past
argue that, in addition, the past is real .Reality "grows" with the coming into
being of determinate reality from an indeterminate or potential reality. "The
world grows by accretion of facts," says Richard Jeffrey .Aristotle and C. D .
Broad also advocate a growing past. Duns Scotus and A. N. Prior are
presentists .

Opposing both presentism and the growing past theory, Hermann Weyl, J.J.C .
Smart, and W.V.O. Quine argue that the objective world simply is .They say
there is no objective ontological difference among the past, the present ,and the
future just as there is no ontological difference between here and there. This
position is called the" block universe "position because it regards reality as a
single block of spacetime with its time slices ordered by the temporally-before
relation, as in a Minkowski spacetime diagram ,although it is understood that not
all spacetimes can be given Minkowski diagrams. It is mental perspectives only
that divide the block into a past part, a present part, and a future part. William
James coined the term" block universe," but the theory is also commonly called
the "static theory of time" and "eternalism." Some, but not all, proponents of the
block universe will say that the future is real, but it doesn't exist; and they will
say that something is real if it has existed, does exist, or will exist.

The presentist and the advocate of the growing past will usually unite in
opposition to the block universe on the grounds that it misses the special" open"
character of the future and the equally significant point that the present is so
much more "vivid" than any other time-slice of spacetime. The advocates of the
block universe counter that only the block universe can make sense of
relativity's implication that, if people are in certain relative motions, an event in
person A's present can be in person B's future and in person C's past. Presentism
and the growing-past theories must suppose that this event is both real and
unreal because it's real for A but not real for B. Surely that conclusion is
unacceptable, they claim. Their two key assumptions here are that relativity does
provide an accurate account of the spatiotemporal relations among events, and
that if there is some frame of reference in which two events are simultaneous ,
then if one of the events is real, so is the other.

   Physics and Philosophy                                            Musa Akrami

Opponents of the block universe charge that it doesn't provide an accurate
account of the way things are because it leaves out "the now" or "the present ".
This metaphysical dispute was fueled by Einstein who said9

Since there exists in the four dimensional structure no longer any slices which
represent "now " appears more natural to think of physical reality
as a four dimensional existence instead of, as hitherto, the evolution of a three
dimensional existence.

Many philosophers, however, do not agree with Einstein .

This philosophical dispute has taken a linguistic turn by focusing upon a
question about language: "Are predictions true or false at the time they are
uttered?" Those who believe in the block universe (and thus in the determinate
reality of the future) will answer "Yes" while a "No" will be given by presentists
and advocates of the growing past. The issue is whether contingent sentences
uttered now about future events are true or false now rather than true or false
only in the future at the time the predicted event is supposed to occur.

Suppose someone says, "Tomorrow the admiral will start a sea battle." And
suppose that tomorrow the admiral orders a sneak attack on the enemy ships.
And suppose that this action starts a sea battle. Advocates of the block universe
argue that, if so, then the above sentence was true all along .Truth is eternal or
fixed, they say, and "is true" is a tenseless predicate, not one that merely says "is
true now." These philosophers point favorably to the ancient Greek philosopher
Chrysippus who was convinced that a contingent sentence about the future is
true or false, and it can't be any value in between such as " indeterminate". Many
others, following a suggestion from Aristotle, argue that the sentence is not true
until it's known to be true, namely at the time at which the sea battle occurs. The
sentence wasn't true before the battle occurred. In other words, predictions have
no (classical) truth values at the time they are uttered. Predictions fall into the
"truth value gap." This position that contingent sentences have no truth values is
called the Aristotelian position because many researchers throughout history
have taken Aristotle to be holding the position in chapter 9 of On Interpretation-
-although today it is not so clear that Aristotle himself held it.

The principal motive for adopting the Aristotelian position arises from the belief
that if sentences about future human actions are now true, then humans are fated
(or determined) to perform those actions, and so humans have no free will. To
defend free will, we must deny truth values to predictions.

   Physics and Philosophy                                             Musa Akrami

The Aristotelian argument against predictions being true or false has been
discussed as much as any in the history of philosophy, but it faces a series of
challenges. First, if there really is no free will, or if free will is compatible with
fatalism (or determinism), then the motivation to deny truth values to predictions
is undermined.

Second, if it is true that you will perform an action in the future, it doesn't follow
that now you won't perform it freely, nor that you aren't free to do otherwise, but
only that you won't do otherwise. For more on this point about modal logic, see
Foreknowledge and Free Will.

A third challenge arises from moral discussions about the interests of people
who are as yet unborn. Quine argues that if we have an obligation to conserve
the environment for these people, then we are treating them as being as real as
the people around us now. Only the block universe view can make sense of this

A fourth challenge, from Quine and others, claims the Aristotelian position
wreaks havoc with the logical system we use to reason and argue with
predictions. For example, here is a deductively valid argument9

There will be a sea battle tomorrow.

If there will be a sea battle tomorrow, then we should wake up the admiral.

So, we should wake up the admiral.

Without the premises in this argument having truth values, that is, being true or
false, we cannot properly assess the argument using the standard of deductive
validity because this standard is about the relationships among truth values of
the component statements. Unfortunately, the Aristotelian position says that
some of these components are neither true nor false, so Aristotle's position is

In reaction to this fourth challenge, proponents of the Aristotelian argument
claim that if Quine would embrace tensed propositions and expand his classical
logic to a tense logic ,he could avoid those difficulties in assessing the validity
of arguments that involve sentences having future tense .

Russell, Quine, Grünbaum, and Horwich object to assigning special ontological
status to the present. According to Quine, the analysts should in principle be able
to eliminate the temporal indexical words because their removal is needed for

   Physics and Philosophy                                           Musa Akrami

fixed truth and falsity of our sentences [fixed in the sense of being eternal
sentences whose truth values aren't relative because the indicator words have
been replaced by times, places and names, and whose verbs are treated as
tenseless], and having fixed truth values is crucial for the logical system used to
clarify science. "To formulate logical laws in such a way as not to depend thus
upon the assumption of fixed truth and falsity would be decidedly awkward and
complicated, and wholly unrewarding," says Quine .

Philosophers are still very divided on the issues of whether only the present is
real, what sort of logic is correct, and whether future contingent propositions
have truth values .

10. Are there essentially tensed facts ?
What is the significance of saying that an event occurred in the past, the present,
or the future? There are two major answers. One answer is that these distinctions
represent objective features of reality that aren't captured by the popular "block
universe" approach with its reliance on tenseless facts. This answer takes tenses
very seriously and is called the tensed theory of time ,or the A-theory in
McTaggart's sense of A vs. B. A second answer to the question of the
significance of references to tenses is that these distinctions are subjective
features of the perspective from which we view the universe .

On the tenseless theory of time ,or the B-theory ,whether the birth of Mohammed
occurs here depends on the speaker's perspective; similarly ,whether the birth
occurs now is equally subjective. The proponent of the tenseless view does not
deny the importance or coherence of talk about the past but will say that talk
about the past is really talk about our own relation to events. The assertion that
Mohammed's birth is a past event might be analyzed as asserting that the birth
event happens before the event of writing this sentence. Pointing out the
relativity of simultaneity in Einstein's theory of relativity, the B-theorist also
argues that an event's being present is relative to reference frame, a point that is
missed by the A-theorist.

This controversy is often presented as a dispute about whether tensed facts exist,
with advocates of the tenseless theory objecting to tensed facts. The primary
function of tensed facts is to make tensed sentences true. For the purposes of
making the point, let's uncritically accept the Correspondence Theory of Truth
and apply it to the past tense sentence9

Custer died in Montana.

   Physics and Philosophy                                            Musa Akrami

If we apply the Correspondence Theory directly to this sentence, we would say

The sentence "Custer died in Montana" is true because it corresponds to the
tensed fact that Custer died in Montana.

Opponents of tensed facts argue that the Correspondence Theory should be
applied only indirectly. One approach, the classical tenseless approach, argues
that the Correspondence Theory should be applied only to the result of analyzing
away tensed sentences into equivalent sentences that don't use tenses. The
sentence "Custer died in Montana" has this equivalent9

There is a time t such that Custer dies in Montana at time t, and time t is before
the time of the utterance of the sentence "Custer died in Montana".

In this analysis, the verb dies is tenseless; it is not present tensed. Applying the
Correspondence Theory to this new sentence yields9

The sentence "Custer died in Montana" is true because it corresponds to the
tenseless fact that there is a time t such that Custer dies in Montana at time t, and
time t is before the time of the utterance of" Custer died in Montana".

This analysis of tenses without appeal to tensed facts is challenged. It can work
only for utterances, but a sentence can be true even if never uttered by anyone.
There are other challenges. Roderick Chisholm and A. N. Prior claim that the
"is" in the sentence "It's now midnight" is essentially present tensed because
there is no translation using only tenseless verbs. Trying to analyze it as, say,
"There is a time t such that t = midnight" is to miss the essential reference to the
present in the original sentence. The latter sentence is always true, but the
original is not, so the tenseless analysis fails. There is no escape by adding "and t
is now" because this last indexical still needs analysis, and we've gone in a
circle .

Chisholm and Prior say that true sentences using the temporal indexical terms
"now," "before now," and "happened yesterday" are part of the facts of the world
that science should account for, and science fails to do this because it doesn't
recognize them as being real facts. Science so far restricts itself to eternal facts,
such as in the Minkowski-like spacetime representation of events. These events
are sets of spacetime points. For such events, the reference to time and place is
explicit. A Minkowski spacetime diagram displays only what happens before
what, but not which time is present time, or past, or future. What is missing from

   Physics and Philosophy                                           Musa Akrami

the diagram, say Chisholm and Prior, is some moving point on the time axis
representing the observer's" now" as time flows up the diagram.

In the same spirit, Michael Dummett argues that you can have a complete
description of a set of objects even if you haven't said which objects are near and
which are far, but you cannot have a complete description of those objects
without specifying which events are happening now and which are not.

Earlier, Prior [1959] had argued that after a painful event, one says, e.g., "Thank
goodness that's over," and [this]...says something which it is impossible that any
use of a tenseless copula with a date should convey. It certainly doesn't mean
the same as, e.g., "Thank goodness the date of the conclusion of that thing is
Friday, June 15, 1954," even if it be said then. (Nor, for that matter, does it mean
"Thank goodness the conclusion of that thing is contemporaneous with this
utterance." Why should anyone thank goodness for that.)?

D. H. Mellor, who advocates a newer subjective theory of tenses, argues that the
truth conditions of any tensed sentence can be explained without tensed facts
even if Chisholm and Prior are correct that some tensed sentences can't be
translated into tenseless ones. Mellor would say it is not the pastness of the
painful event that explains why I say, "Thank goodness that's over." My
gladness is explained by my belief that the event is past ,plus its being true that
the event occurs before now. Tenseless facts can explain all this. In addition,
tenseless sentences can be used to explain the logical relations between tensed
sentences: that one tensed sentence implies another, is inconsistent with yet
another, and so forth. Then Ockham's Razor is applied. If we can do without
essentially tensed facts, then we should say essentially tensed facts do not exist.
To summarize, tensed facts were presumed to be needed to account for the truth
of tensed talk; but the analysis shows that ordinary tenseless facts are adequate.
So, there are no essentially tensed facts.

11. What is temporal logic, the symbolic logic of
time ?
Temporal logic is the representation of information about time by using the
methods of symbolic logic. The classical approach to temporal logic is via tense
logic, a formalism that adds tense operators to an existing system of symbolic
logic. The pioneer in the late 1950's was A. N. Prior. He created a new
symbolic logic to describe our use of time words such as "now," "happens

   Physics and Philosophy                                             Musa Akrami

before," "afterwards," "always," and "sometimes". The relationships that
propositions have to the past, present, and future help to determine their truth-
value. A proposition, such as "Socrates is sitting down" is allowed to be true at
one time and false at another time .

Prior was the first to appreciate that time concepts are similar in structure to
modal concepts such as "it is possible that" and "it is necessary that," and so he
adapted modal propositional logic for his tense logic. Dummett and Lemmon
also made major, early contributions to tense logic .

In one standard system of the logic of past time, the S4.3 system, the usual
modal operator "it is possible that" is re-interpreted to mean "at some past time it
was the case that." Let the letter "P" represent this operator, and add to the
axioms of classical propositional logic the modal-like axiom P(p v q) iff Pp v
Pq. The axiom says that for any two present-tensed propositions p and q, at some
past time it was the case that p or q if and only if either at some past time it was
the case that p or at some past time it was the case that q. The S4.3 system's key
axiom is the equivalence

Pp & Pq iff P(p & q) v P(p & Pq) v P(q & Pp).

This axiom captures our ordinary conception of time as a linear succession of
states of the world. Another axiom might state that if Q is true, then it will
always be true that Q has been true at some time. Prior and others have
suggested a wide variety of axioms for tense logic, but logicians still disagree
about what axioms are needed to capture correct beliefs about time as theorems .
Some extension of classical tense logic is needed to express "Q has been true for
the past three days ".

The concept of being in the past is usually treated by metaphysicians as a
predicate that assigns properties to events, but in this tense logic the concept is
treated as an operator P upon propositions, and this difference in treatment is
objectionable to some metaphysicians .

The other major approach to temporal logic does not use a tense logic .Instead,
it formalizes temporal reasoning within a first-order logic without modal-like
tense operators. This so-called method of "temporal arguments" adds an
additional variable, a time argument, to any predicate involving time in order to
indicate how its satisfaction depends on time. A predicate such as "is less than
seven" doesn't involve time, but the predicate "is resting" does. If" x is resting"
is represented classically as R(x), where R is a one-argument predicate, then it
would be represented in temporal logic as R(x,t) and would be interpreted as

   Physics and Philosophy                                          Musa Akrami

saying x has property R at time t. R has been changed to a two-argument
predicate by adding a "temporal argument." The time variable "t "is treated as a
new sort of variable with its own axioms. These axioms might allow time to be
a dense linear ordering without endpoints, or to be even more like the real
numbers .

Occasionally the method of temporal arguments uses a special constant symbol ,
say "n", to denote now, the present time. This helps with the translation of
common temporal statements. For example, the statement that Q has always
been true may be translated into first-order temporal logic as

( t)[(t < n) → Q(t)].

The first person to give a clear presentation of the implications of treating
declarative sentences as being neither true nor false was the Polish logician Jan
Lukasiewicz in 1920. To carry out Aristotle's suggestion that future contingent
sentences don't yet have truth values, he developed a three-valued symbolic
logic, with all grammatical declarative sentences having the truth-values of True,
False, or else Indeterminate [T, F, or I]. Contingent sentences about the future,
such as Aristotle's prediction that there will be a sea battle tomorrow, are
assigned an I. Truth tables for the connectives of propositional logic are
redefined to maintain logical consistency and to maximally preserve our
intuitions about truth and falsehood. See Haack (1974) for more details about
this application of three-valued logic.

12. Supplement of frequently asked questions
      What are proper times, coordinate systems, and Lorentz transformations ?
      What is an event?
      What is a reference frame ?
      What is an inertial frame?
      What is spacetime?
      What is a Minkowski diagram ?
      What are the metric and the interval ?
      Does the theory of relativity imply time is partly space?
      Is time the fourth dimension?
      Is time infinite?
      Is there more than one kind of physical time?
      How is time relative to the observer?

   Physics and Philosophy                                           Musa Akrami

      What are the relativity and conventionality of simultaneity?
      What is the difference between the past and the absolute past?
      What is time dilation?
      How does gravity affect time?
      What happens to time near a black hole?
      What is the solution to the twins paradox (clock paradox?)
      What is the solution to Zeno's paradoxes?
      How do time coordinates get assigned to points of spacetime?
      How do dates get assigned to actual events?
      What is essential to being a clock?
      What is our standard clock?
      Why are some standard clocks better than others?

References and Further Reading
Callender, Craig, and Ralph Edney .Introducing Time ,Totem Books, USA ,

A cartoon-style book covering most of the topics in this article in a more
elementary way. Each page is two-thirds graphics and one-third text.

Davies, Paul .About Time: Einstein's Unfinished Revolution ,Simon & Schuster,

An easy to read survey of the impact of the theory of relativity on our
understanding of time.

Davies, Paul .How to Build a Time Machine ,Viking Penguin, 2002.

A popular exposition of the details behind the possibilities of time travel .

Grünbaum, Adolf. "Relativity and the Atomicity of Becoming ",Review of
Metaphysics ,51-1951 ,pp. 143-186.

An attack on the notion of time's flow, and a defense of the treatment of time
and space as being continua and of physical processes as being aggregates of
point-events .

Haack, Susan .Deviant Logic ,Cambridge University Press, 1974.

   Physics and Philosophy                                           Musa Akrami

Chapter 4 contains a clear account of Aristotle's argument for truth-value gaps,
and its development in Lukasiewicz's three-valued logic.

Hawking, Stephen .A Brief History of Time ,Updated and Expanded Tenth
Anniversary Edition, Bantam Books, 1996.

A leading theoretical physicist provides introductory chapters on space and time,
black holes, the origin and fate of the universe ,the arrow of time, and time

Horwich, Paul .Asymmetries in Time ,The MIT Press, 1987.

A monograph that relates the central problems of time to other problems in
metaphysics, philosophy of science, philosophy of language and philosophy of
action .

Le Poidevin, Robin and Murray MacBeath ,The Philosophy of Time ,Oxford
University Press, 1993.

A collection of twelve influential articles on the passage of time, subjective
facts, the reality of the future, the unreality of time, time without change, causal
theories of time, time travel, causation ,empty time, topology, possible worlds,
tense and modality, direction and possibility, and thought experiments about
time. Difficult reading for undergraduates.
Mellor, D. H .Real Time II ,International Library of Philosophy, 1998 .

This monograph presents a subjective theory of tenses. Mellor argues that the
truth conditions of any tensed sentence can be explained without tensed facts .

Prior, A. N. "Thank Goodness that's Over ",Philosophy, 34 ,)1959( p.17 .

Argues that a tenseless or B-theory of time fails to account for our relief that
painful past events are in the past rather than in the present.

Prior, A. N .Past, Present and Future ,Oxford University Press.1967 ,

A pioneering work in temporal logic, the symbolic logic of time, which permits
propositions to be true at one time and false at another .

Prior, A. N. "The Notion of the Present ",Studium Generale ,volume 23 ,1971 ,
pp. 245-8.

A brief defense of presentism, the view that the past and the future aren't real.

   Physics and Philosophy                                         Musa Akrami

Salmon, Wesley C. (ed.) .Zeno's Paradoxes ,The Bobbs-Merrill Company ,Inc.,

A collection of the most influential articles about Zeno's Paradoxes written in
the period from 1911 to 1965. Salmon provides an excellent annotated
bibliography of further readings.

Sciama, Dennis. "Time 'Paradoxes' in Relativity," in The Nature of Time edited
by Raymond Flood and Michael Lockwood, Basil Blackwell, 1986 ,pp. 6-21.

A good account of the twins paradox or clock paradox .

Shoemaker, Sydney. "Time without Change ",Journal of Philosophy ,)1969( 66 ,
pp. 363-381.

A thought experiment designed to show us how time could exist even without
any change in the universe.

Sorabji, Richard .Matter, Space & ,Motion: Theories in Antiquity and Their
Sequel .Cornell University Press, 1988.

Chapter 10 discusses ancient and contemporary accounts of circular time .

Tegmark, Max. "Parallel Universes ",Scientific American ,May 2003, pp.51-41 .

A clear presentation of the multiverse theory of kinds of parallel universes.
Attention is directed toward some of the philosophical implications. He argues
that you must have an exact duplicate of yourself, down to the very atoms and
memories, in another galaxy that is about 11 to the 10 to the 28 meters from

Van Fraassen, Bas C .An Introduction to the Philosophy of Time and Space ,
Columbia University Press, 1985.

An advanced undergraduate textbook by an important philosopher of science.

Veneziano, Gabriele. "The Myth of the Beginning of Time ",Scientific
American ,May 2004, pp. 54-65.

An account of string theory's impact on our understand of time's origin.

   Physics and Philosophy                                       Musa Akrami

Chapter14. Experiment in Physics
      1. Experimental Results
          o A. The Case For Learning From Experiment
                   .1An Epistemology of Experiment
                   .2Galison's Elaboration
          o B. The Case Against Learning From Experiment
                   .1Collins and the Experimenters' Regress
                   .2Pickering on Communal Opportunism and Plastic
                   .3Critical Responses to Pickering
                   .4Pickering and the Dance of Agency
                   .5Hacking's "Social Construction of What "?
      2. The Roles of Experiment
          o A. A Life of Its Own
          o B. Confirmation and Refutation
                   .1The Discovery of Parity Nonconservation: A Crucial
                   .2The Discovery of CP Violation: A Persuasive Experiment
                   .3The Discovery of Bose-Einstein Condensation:
                   Confirmation After 70 Years
          o C. Complications
                   .1The Fall of the Fifth Force
                   .2Right Experiment, Wrong Theory: the Stern Gerlach
                   .3Sometimes Refutation Doesn't Work: The Double
                   Scattering of Electrons
          o D. Other Roles
                   .1Evidence for a New Entity: J.J. Thomson and the Electron
                   .2The Articulation of Theory: Weak Interactions
      3. Conclusion
            Bibliography

By Allan Franklin

    Physics and Philosophy                                          Musa Akrami

Introductory remark
Physics, and natural science in general, is a reasonable enterprise based on valid
experimental evidence, criticism, and rational discussion. It provides us with
knowledge of the physical world, and it is experiment that provides the evidence
that grounds this knowledge. Experiment plays many roles in science. One of its
important roles is to test theories and to provide the basis for scientific
knowledge. ]1[ It can also call for a new theory, either by showing that an
accepted theory is incorrect, or by exhibiting a new phenomenon that is in need
of explanation. Experiment can provide hints toward the structure or
mathematical form of a theory and it can provide evidence for the existence of
the entities involved in our theories. Finally, it may also have a life of its own,
independent of theory. Scientists may investigate a phenomenon just because it
looks interesting. Such experiments may provide evidence for a future theory to
explain. [Examples of these different roles will be presented below.] As we shall
see below, a single experiment may play several of these roles at once .

If experiment is to play these important roles in science then we must have good
reasons to believe experimental results, for science is a fallible enterprise.
Theoretical calculations, experimental results, or the comparison between
experiment and theory may all be wrong. Science is more complex than " The
scientist proposes, Nature disposes." It may not always be clear what the scientist
is proposing. Theories often need to be articulated and clarified. It also may not
be clear how Nature is disposing. Experiments may not always give clear-cut
results, and may even disagree for a time .

In what follows, the reader will find an epistemology of experiment, a set of
strategies that provides reasonable belief in experimental results. Scientific
knowledge can then be reasonably based on these experimental results .

   Physics and Philosophy                                            Musa Akrami

1. Experimental Results
A. The Case For Learning From Experiment
1. An Epistemology of Experiment
It has been two decades since Ian Hacking asked, "Do we see through a
microscope?" (Hacking 1981 .)Hacking's question really asked how do we come
to believe in an experimental result obtained with a complex experimental
apparatus? How do we distinguish between a valid result ]2[and an artifact
created by that apparatus? If experiment is to play all of the important roles in
science mentioned above and to provide the evidential basis for scientific
knowledge, then we must have good reasons to believe in those results. Hacking
provided an extended answer in the second half of Representing and
Intervening .)1983( He pointed out that even though an experimental apparatus
is laden with, at the very least, the theory of the apparatus, observations remain
robust despite changes in the theory of the apparatus or in the theory of the
phenomenon. His illustration was the sustained belief in microscope images
despite the major change in the theory of the microscope when Abbe pointed out
the importance of diffraction in its operation .One reason Hacking gave for this
is that in making such observations the experimenters intervened--they
manipulated the object under observation. Thus ,in looking at a cell through a
microscope, one might inject fluid into the cell or stain the specimen. One
expects the cell to change shape or color when this is done. Observing the
predicted effect strengthens our belief in both the proper operation of the
microscope and in the observation. This is true in general. Observing the
predicted effect of an intervention strengthens our belief in both the proper
operation of the experimental apparatus and in the observations made with it .

Hacking also discussed the strengthening of one's belief in an observation by
independent confirmation. The fact that the same pattern of dots--dense bodies
in cells--is seen with "different" microscopes, (e.g. ordinary, polarizing ,phase-
contrast, fluorescence, interference, electron, acoustic etc.) argues for the
validity of the observation. One might question whether "different" is a theory-
laden term. After all, it is our theory of light and of the microscope that allows
us to consider these microscopes as different from each other .Nevertheless, the
argument holds. Hacking correctly argues that it would be a preposterous
coincidence if the same pattern of dots were produced in two totally different
kinds of physical systems. Different apparatuses have different backgrounds and
systematic errors, making the coincidence, if it is an artifact, most unlikely. If it

   Physics and Philosophy                                          Musa Akrami

is a correct result, and the instruments are working properly, the coincidence of
results is understandable .

Hacking's answer is correct as far as it goes. It is, however, incomplete .What
happens when one can perform the experiment with only one type of apparatus,
such as an electron microscope or a radio telescope, or when intervention is
either impossible or extremely difficult? Other strategies are needed to validate
the observation. ]3[ These may include 9

      1) Experimental checks and calibration, in which the experimental
      apparatus reproduces known phenomena. For example, if we wish to
      argue that the spectrum of a substance obtained with a new type of
      spectrometer is correct, we might check that this new spectrometer could
      reproduce the known Balmer series in hydrogen. If we correctly observe
      the Balmer Series then we strengthen our belief that the spectrometer is
      working properly. This also strengthens our belief in the results obtained
      with that spectrometer. If the check fails then we have good reason to
      question the results obtained with that apparatus .

      2) Reproducing artifacts that are known in advance to be present. An
      example of this comes from experiments to measure the infrared spectra
      of organic molecules (Randall et al. 1949). It was not always possible to
      prepare a pure sample of such material. Sometimes the experimenters had
      to place the substance in an oil paste or in solution. In such cases, one
      expects to observe the spectrum of the oil or the solvent, superimposed on
      that of the substance. One can then compare the composite spectrum with
      the known spectrum of the oil or the solvent. Observation then of this
      artifact gives confidence in other measurements made with the
      spectrometer .

      3) Elimination of plausible sources of error and alternative explanations of
      the result (the Sherlock Holmes strategy.) ]4[ Thus, when scientists claimed
      to have observed electric discharges in the rings of Saturn, they argued for
      their result by showing that it could not have been caused by defects in the
      telemetry, interaction with the environment of Saturn, lightning, or dust.
      The only remaining explanation of their result was that it was due to
      electric discharges in the rings--there was no other plausible explanation
      of the observation. (In addition, the same result was observed by both
      Voyager 1 and Voyager 2. This provided independent confirmation.
      Often, several epistemological strategies are used in the same

Physics and Philosophy                                          Musa Akrami

   4) Using the results themselves to argue for their validity. Consider the
   problem of Galileo's telescopic observations of the moons of Jupiter.
   Although one might very well believe that his primitive, early telescope
   might have produced spurious spots of light, it is extremely implausible
   that the telescope would create images that they would appear to be a
   eclipses and other phenomena consistent with the motions of a small
   planetary system. It would have been even more implausible to believe
   that the created spots would satisfy Kepler's Third Law (R3/T2 = constant).
   A similar argument was used by Robert Millikan to support his
   observation of the quantization of electric charge and his measurement of
   the charge of the electron. Millikan remarked " ,The total number of
   changes which we have observed would be between one and two
   thousand, and in not one single instance has there been any change which
   did not represent the advent upon the drop of one definite invariable
   quantity of electricity or a very small multiple of that quantity ("Millikan
   1911, p .)361 .In both of these cases one is arguing that there was no
   plausible malfunction of the apparatus, or background, that would explain
   the observations .

   5) Using an independently well-corroborated theory of the phenomena to
   explain the results. This was illustrated in the discovery of the W ±,the
   charged intermediate vector boson required by the Weinberg-Salam
   unified theory of electroweak interactions. Although these experiments
   used very complex apparatuses and used other epistemological strategies
   (for details see (Franklin ,1986 pp. 170-72)) I believe that the agreement
   of the observations with the theoretical predictions of the particle
   properties helped to validate the experimental results. In this case the
   particle candidates were observed in events that contained an electron
   with high transverse momentum and in which there were no particle jets,
   just as predicted by the theory. In addition, the measured particle mass of
   81 ± 5 GeV/c2 and 80+10-6, GeV/c2found in the two experiments (note the
   independent confirmation also), was in good agreement with the
   theoretical prediction of 82 ± 2.4 GeV/c2. It was very improbable that any
   background effect, which might mimic the presence of the particle ,would
   be in agreement with theory .

   6) Using an apparatus based on a well-corroborated theory. In this case
   the support for the theory inspires confidence in the apparatus based on
   that theory. This is the case with the electron microscope and the radio
   telescope ,whose operations are based on a well-supported theories,
   although other strategies are also used to validate the observations made
   with these instruments .

   Physics and Philosophy                                             Musa Akrami

      7) Using statistical arguments. An interesting example of this arose in the
      1961s when the search for new particles and resonances occupied a
      substantial fraction of the time and effort of those physicists working in
      experimental high-energy physics. The usual technique was to plot the
      number of events observed as a function of the invariant mass of the final-
      state particles and to look for bumps above a smooth background. The
      usual informal criterion for the presence of a new particle was that it
      resulted in a three standard-deviation effect above the background, a result
      that had a probability of 0.27% of occurring in a single bin. This criterion
      was later changed to four standard deviations, which had a probability of
      0.0064% when it was pointed out that the number of graphs plotted each
      year by high-energy physicists made it rather probable, on statistical
      grounds, that a three standard-deviation effect would be observed .

These strategies along with Hacking's intervention and independent
confirmation constitute an epistemology of experiment. They provide us with
good reasons for belief in experimental results, They do not ,however, guarantee
that the results are correct. There are many experiments in which these strategies
are applied, but whose results are later shown to be incorrect (examples will be
presented below). Experiment is fallible. Neither are these strategies exclusive or
exhaustive. No single one of them, or fixed combination of them, guarantees the
validity of an experimental result .Physicists use as many of the strategies as
they can conveniently apply in any given experiment .

2. Galison's Elaboration

In How Experiments End )1987( Peter Galison extended the discussion of
experiment to more complex situations. In his histories of the measurements of
the gyromagnetic ratio of the electron, the discovery of the muon, and the
discovery of weak neutral currents, he considered a series of experiments
measuring a single quantity, a set of different experiments culminating in a
discovery, and two high- energy physics experiments performed by large groups
with complex experimental apparatus .

Galison's view is that experiments end when the experimenters believe that they
have a result that will stand up in court--a result that I believe includes the use of
the epistemological strategies discussed earlier. Thus, David Cline ,one of the
weak neutral-current experimenters remarked, "At present I don't see how to
make these effects [the weak neutral current event candidates] go away "
(Galison, 1987, p. 235) .

   Physics and Philosophy                                           Musa Akrami

Galison emphasizes that, within a large experimental group, different members
of the group may find different pieces of evidence most convincing. Thus, in the
Gargamelle weak neutral current experiment, several group members found the
single photograph of a neutrino-electron scattering event particularly important,
whereas for others the difference in spatial distribution between the observed
neutral current candidates and the neutron background was decisive .Galison
attributes this, in large part, to differences in experimental traditions, in which
scientists develop skill in using certain types of instruments or apparatus. In
particle physics, for example, there is the tradition of visual detectors, such as
the cloud chamber or the bubble chamber ,in contrast to the electronic tradition
of Geiger and scintillation counters and spark chambers. Scientists within the
visual tradition tend to prefer "golden events" that clearly demonstrate the
phenomenon in question, whereas those in the electronic tradition tend to find
statistical arguments more persuasive and important than individual events. (For
further discussion of this issue see Galison (1997)) .

Galison points out that major changes in theory and in experimental practice and
instruments do not necessarily occur at the same time. This persistence of
experimental results provides continuity across these conceptual changes. Thus ,
the experiments on the gyromagnetic ratio spanned classical electromagnetism ,
Bohr's old quantum theory, and the new quantum mechanics of Heisenberg and
Schrodinger. Robert Ackermann has offered a similar view in his discussion of
scientific instruments .

      The advantages of a scientific instrument are that it cannot change
      theories. Instruments embody theories, to be sure, or we wouldn't have
      any grasp of the significance of their operation....Instruments create an
      invariant relationship between their operations and the world, at least
      when we abstract from the expertise involved in their correct use. When
      our theories change, we may conceive of the significance of the
      instrument and the world with which it is interacting differently, and the
      datum of an instrument may change in significance, but the datum can
      nonetheless stay the same, and will typically be expected to do so. An
      instrument reads 2 when exposed to some phenomenon. After a change in
      theory, ]5[ it will continue to show the same reading, even though we may
      take the reading to be no longer important, or to tell us something other
      than what we thought originally (Ackermann 1985, p. 33) .

Galison also discusses other aspects of the interaction between experiment and
theory. Theory may influence what is considered to be a real effect ,demanding
explanation, and what is considered background. In his discussion of the
discovery of the muon, he argues that the calculation of Oppenheimer and

   Physics and Philosophy                                          Musa Akrami

Carlson, which showed that showers were to be expected in the passage of
electrons through matter, left the penetrating particles, later shown to be muons,
as the unexplained phenomenon. Prior to their work, physicists thought the
showering particles were the problem, whereas the penetrating particles seemed
to be understood .

The role of theory as an "enabling theory," (i.e., one that allows calculation or
estimation of the size of the expected effect and also the size of expected
backgrounds) is also discussed by Galison. (See also (Franklin 1995 b) and the
discussion of the Stern-Gerlach experiment below). Such a theory can help to
determine whether an experiment is feasible. Galison also emphasizes that
elimination of background that might simulate or mask an effect is central to the
experimental enterprise, and not a peripheral activity. In the case of the weak
neutral current experiments, the existence of the currents depended crucially on
showing that the event candidates could not all be due to neutron background ]6[.

There is also a danger that the design of an experiment may preclude
observation of a phenomenon. Galison points out that the original design of one
of the neutral current experiments, which included a muon trigger, would not
have allowed the observation of neutral currents. In its original form the
experiment was designed to observe charged currents, which produce a high
energy muon. Neutral currents do not. Therefore, having a muon trigger
precluded their observation. Only after the theoretical importance of the search
for neutral currents was emphasized to the experimenters was the trigger
changed. Changing the design did not, of course, guarantee that neutral currents
would be observed .

Galison also shows that the theoretical presuppositions of the experimenters may
enter into the decision to end an experiment and report the result. Einstein and
de Haas ended their search for systematic errors when their value for the
gyromagnetic ratio of the electron ,g ,1 = agreed with their theoretical model of
orbiting electrons. This effect of presuppositions might cause one to be skeptical
of both experimental results and their role in theory evaluation. Galison's history
shows, however, that, in this case, the importance of the measurement led to
many repetitions of the measurement. This resulted in an agreed-upon result that
disagreed with theoretical expectations .

Recently, Galison has modified his views. In Image and Logic ,an extended
study of instrumentation in 20th-century high-energy physics, Galison )1997(
has extended his argument that there are two distinct experimental traditions
within that field--the visual (or image) tradition and the electronic( or logic)
tradition. The image tradition uses detectors such as cloud chambers or bubble

   Physics and Philosophy                                           Musa Akrami

chanbers, which provide detailed and extensive information about each
individual event. The electronic detectors used by the logic tradition, such as
geiger counters, scintillation counters, and spark chambers, provide less detailed
information about individual events, but detect more events. Galison's view is
that experimenters working in these two traditions form distinct epistemic and
linguistic groups that rely on different forms of argument. The visual tradition
emphasizes the single "golden" event. "On the image side resides a deep-seated
commitment to the 'golden event': the single picture of such clarity and
distinctness that it commands acceptance." (Galison, 1997, p 22 (.The golden
event was the exemplar of the image tradition: an individual instance so
complete and well defined, so 'manifestly' free of distortion and background that
no further data had to be involved" (p. 23). Because the individual events
provided in the logic detectors containded less detailed information than the
pictures of the visual tradition, statistical arguments based on large numbers of
events were required .

Kent Staley (1999) disagrees. He argues that the two traditions are not as distinct
as Galison believes 9

      I show that discoveries in both traditions have employed the same
      statistical [I would add "and/or probabilistic"] form of argument, even
      when basing discovery claims on single, golden events. Where Galison
      sees an epistemic divide between two communities that can only be
      bridged by creole- or pidgin-like 'interlanguage,' there is in fact a shared
      commitment to a statistical form of experimental argument. (P. 96) .

Staley believes that although there is certainly epistemic continuity within a
given tradition, there is also a continuity between the traditions. This does not, I
believe, mean that the shared commitmeny comprises all of the arguments
offered in any particular instance, but rather that the same methods are often
used by both communities. Galison does not deny that statistical methods are
used in the image tradition, but he thinks that they are relatively unimportant .
"While statistics could certainly be used within the image tradition, it was by no
means necessary for most applications" (Galison, 1997, p. 451). In contrast ,
Galison believes that arguments in the logic tradition "were inherently and
inalienably statistical. Estimation of probable errors and the statistical excess
over background is not a side issue in these detectors--it is central to the
possibilty of any demonstration at all" (p. 451) .

Although a detailed discussion of the disagreement between Staley and Galison
would take us too far from the subject of this essay, they both agree that
arguments are offered for the correctness of experimental results. Their

   Physics and Philosophy                                           Musa Akrami

disagreement concerns the nature of those arguments. (For further discussion see
Franklin, (2002), pp. 9-17) .

B. The Case Against Learning From Experiment
1. Collins and the Experimenters' Regress
Collins ,Pickering, and others, have raised objections to the view that
experimental results are accepted on the basis of epistemological arguments.
They point out that "a sufficiently determined critic can always find a reason to
dispute any alleged ‘result’" (MacKenzie 1989, p. 412). Harry Collins, for
example, is well known for his skepticism concerning both experimental results
and evidence. He develops an argument that he calls the "experimenters' regress"
(Collins 1985 ,chapter 4, pp. 79-111): What scientists take to be a correct result
is one obtained with a good, that is, properly functioning, experimental
apparatus. But a good experimental apparatus is simply one that gives correct
results. Collins claims that there are no formal criteria that one can apply to
decide whether or not an experimental apparatus is working properly. In
particular, he argues that calibrating an experimental apparatus by using a
surrogate signal cannot provide an independent reason for considering the
apparatus to be reliable .

In Collins' view the regress is eventually broken by negotiation within the
appropriate scientific community, a process driven by factors such as the career,
social, and cognitive interests of the scientists, and the perceived utility for
future work, but one that is not decided by what we might call epistemological
criteria, or reasoned judgment. Thus, Collins concludes that his regress raises
serious questions concerning both experimental evidence and its use in the
evaluation of scientific hypotheses and theories. Indeed, if no way out of the
regress can be found, then he has a point .

Collins strongest candidate for an example of the experimenters' regress is
presented in his history of the early attempts to detect gravitational radiation, or
gravity waves. (For more detailed discussion of this episode see Collins 1985;
1994; Franklin 1994; 1997a) In this case, the physics community was forced to
compare Weber's claims that he had observed gravity waves with the reports
from six other experiments that failed to detect them. On the one hand ,Collins
argues that the decision between these conflicting experimental results could not
be made on epistemological or methodological grounds--he claims that the six
negative experiments could not legitimately be regarded as replications ]7[and
hence become less impressive. On the other hand, Weber's apparatus, precisely

   Physics and Philosophy                                           Musa Akrami

because the experiments used a new type of apparatus to try to detect a hitherto
unobserved phenomenon ]8[ could not be subjected to standard calibration
techniques .

The results presented by Weber's critics were not only more numerous, but they
had also been carefully cross-checked. The groups had exchanged both data and
analysis programs and confirmed their results. The critics had also investigated
whether or not their analysis procedure, the use of a linear algorithm, could
account for their failure to observe Weber's reported results .They had used
Weber's preferred procedure, a nonlinear algorithm, to analyze their own data,
and still found no sign of an effect. They had also calibrated their experimental
apparatuses by inserting acoustic pulses of known energy and finding that they
could detect a signal. Weber, on the other hand, as well as his critics using his
analysis procedure, could not detect such calibration pulses .

There were, in addition, several other serious questions raised about Weber's
analysis procedures. These included an admitted programming error that
generated spurious coincidences between Weber's two detectors, possible
selection bias by Weber, Weber's report of coincidences between two detectors
when the data had been taken four hours apart, and whether or not Weber's
experimental apparatus could produce the narrow coincidences claimed .

It seems clear that the critics' results were far more credible than Weber's .They
had checked their results by independent confirmation, which included the
sharing of data and analysis programs. They had also eliminated a plausible
source of error, that of the pulses being longer than expected, by analyzing their
results using the nonlinear algorithm and by explicitly searching for such long
pulses. ]9[ They had also calibrated their apparatuses by injecting pulses of
known energy and observing the output .

Contrary to Collins, I believe that the scientific community made a reasoned
judgment and rejected Weber's results and accepted those of his critics .
Although no formal rules were applied (e.g. if you make four errors, rather than
three, your results lack credibility; or if there are five, but not six ,conflicting
results, your work is still credible) the procedure was reasonable .

Pickering has argued that the reasons for accepting results are the future utility
of such results for both theoretical and experimental practice and the agreement
of such results with the existing community commitments. In discussing the
discovery of weak neutral currents, Pickering states ,

   Physics and Philosophy                                             Musa Akrami

      Quite simply, particle physicists accepted the existence of the neutral
      current because they could see how to ply their trade more profitably in a
      world in which the neutral current was real. (1984b, p. 87)

      Scientific communities tend to reject data that conflict with group
      commitments and, obversely, to adjust their experimental techniques to
      tune in on phenomena consistent with those commitments. (1981, p. 236)

The emphasis on future utility and existing commitments is clear. These two
criteria do not necessarily agree. For example, there are episodes in the history
of science in which more opportunity for future work is provided by the
overthrow of existing theory. (See, for example, the history of the overthrow of
parity conservation and of CP symmetry discussed below and in (Franklin 1986,
Ch. 1, 3)) .

2. Pickering on Communal Opportunism and Plastic Resources
Pickering has recently offered a different view of experimental results. In his
view the material procedure (including the experimental apparatus itself along
with setting it up, running it, and monitoring its operation), the theoretical model
of that apparatus, and the theoretical model of the phenomena under
investigation are all plastic resources that the investigator brings into relations of
mutual support. (Pickering 1987; Pickering 1989 ) .He says 9
       Achieving such relations of mutual support is, I suggest, the defining
       characteristic of the successful experiment. (1987, p. 199)
He uses Morpurgo's search for free quarks, or fractional charges of 3/1 e or 2/3
e ,where e is the charge of the electron. (See also (Gooding 1992)). Morpurgo
used a modern Millikan-type apparatus and initially found a continuous
distribution of charge values .Following some tinkering with the apparatus,
Morpurgo found that if he separated the capacitor plates he obtained only
integral values of charge. "After some theoretical analysis, Morpurgo concluded
that he now had his apparatus working properly, and reported his failure to find
any evidence for fractional charges" (Pickering 1987, p. 197) .

Pickering goes on to note that Morpurgo did not tinker with the two competing
theories of the phenomena then on offer, those of integral and fractional charge 9

      The initial source of doubt about the adequacy of the early stages of the
      experiment was precisely the fact that their findings--continuously
      distributed charges--were consonant with neither of the phenomenal
      models which Morpurgo was prepared to countenance. And what
      motivated the search for a new instrumental model was Morpurgo's

   Physics and Philosophy                                           Musa Akrami

      eventual success in producing findings in accordance with one of the
      phenomenal models he was willing to accept

      The conclusion of Morpurgo's first series of experiments, then, and the
      production of the observation report which they sustained, was marked by
      bringing into relations of mutual support of the three elements I have
      discussed: the material form of the apparatus and the two conceptual
      models, one instrumental and the other phenomenal. Achieving such
      relations of mutual support is, I suggest, the defining charactersitic of the
      successful experiment.(P. 199)

Pickering has made several important and valid points concerning experiment .
Most importantly, he has emphasized that an experimental apparatus is initially
rarely capable of producing a valid experimental results and that some
adjustment, or tinkering, is required before it does. He has also recognized that
both the theory of the apparatus and the theory of the phenomena can enter into
the production of a valid experimental result. What I wish to question ,however,
is the emphasis he places on these theoretical components. From Millikan
onwards, experiments had strongly supported the existence of a fundamental
unit of charge and charge quantization. The failure of Morpurgo's apparatus
produce measurements of integral charge indicated that it was not operating
properly and that his theoretical understanding of it was faulty. It was the failure
to produce measurements in agreement with what was already known ( i.e., the
failure of an important experimental check) that caused doubts about Morpurgo's
measurements. This was true regardless of the theoretical models available, or
those that Morpurgo was willing to accept. It was only when Morpurgo's
apparatus could reproduce known measurements that it could be trusted and
used to search for fractional charge. To be sure, Pickering has allowed a role for
the natural world in the production of the experimental result, but it does not
seem to be decisive .

3. Critical Responses to Pickering
Ackermann has offered a modification of Pickering's view. He suggests that the
experimental apparatus itself is a less plastic resource then either the theoretical
model of the apparatus or that of the phenomenon .
      To repeat, changes in A [the apparatus] can often be seen (in real time,
      without waiting for accommodation by B [the theoretical model of the
      apparatus]) as improvements, whereas ‘improvements’ in B don't begin to
      count unless A is actually altered and realizes the improvements
      conjectured. It's conceivable that this small asymmetry can account,

   Physics and Philosophy                                          Musa Akrami

      ultimately, for large scale directions of scientific progress and for the
      objectivity and rationality of those directions. (Ackermann 1991, p. 456)

Hacking (1992) has also offered a more complex version of Pickering's later
view. He suggests that the results of mature laboratory science achieve stability
and are self-vindicating when the elements of laboratory science are brought into
mutual consistency and support. These are (1) ideas: questions ,background
knowledge, systematic theory, topical hypotheses, and modeling of the
apparatus; (2) things: target, source of modification, detectors, tools, and data
generators; and (3) marks and the manipulation of marks: data, data assessment,
data reduction, data analysis, and interpretation .

      Stable laboratory science arises when theories and laboratory equipment
      evolve in such a way that they match each other and are mutually self-
      vindicating. (1992, p. 56)

      We invent devices that produce data and isolate or create phenomena, and
      a network of different levels of theory is true to these phenomena.
      Conversely we may in the end count them only as phenomena only when
      the data can be interpreted by theory. (pp. 57-8)

One might ask whether such mutual adjustment between theory and
experimental results can always be achieved? What happens when an
experimental result is produced by an apparatus on which several of the
epistemological strategies, discussed earlier, have been successfully applied, and
the result is in disagreement with our theory of the phenomenon? Accepted
theories can be refuted. Several examples will be presented below .

Hacking himself worries about what happens when a laboratory science that is
true to the phenomena generated in the laboratory, thanks to mutual adjustment
and self-vindication, is successfully applied to the world outside the laboratory.
Does this argue for the truth of the science. In Hacking's view it does not. If
laboratory science does produce happy effects in the "untamed world,... it is not
the truth of anything that causes or explains the happy effects" (1992, p. 60) .

4. Pickering and the Dance of Agency
Recently Pickering has offered a somewhat revised account of science. "My
basic image of science is a performative one, in which the performances the
doings of human and material agency come to the fore. Scientists are human
agents in a field of material agency which they struggle to capture in machines
(Pickering, 1995, p. 21)." He then discusses the complex interaction between

   Physics and Philosophy                                          Musa Akrami

human and material agency, which I interpret as the interaction between
experimenters, their apparatus, and the natural world .
      The dance of agency, seen asymmetrically from the human end, thus takes
      the form of a dialectic of resistance and accommodations ,where
      resistance denotes the failure to achieve an intended capture of agency in
      practice, and accommodation an active human strategy of response to
      resistance ,which can include revisions to goals and intentions as well as
      to the material form of the machine in question and to the human frame of
      gestures and social relations that surround it (p. 22) .

Pickering's idea of resistance is illustrated by Morpurgo's observation of
continuous, rather than integral or fractional, electrical charge, which did not
agree with his expectations. Morpurgo's accommodation consisted of changing
his experimental apparatus by using a larger separation between his plates, and
also by modifying his theoretical account of the apparatus. That being done,
integral charges were observed and the result stabilized by the mutual agreement
of the apparatus, the theory of the apparatus, and the theory of the phenomenon .
Pickering notes that "the outcomes depend on how the world is (p. 182)." "In
this way, then ,how the material world is leaks into and infects our
representations of it in a nontrivial and consequential fashion. My analysis thus
displays an intimate and responsive engagement between scientific knowledge
and the material world that is integral to scientific practice (p. 183) ".

Nevertheless there is something confusing about Pickering's invocation of the
natural world. Although Pickering acknowledges the importance of the natural
world, his use of the term "infects" seems to indicate that he isn't entirely happy
with this. Nor does the natural world seem to have much efficacy. It never seems
to be decisive in any of Pickering's case studies. Recall that he argued that
physicists accepted the existence of weak neutral currents because "they could
ply their trade more profitably in a world in which the neutral current was real."
In his account, Morpurgo's observation of continuous charge is important only
because it disagrees with his theoretical models of the phenomenon. The fact
that it disagreed with numerous previous observations of integral charge doesn't
seem to matter. This is further illustrated by Pickering's discussion of the
conflict between Morpurgo and Fairbank. As we have seen, Morpurgo reported
that he did not observe fractional electrical charges .On the other hand, in the
late 1970s and early 1980s, Fairbank and his collaborators published a series of
papers in which they claimed to have observed fractional charges (See, for
example, LaRue, Phillips et al. 1981 ) .Faced with this discord Pickering
concludes ,

   Physics and Philosophy                                           Musa Akrami

             In Chapter 3, I traced out Morpurgo's route to his findings in terms
             of the particular vectors of cultural extension that he pursued, the
             particular resistances and accommodations thus precipitated, and
             the particular interactive stabilizations he achieved. The same could
             be done, I am sure, in respect of Fairbank. And these tracings are all
             that needs to said about their divergence .It just happened that the
             contingencies of resistance and accommodation worked out
             differently in the two instances. Differences like these are, I think ,
             continually bubbling up in practice, without any special causes
             behind them (pp212-211 .) .

The natural world seems to have disappeared from Pickering's account. There is
a real question here as to whether or not fractional charges exist in nature .The
conclusions reached by Fairbank and by Morpurgo about their existence cannot
both be correct. It seems insufficient to merely state, as Pickering does, that
Fairbank and Morpurgo achieved their individual stabilizations and to leave the
conflict unresolved. (Pickering does comment that one could follow the
subsequent history and see how the conflict was resolved, and he does give some
brief statements about it, but its resolution is not important for him). At the very
least, I believe, one should consider the actions of the scientific community.
Scientific knowledge is not determined individually, but communally .Pickering
seems to acknowledge this. "One might, therefore, want to set up a metric and
say that items of scientific knowledge are more or less objective depending on
the extent to which they are threaded into the rest of scientific culture, socially
stabilized over time, and so on. I can see nothing wrong with thinking this
way.... (p. 196)." The fact that Fairbank believed in the existence of fractional
electrical charges, or that Weber strongly believed that he had observed gravity
waves, does not make them right. These are questions about the natural world
that can be resolved. Either fractional charges and gravity waves exist or they
don't, or to be more cautious we might say that we have good reasons to support
our claims about their existence, or we do not .

Another issue neglected by Pickering is the question of whether a particular
mutual adjustment of theory, of the apparatus or the phenomenon, and the
experimental apparatus and evidence is justified. Pickering seems to believe that
any such adjustment that provides stabilization, either for an individual or for the
community, is acceptable. I do not. Experimenters sometimes exclude data and
engage in selective analysis procedures in producing experimental results. These
practices are, at the very least, questionable as is the use of the results produced
by such practices in science. There are, I believe ,procedures in the normal
practice of science that provide safeguards against them. (For details see
Franklin, 2002, Section 1) .

   Physics and Philosophy                                           Musa Akrami

The difference between our attitudes toward the resolution of discord is one of
the important distinctions between my view of science and Pickering's. I do not
believe it is sufficient simply to say that the resolution is socially stabilized. I
want to know how that resolution was achieved and what were the reasons
offered for that resolution. If we are faced with discordant experimental results
and both experimenters have offered reasonable arguments for their correctness,
then clearly more work is needed. It seems reasonable, in such cases, for the
physics community to search for an error in one, or both, of the experiments .

Pickering discusses yet another difference between our views. He sees
traditional philosophy of science as regarding objectivity "as stemming from a
peculiar kind of mental hygiene or policing of thought. This police function
relates specifically to theory choice in science, which,... is usually discussed in
terms of the rational rules or methods responsible for closure in theoretical
debate (p. 197)." He goes on to remark that ,

      The most action in recent methodological thought has centered on
      attempts like Allan Franklin's to extend the methodological approach to
      experiments by setting up a set of rules for their proper performance.
      Franklin thus seeks to extend classical discussions of objectivity to the
      empirical base of science (a topic hitherto neglected in the philosophical
      tradition but one that, of course the mangle [Pickering's view] also
      addresses). For an argument between myself and Franklin on the same
      lines as that laid out below, see ( Franklin 1990, Chapter 8; Franklin
      1991); and (Pickering 1991); and for commentaries related to that debate,
      (Ackermann 1991) and (Lynch 1991) (p197 .) ".

For further discussion see (Franklin 1993b)). Although I agree that my
epistemology of experiment is designed to offer good reasons for belief in
experimental results, I do not agree with Pickering that they are a set of rules. I
regard them as a set of strategies, from which physicists choose, in order to
argue for the correctness of their results. As noted above, I do not think the
strategies offered are either exclusive or exhaustive .

There is another point of disagreement between Pickering and myself. He claims
to be dealing with the practice of science, and yet he excludes certain practices
from his discussions. One scientific practice is the application of the
epistemological strategies I have outlined above to argue for the correctness of
an experimental results. In fact, one of the essential features of an experimental
paper is the presentation of such arguments. I note further that writing such
papers, a performative act, is also a scientific practice and it would seem
reasonable to examine both the structure and content of those papers .

   Physics and Philosophy                                           Musa Akrami

5. Hacking's The Social Construction of What?
Recently Ian Hacking (1999, chapter 3) has provided an incisive and interesting
discussion of the issues that divide the constructivists (Collins, Pickering ,etc.)
from the rationalists, like myself. He sets out three sticking points between the
two views: 1) contingency, 2) nominalism, and 3) external explanations of
stability .

Contingency is the idea that science is not predetermined, that it could have
developed in any one of several successful ways. This is the view adopted by
constructivists. Hacking illustrates this with Pickering's account of high-energy
physics during the 1970s during which the quark model came to dominate. (See
Pickering 1984a) .

      The constructionist maintains a contingency thesis. In the case of physics,
      (a) physics theoretical, experimental, material) could have developed in,
      for example, a nonquarky way, and, by the detailed standards that would
      have evolved with this alternative physics, could have been as successful
      as recent physics has been by its detailed standards. Moreover, (b) there is
      no sense in which this imagined physics would be equivalent to present
      physics. The physicist denies that. (Hacking 1999, pp. 78-79) .

      To sum up Pickering's doctrine: there could have been a research program
      as successful ("progressive") as that of high-energy physics in the 1970s,
      but with different theories, phenomenology, schematic descriptions of
      apparatus, and apparatus, and with a different, and progressive, series of
      robust fits between these ingredients. Moreover and this is something
      badly in need of clarification the "different" physics would not have been
      equivalent to present physics. Not logically incompatible with, just
      different .

      The constructionist about (the idea) of quarks thus claims that the upshot
      of this process of accommodation and resistance is not fully
      predetermined .Laboratory work requires that we get a robust fit between
      apparatus, beliefs about the apparatus, interpretations and analyses of
      data, and theories .Before a robust fit has been achieved, it is not
      determined what that fit will be. Not determined by how the world is, not
      determined by technology now in existence, not determined by the social
      practices of scientists, not determined by interests or networks, not
      determined by genius, not determined by anything (pp. 72-73, emphasis
      added) .

   Physics and Philosophy                                          Musa Akrami

Much depends here on what Hacking means by "determined.." If he means
entailed then I agree with him. I doubt that the world, or more properly, what we
can learn about it, entails a unique theory. If not, as seems more plausible ,he
means that the way the world is places no restrictions on that successful science,
then I disagree strongly. I would certainly wish to argue that the way the world
is restricts the kinds of theories that will fit the phenomena, the kinds of
apparatus we can build, and the results we can obtain with such apparatuses. To
think otherwise seems silly. Consider a homey example, it seems to me highly
unlikely, an understatement, that someone can come up with a successful theory
in which objects whose density is greater than that of air fall upwards. This is
not, I believe, a caricature of the view Hacking describes. Describing Pickering's
view, he states, "Physics did not need to take a route that involved Maxwell's
Equations, the Second Law of Thermodynamics, or the present values of the
velocity of light (p. 70)." Although I have some sympathy for this view as
regards Maxwell's Equations or the Second Law of Thermodynamics, I do not
agree about the value of the speed of light. That is determined by the way the
world is. Any successful theory of light must give that value for its speed .

At the other extreme are the "inevitablists," among whom Hacking classifies
most scientists. He cites Sheldon Glashow, a Nobel Prize winner, "Any
intelligent alien anywhere would have come upon the same logical system as we
have to explain the structure of protons and the nature of supernovae (Glashow
 ,1992p. 28) ".

Another difference between Pickering and myself on contingency concerns the
question of not whether an alternative is possible, but rather whether there are
reasons why that alternative should be pursued. Pickering seems to identify can
with ought .

In the late 1970s there was a disagreement between the results of low-energy
experiments on atomic parity violation (the violation of left-right symmetry)
performed at the University of Washington and at Oxford University and the
result of a high-energy experiment on the scattering of polarized electrons from
deuterium (the SLAC E122 experiment). The atomic-parity violation
experiments failed to observe the parity-violating effects predicted by the
Weinberg- Salam (W-S) unified theory of electroweak interactions, whereas the
SLAC experiment observed the predicted effect. In my view, these early atomic
physics results were quite uncertain in themselves and that uncertainty was
increased by positive results obtained in similar experiments at Berkeley and
Novosibirsk. At the time the theory had other evidential support, but was not
universally accepted. Pickering and I are in agreement that the W-S theory was
accepted on the basis of the SLAC E122 result. We differ dramatically in our

   Physics and Philosophy                                           Musa Akrami

discussions of the experiments Our difference on contingency concerns a
particular theoretical alternative that was proposed at the time to explain the
discrepancy between the experimental results .

Pickering asked why a theorist might not have attempted to find a variant of
electroweak gauge theory that might have reconciled the Washington-Oxford
atomic parity results with the positive E122 result. (What such a theorist was
supposed to do with the supportive atomic parity results later provided by
experiments at Berkeley and at Novosibirsk is never mentioned). "But though it
is true that E122 analysed their data in a way that displayed the improbability
[the probability of the fit to the hybrid model was 6 x 10 4-] of a particular class
of variant gauge theories, the so-called 'hybrid models,' I do not believe that it
would have been impossible to devise yet more variants" (Pickering 1991, p.
462). Pickering notes that open-ended recipes for constructing such variants had
been written down as early as 1972 (p. 467). I agree that it would have been
possible to do so, but one may ask whether or not a scientist might have wished
to do so. If the scientist agreed with my view that the SLAC E122 experiment
provided considerable evidential weight in support of the W-S theory and that a
set of conflicting and uncertain results from atomic parity-violation experiments
gave an equivocal answer on that support ,what reason would they have had to
invent an alternative ?

This is not to suggest that scientists do not, or should not, engage in speculation,
but rather that there was no necessity to do so in this case .Theorists often do
propose alternatives to existing, well-confirmed theories .

Constructivist case studies always seem to result in the support of existing ,
accepted theory (Pickering 1984a; 1984b; 1991; Collins 1985; Collins and Pinch
1993). One criticism implied in such cases is that alternatives are not
considered, that the hypothesis space of acceptable alternatives is either very
small or empty. I don't believe this is correct. Thus, when the experiment of
Christenson et al. (1964) detected Ko 2decay into two pions, which seemed to
show that CP symmetry (combined particle-antiparticle and space inversion
symmetry) was violated, no fewer than 10 alternatives were offered. These
included 1) the cosmological model resulting from the local dysymmetry of
matter and antimatter, 2) external fields, 3) the decay of the Ko 2into a Ko 1with
the subsequent decay of the Ko 1into two pions, which was allowed by the
symmetry, 4) the emission of another neutral particle, "the paritino," in the Ko 2
decay, similar to the emission of the neutrino in beta decay, 5) that one of the
pions emitted in the decay was in fact a "spion," a pion with spin one rather than
zero, 6) that the decay was due to another neutral particle, the L, produced
coherently with the Ko 7 ) the existence of a "shadow" universe, which interacted

   Physics and Philosophy                                          Musa Akrami

with out universe only through the weak interactions, and that the decay seen
was the decay of the" shadow Ko ,2" 8)the failure of the exponential decay law ,
9) the failure of the principle of superposition in quantum mechanics, and 10)
that the decay pions were not bosons .

As one can see, the limits placed on alternatives were not very stringent. By the
end of 1967, all of the alternatives had been tested and found wanting ,leaving
CP symmetry unprotected. Here the differing judgments of the scientific
community about what was worth proposing and pursuing led to a wide variety
of alternatives being tested .

Hacking's second sticking point is nominalism, or name-ism. He notes that in its
most extreme form nominalism denies that there is anything in common or
peculiar to objects selected by a name, such as "Douglas fir" other than that they
are called Douglas fir. Opponents contend that good names, or good accounts of
nature, tell us something correct about the world. This is related to the realism-
antirealism debate concerning the status of unobservable entities that has
plagued philosophers for millennia. For example Bas van Fraassen (1980), an
antirealist, holds that we have no grounds for belief in unobservable entities such
as the electron and that accepting theories about the electron means only that we
believe that the things the theory says about observables is true. A realist claims
that electrons really exist and that as, for example, Wilfred Sellars remarked, "to
have good reason for holding a theory is ipso facto to have good reason for
holding that the entities postulated by the theory exist (Sellars 1962, p. 97)." In
Hacking's view a scientific nominalist is more radical than an antirealist and is
just as skeptical about fir trees as they are about electrons. A nominalist further
believes that the structures we conceive of are properties of our representations
of the world and not of the world itself. Hacking refers to opponents of that view
as inherent structuralists .

Hacking also remarks that this point is related to the question of " scientific
facts." Thus, constructivists Latour and Woolgar originally entitled their book
Laboratory Life: The Social Construction of Scientific Facts .)1979( Andrew
Pickering entitled his history of the quark model Constructing Quarks( Pickering
1984a). Physicists argue that this demeans their work. Steven Weinberg, a realist
and a physicist, criticized Pickering's title by noting that no mountaineer would
ever name a book Constructing Everest .For Weinberg, quarks and Mount
Everest have the same ontological status. They are both facts about the world.
Hacking argues that constructivists do not, despite appearances, believe that
facts do not exist, or that there is no such thing as reality. He cites Latour and
Woolgar" that 'out-there-ness' is a consequence of scientific work rather than its

   Physics and Philosophy                                            Musa Akrami

cause (Latour and Woolgar 1986, p. 180)." I agree with Hacking when he
concludes that ,

      Latour and Woolgar were surely right. We should not explain why some
      people believe that p by saying that p is true, or corresponds to a fact, or
      the facts. For example: someone believes that the universe began with
      what for brevity we call a big bang. A host of reasons now supports this
      belief. But after you have listed all the reasons, you should not add, as if it
      were an additional reason for believing in the big bang, 'and it is true that
      the universe began with a big bang.' Or 'and it is a fact.'This observation
      has nothing peculiarly to do with social construction. It could equally
      have been advanced by an old-fashioned philosopher of language. It is a
      remark about the grammar of the verb 'to explain' (Hacking 1999, pp. 80-
      81) .

I would add, however, that the reasons Hacking cites as supporting that belief
are given to us by valid experimental evidence and not by the social and
personal interests of scientists. I'm not sure that Latour and Woolgar would
agree. My own position is one that one might reasonably call conjectural
realism. I believe that we have good reasons to believe in facts, and in the
entities involved in our theories, always remembering, of course, that science is
fallible .

Hacking's third sticking point is the external explanations of stability .

      The constructionist holds that explanations for the stability of scientific
      belief involve, at least in part, elements that are external to the content of
      science. These elements typically include social factors, interests ,
      networks, or however they be described. Opponents hold that whatever be
      the context of discovery, the explanation of stability is internal to the
      science itself (Hacking 1999, p. 92) .

      Rationalists think that most science proceeds as it does in the light of good
      reasons produced by research. Some bodies of knowledge become stable
      because of the wealth of good theoretical and experimental reasons that
      can be adduced for them. Constructivists think that the reasons are not
      decisive for the course of science. Nelson (1994) concludes that this issue
      will never be decided .Rationalists, at least retrospectively, can always
      adduce reasons that satisfy them. Constructivists, with equal ingenuity,
      can always find to their own satisfaction an openness where the upshot of
      research is settled by something other than reason. Something external.

   Physics and Philosophy                                           Musa Akrami

      That is one way of saying we have found an irresoluble "sticking point"
      (pp. 91-92 (

Thus, there is a rather severe disagreement on the reasons for the acceptance of
experimental results. For some, like Staley, Galison and myself, it is because of
epistemological arguments. For others, like Pickering, the reasons are utility for
future practice and agreement with existing theoretical commitments. Although
the history of science shows that the overthrow of a well-accepted theory leads
to an enormous amount of theoretical and experimental work, proponents of this
view seem to accept it as unproblematical that it is always agreement with
existing theory that has more future utility. Hacking and Pickering also suggest
that experimental results are accepted on the basis of the mutual adjustment of
elements which includes the theory of the phenomenon .

Nevertheless, everyone seems to agree that a consensus does arise on
experimental results .

2. The Roles of Experiment
A. A Life of Its Own
Although experiment often takes its importance from its relation to theory,
Hacking pointed out that it often has a life of its own, independent of theory. He
notes the pristine observations of Carolyn Herschel's discovery of comets,
William Herschel's work on "radiant heat," and Davy's observation of the gas
emitted by algae and the flaring of a taper in that gas. In none of these cases did
the experimenter have any theory of the phenomenon under investigation. One
may also note the nineteenth century measurements of atomic spectra and the
work on the masses and properties on elementary particles during the 1960s.
Both of these sequences were conducted without any guidance from theory .

In deciding what experimental investigation to pursue, scientists may very well
be influenced by the equipment available and their own ability to use that
equipment (McKinney 1992). Thus, when the Mann-O'Neill collaboration was
doing high energy physics experiments at the Princeton-Pennsylvania
Accelerator during the late 1960s, the sequence of experiments was (1)
measurement of the K +decay rates, (2) measurement of the K+ e3 branching ratio
and decay spectrum, (3) measurement of the K+e2 branching ratio, and (4)
measurement of the form factor in K+e3 decay. These experiments were

   Physics and Philosophy                                          Musa Akrami

performed with basically the same experimental apparatus, but with relatively
minor modifications for each particular experiment. By the end of the sequence
the experimenters had become quite expert in the use of the apparatus and
knowledgeable about the backgrounds and experimental problems. This allowed
the group to successfully perform the technically more difficult experiments
later in the sequence. We might refer to this as "instrumental loyalty" and the
"recycling of expertise" (Franklin 1997b). This meshes nicely with Galison's
view of experimental traditions. Scientists, both theorists and experimentalists,
tend to pursue experiments and problems in which their training and expertise
can be used .

Hacking also remarks on the "noteworthy observations" on Iceland Spar by
Bartholin, on diffraction by Hooke and Grimaldi, and on the dispersion of light
by Newton. "Now of course Bartholin, Grimaldi, Hooke, and Newton were not
mindless empiricists without an ‘idea’ in their heads. They saw what they saw
because they were curious, inquisitive, reflective people. They were attempting
to form theories. But in all these cases it is clear that the observations preceded
any formulation of theory" (Hacking 1983, p. 156). In all of these cases we may
say that these were observations waiting for, or perhaps even calling for, a
theory. The discovery of any unexpected phenomenon calls for a theoretical
explanation .

B. Confirmation and Refutation
Nevertheless several of the important roles of experiment involve its relation to
theory. Experiment may confirm a theory, refute a theory, or give hints to the
mathematical structure of a theory .

1. The Discovery of Parity Nonconservation: A Crucial
Let us consider first an episode in which the relation between theory and
experiment was clear and straightforward. This was a " crucial" experiment, one
that decided unequivocally between two competing theories, or classes of
theory. The episode was that of the discovery that parity, mirror-reflection
symmetry or left-right symmetry, is not conserved in the weak interactions. (For
details of this episode see Franklin (1986, Ch. 1)) .Experiments showed that in
the beta decay of nuclei the number of electrons emitted in the same direction as
the nuclear spin was different from the number emitted opoosite to the spin
direction. This was a clear demonstartion of parity vilation in the weak
interactions .

   Physics and Philosophy                                            Musa Akrami

2. The Discovery of CP Violation: A Persuasive Experiment
After the discovery of parity and charge conjugation nonconservation, and
following a suggestion by Landau, physicists considered CP ( combined parity
and particle-antiparticle symmetry), which was still conserved in the
experiments, as the appropriate symmetry. One consequence of this scheme ,if
CP were conserved, was that the K1o meson could decay into two pions, whereas
the K2o meson could not. ]11[ Thus, observation of the decay of K2o into two pions
would indicate CP violation. The decay was observed by a group at Princeton
University. Although several alternative explanations were offered, experiments
eliminated each of the alternatives leaving only CP violation as an explanation
of the experimental result. (For details of this episode see Franklin (1986, Ch.

3. The Discovery of Bose-Einstein Condensation: Confirmation
After 70 Years
In both of the episodes discussed previously, those of parity nonconservation
and of CP violation, we saw a decision between two competing classes of
theories. This episode, the discovery of Bose-Einstein condensation (BEC),
illustrates the confirmation of a specific theoretical prediction 70 years after the
theoretical prediction was first made. Bose (1924) and Einstein (1924; 1925)
predicted that a gas of noninteracting bosonic atoms will, below a certain
temperature, suddenly develop a macroscopic population in the lowest energy
quantum state. ]11[

C. Complications
In the three episodes discussed in the previous section, the relation between
experiment and theory was clear. The experiments gave unequivocal results and
there was no ambiguity about what theory was predicting. None of the
conclusions reached has since been questioned. Parity and CP symmetry are
violated in the weak interactions and Bose-Einstein condensation is an accepted
phenomenon. In the practice of science things are often more complex.
Experimental results may be in conflict, or may even be incorrect. Theoretical
calculations may also be in error or a correct theory may be incorrectly applied.
There are even cases in which both experiment and theory are wrong. As noted
earlier, science is fallible. In this section I will briefly discuss several episodes
which illustrate these complexities .

1. The Fall of the Fifth Force

   Physics and Philosophy                                            Musa Akrami

The episode of the fifth force is the case of a refutation of an hypoothesis, but
only after a disagreement between experimental results was resolved. The "Fifth
Force" was a proposed modification of Newton's Law of Universal Gravitation.
The initial experiments gave conflicting results: one supported the existence of
the Fifth Force whereas the other argued against it. After numerous repetitions
of the experiment, the discord was resolved and a consensus reached that the
Fifth Force did not exist.

2. Right Experiment, Wrong Theory: The Stern-Gerlach
The Stern-Gerlach experiment was regarded as crucial at the time it was
performed, but, in fact, wasn't. In the view of the physics community it decided
the issue between two theories, refuting one and supporting the other. In the
light of later work, however, the refutation stood, but the confirmation was
questionable. In fact, the experimental result posed problems for the theory it
had seemingly confirmed. A new theory was proposed and although the Stern-
Gerlach result initially also posed problems for the new theory, after a
modification of that new theory, the result confirmed it. In a sense, it was crucial
after all. It just took some time .

The Stern-Gerlach experiment provides evidence for the existence of electron
spin. These experimental results were first published in 1922, although the idea
of electron spin wasn't proposed by Goudsmit and Uhlenbeck until 1925 (1925 ;
1926) .One might say that electron spin was discovered before it was invented .

3. Sometimes Refutation Doesn't Work: The Double-Scattering of
In the last section we saw some of the difficulty inherent in experiment-theory
comparison. One is sometimes faced with the question of whether the
experimental apparatus satisfies the conditions required by theory ,or
conversely, whether the appropriate theory is being compared to the
experimental result. A case in point is the history of experiments on the double-
scattering of electrons by heavy nuclei (Mott scattering) during the 1931 s and
the relation of these results to Dirac's theory of the electron, an episode in which
the question of whether or not the experiment satisfied the conditions of the
theoretical calculation was central. Initially, experiments disagreed with Mott's
calculation, casting doubt on the underlying Dirac theory .After more than a
decade of work, both experimental and theoretical, it was realized that there was

   Physics and Philosophy                                            Musa Akrami

a background effect in the experiments that masked the predicted effect. When
the background was eliminated experiment and theory agreed .

D. Other Roles
1. Evidence for a New Entity: J.J. Thomson and the Electron
Experiment can also provide us with evidence for the existence of the entities
involved in our theories. J.J. Thomson's experiments on cathode rays provided
grounds for belief in the existence of electrons.

2. The Articulation of Theory: Weak Interactions
Experiment can also help to articulate a theory .Experiments on beta decay
during from the 1930s to the 1950s detremined the precise mathematical form of
Fermi's theory of beta decay.

3. Conclusion
In this essay varying views on the nature of experimental results have been
presented. Some argue that the acceptance of experimental results is based on
epistemological arguments ,whereas others base acceptance on future utility,
social interests, or agreement with existing community commitments. Everyone
agrees , however, that for whatever reasons, a consensus is reached on
experimental results. These results then play many important roles in physics
and we have examined several of these roles, although certainly not all of them.
We have seen experiment deciding between two competing theories, calling for
a new theory, confirming a theory ,refuting a theory, providing evidence that
determined the mathematical form of a theory, and providing evidence for the
existence of an elementary particle involved in an accepted theory. We have also
seen that experiment has a life of its own, independent of theory. If, as I believe,
epistemological procedures provide grounds for reasonable belief in
experimental results, then experiment can legitimately play the roles I have
discussed and can provide the basis for scientific knowledge .

  Physics and Philosophy                                         Musa Akrami

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Other Suggested Reading
     Ackermann, R. 1988. "Experiments as the Motor of Scientific Progress ."
      Social Epistemology .335-327 92
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      Kluwer Academic Publishers .
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      Experiment .Cambridge: Cambridge University Press .
     Koertge, N., Ed. 1998 .A House Built on Sand: Exposing Postmodernist
      Myths About Science .Oxford: Oxford University Press .
     Nelson, A. 1994. "How Could Scientific Facts be Socially Constructed ."?
      Studies in History and Philosophy of Science .547-535 9)4(25
     Pickering, A., Ed. 1992 .Science as Practice and Culture .Chicago 9
      University of Chicago Press .
     Pickering, A. 1995 .The Mangle of Practice .Chicago: University of
      Chicago Press .
     Pinch, T. 1986 .Confronting Nature .Dordrecht: Reidel .
     Rasmussen, N. 1993. "Facts, Artifacts, and Mesosomes: Practicing
      Epistemology with the Electron Microscope ."Studies in History and
      Philosophy of Science .265-227 924
     Shapere, D. 1982. "The Concept of Observation in Science and
      Philosophy ."Philosophy of Science.525-482 949


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