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Applications We want to discuss certain creative cases in the history of science within the theoretical framework we have delineated: Case Ι: Johannes Kepler. Case Π: Max Planck. Our double aim is to deepen our understanding of both the theoretical framework and the structure and dynamic of the history of science. 1 Case Ι Johannes Kepler (1571-1630) Why Kepler? What is so special about Kepler? Kepler happened to live in the era of the scientific revolution; he was born after the death of Copernicus (1543) and before the birth of Newton (1642). That era constituted an unprecedented turning point and upheaval in our understanding of nature and in world civilization. It gave birth to modern science at the expense of pre-modern natural philosophy. To understand Kepler is a key to understanding the scientific revolution. After all, Kepler was a seminal figure, a giant, of the scientific revolution, side by side with Copernicus, Gilbert, Galileo, Descartes, Huygens, Leibniz and Newton. Kepler is the founder of modern astronomy (and optics). He radically changed our approach to celestial phenomena by destroying many of the old ways and prejudices. Yet, he never made a clean break with per-modern science. He partook of both pre-modern and modern ways. He was more of a bridge between pre-modern natural philosophy and modern natural science. Accordingly, he could be considered an important key to the history of physical science. He combines in his work and career major elements of both pre-modern natural philosophy and modern science, 2 which makes him an epitome of the totality of physical science – a basic node of scientific development? Let us discuss Kepler’s scientific career in relation to the model we have proposed for scientific production. We want to focus on Kepler’s epistemic heritage, his evolving research project, the tools he employed in his research work, and the way he arrived at his main astronomical discoveries. We shall also comment on the revolutionary features of Kepler’s work. Kepler’s Epistemic Heritage: Kepler’s great contributions were not confined to astronomy, but covered also geometry and optics (he was the founder of scientific optics in Europe). However, we shall focus on his astronomy. The following broad stages characterized Kepler’s astronomical epistemic heritage: 1. Aristotelian physics and cosmology. 2. Hellenistic Astronomy. 3. Arabic Medieval Astronomy. 4. Copernicus. 5. Tycho. 6. Pythagoras. 7. Materialism. 8. Gilbert. 3 1. Elements of Aristotelian Physics The Universe is uncreated. There is neither a starting point nor a terminating point to time. The Universe is finite in volume and variety. Space is the limit and boundary of matter. Thus, it is finite in extent. There is nothing beyond the boundary of the Universe – not even space and time. The Universe is spherical in shape, because the sphere is the perfect shape in solid geometry (a Platonic idea). Nature abhors a vacuum. There are no vacua in the Universe. Being finite, the Universe has a definite centre endowed with specific physical characteristics. It is the only centre of attraction in the Universe. The Earth is located at the centre of the Universe. Its centre coindes with the centre of the Universe. The Earth is spherical – a perfect sphere. [The circumference of the Earth in Graeco – Arabic Science: 1. Aristotle’s Method (4th century BC): The ancients thought that all stars, apart from the planets, the Moon and Sun, are fixed relative to each other, and lie on the surface of a solid sphere rotating around the Earth. They noticed that the axis of rotation passed through the centre of the Earth and the polar star (almost). Thus, the latter remained fixed as the sphere of the stars revolved. Aristotle (and others) noticed that as one travels northwards, the angle made by the polar star with the horizon changes (increases). That was one piece of evidence for the sphericity of the Earth, and was used by Aristotle and others to measure the circumference of the Earth, as follows: 4 α= angle polar star makes with horizon = < AOM C= Earth’s Circumference. | AB | = θ g C 2π 5 2. Eratosthenes` Method (3rd century BC): Eratosthenes noticed that, on 21st June at midday, a gnomon at Syene (modern Aswan) in the south of Egypt does not leave any shadow, but leaves a slight, but noticeable, shadow in Alexandria in the north of Egypt. Eratosthenes knew that the two cities lie almost exactly on the same longitude. To him, this slight difference in the shadow angle was a clear indication of the sphericity of the Earth. By accurately measuring the shadow angle at Alexandria and the distance between Syene and Alexandria, he was able to produce an accurate number for the circumference of the Earth, as follows: S = Syene A = Alexandria α = Shadow Angle 6 α = shadow angle = shadow length gnomon length α = ISAI Hence C. 2π C 3. Biruni’s Method (973-1051 AD): The idea was to measure the horizon angle from the top of a mountain next to a sea coast, and to measure this angle at the foot of the mountain. From these measurements and from measuring the height of the mountain, Biruni obtained an accurate value for the circumference of the Earth, as follows: 7 R= radius of Earth The Universe is fundamentally inhomogeneous. It consists of two qualitatively different realms: Earth and its immediate surroundings and the Heavens. They differ in the following respects: 8 Earth Heavens 1. Obeys specific laws: 1. Obey different specific laws: The laws of Aristotelian the laws of Greek Astronomy; physics; physics is the astronomy is the science of the science of Earth and its heavens. surroundings 2. Subject to change, 2. Immutable and eternal; subject corruption, birth and death. to no change whatsoever. 3. The variety of bodies and 3. The heavens are made of a material entities in it is fifth, eternal substance, called the constituted by four basic ether, or, the quintessence. It is elements: earth, water, air neither heavy nor light. Thus, it and fire. Earth is the heaviest tends to move in uniform circular element and naturally moves motion; it neither falls nor rises towards the centre of the up. All the planets, stars and their Universe, where it settles carriers are made of it. It is down. Water is heavy, but heavenly stuff. less so than earth. Air is light,and,therefore,tends to rise upwards. Fire is lighter still, and tends to rise rapidly towards the periphery of Earth’s surrounding. 4. Bodies tend to move in 4. Celestial bodies move naturally straight lines, whether in uniform circular motion or a downwards or upwards. combination of such motions. Natural motion is either The stars move in a perfect 9 towards the centre of the circular motion round the Earth. universe, or away from it. The Sun, Moon and five planets External forces could cause (Mercury, Venus, Mars, Jupiter, bodies to deviate from their and Saturn) move with complex natural motions (forced motions (varying speeds, sizes motion). and brightnesses, and so-called retrograde motion). The challenge facing ancient astronomers was to describe this complexity with a combination of a limited number of uniform circular motions. 5. Force causes motion 5. There is a total absence of (speed, not acceleration). The gravitation in Aristotelian speed of a falling body is astronomy. Thus, the self-motion directly proportional to its of celestial objects is weight and distance traveled unimagineable. The and inversely proportional to sun,moon,planets and stars are the density of the medium. attached to solid ethereal spheres, Thus, in the vacuum, speed which rotate uniformly around becomes infinite, which is the Earth. The heavens are a absurd. That enforces system of concentric spheres (55 Aristotle’s contention that a such spheres) rotating in various vacuum is impossible. In ways around the Earth, and Aristotelian mechanics, the carrying celestial bodies with cornerstone is speed, and not them. Each celestial body acceleration, and the medium partakes of one or more of such is an essential factor of motions. Hence, the complexity motion. Galileo was to turn of the motion of the sun, moon all that upside down. and planets. Aristotle’s Universe is like an onion, because it does not contain any vacua. If we move form the centre, we pass through the following regions consecutively: earth,water,air,fire,Moon, 10 Mercury, Venus, Sun, Mars, Jupiter, Saturn, Stars. 6. The sphere of stars is moved by an unmoved mover (God?!), and this motion is transmitted to the rest of the Universe, including Earth. 2. Hellenistic Astronomy: Plato laid down the basis of the project of antique astronomy; how to explain the complexity of planetary motion (including the sun and moon) in terms of a limited number of uniform circular motions. Plato’s student, the mathematician, Eudoxos (4th century BC), formulated the first mathematical model embodying the Platonic project. However, it was quantitatively unacceptable. The Geek mathematician, Apollonius (3rd century BC), formulated the rudiments of an alternative, more accurate mathematical model. The Greek astronomer, Hipparchus (2nd century BC), inaugurated Greek astronomy as an exact science, by developing Apollonius’ model and wedding his model very closely to accurate observations. He was deeply influenced by Babylonian astronomy (500 BC- 1 AD). All these contributions were unified and completed in an integrated, comprehensive scientific theory and system by Claudius Ptolemy (2nd century AD), particularly in his great book, Almajest (the Majestic). Adding to Appolonius’ and Hipparchus’ innovations, he invented and employed three major mathematical devices to ―explain‖ and describe the wealth of Babylonian and Greek observations of the sun, moon and planets. He succeeded 11 in building a fairly accurate astronomical system of what we call today the solar system. These devices are: (1). The Eccentric: The planet moves with uniform circular motion about the centre of motion, but the centre is not coincident with the centre of the Earth. (2). Epicycle and Deferent: The planet moves with uniform circular motion about a centre, but the centre itself moves with uniform circular motion about a fixed point. The circle on which the planet moves is called the epicycle, whereas the circle, which carries the epicycle, is called the deferent. The result is a combination of two uniform circular motions. A wide variety of motions could be accurately described with this device by altering the parameters and directions, including retrograde motion. P = Planet Ó = Epicycle centre O = deferent centre (3). The Equant: The planet is suuposed to be moving with uniform circular motion, neither about the centre of the circle nor about the Earth, but about a fictitious point at a distance from both, called the equant. 12 3. Arabic Medieval Astronomy: Arabic astronomy started at the end of the 8th century AD and lasted till the 16th century. It passed through the following stages: - The translation phase: whereby the major Greek, Sanskrit, Persian and Syriac astronomical texts were translated (several times) into Arabic. - The correction and updating phase whereby fresh calculations and observations were made, on the basis of which many Ptolemaic parameters were corrected and updated. - The critique of Ptolemy phase: The great Arab physicist, Al-Hassan Ibn Al-Haitham (Al-Hazen), initiated a critical tradition in Arabic astronomy, called Al-Shukuk tradition, meaning casting doubts on the Ptolemaic system. This tradition subjected Ptolemy to a thorough theoretical critique. In particular, it emphasized the observation that the Ptolmaic devices deviated from the principles of Aristotelian physics, particularly the principle of uniform circular motion. Most critiques centred on the equant, which was generally considered an aberration. To Arabic scientists, this contradiction between mathematical astronomy and physics was intolerable. This accounts for their general dissatisfaction with Ptolemaic astronomy. - The new model construction phase: Having critiqued Ptolemy on the basis of Aristotle, Arabic astronomers embarked on constructing new models for celestial motions alternative to Ptolemaic models. Those astronomers strove to make their new models as accurate as Ptolemy’s models, without deviating from 13 Aristotelian principles. That is these models were as close as possible to Aristotelian principles without compromising the accuracy of Ptolemy’s models. In particular, they all strove to eliminate the equant and replace it with a set of uniform circular motions. They invented new mathematical techniques for this purpose, such as the Urdi lemma and Tusi couple, and arrived at very elegant semi-Aristotelian models. Formost amongst those astronomers were: al-Urdi, Al-Tusi, Al- Shirazi and Ibn Al-Shatir. The main centres of this activity were Damascus and Maragha in North-Western Iran. There is mounting evidence that these new models were transmitted to Europe, and that Copernicus was well aware of some of them when he started developing his heliocentric model. 4. Copernicus (1473-1543): Nicolaus Copernicus (a pole or German) initiated the scientific revolution, which culminated in Newtonian mechanics, the paradigm of the new physics. His age was the Renaissance age of discovery (America was discovered by the Europeans in 1492) — an age of unprecedented expansion at all levels. He studied astronomy and medicine in Renaissance Italy (Bologna), but lived most of his life as a clerical official (as the canon of Frauenberg) in Poland — a rather quiet and secluded life. Copernicus was famous for proposing a helio-centric model of the universe, reducing Earth to a mere moving planet. Here is a schematic figure showing the order of the planets. 14 The idea of a moving Earth was indeed proposed in antiquity (some Babylonians, Philolaos the Pythagorean, Heraclides of Pontus, Aristarchus of Samos, Aryabhatta of India), but it was a peripheral idea. Copernicus not only revived the idea but also turned it into a detailed mathematical and astronomical scheme comparable in sophistication and explanatory and predictive power to, if not superior to, Ptolemy’s system. He spent almost forby years in formulating it. Aroud 1514, he produced the first written account of his helio-centric scheme, which was a 40-page manuscript outlining the principles of his system, the basis of his later elaboration. It was distributed on a very limited scale, and was known ever since as the Commentariolus. The Roman Catholic Church approved of it, but Martin Luther condermned it with vehemence. His major work, commonly called De Revolutionibus (On the Revolutions of the Celestial Spheres), was published in 1543, and it is said that he received the first copy of it when he was on his dying bed. It contained a detailed comprehensive elaboration of his helio-centric system, and is comparable, in scope and mathematical sophistication, to Ptolemy’s Al-Majest — a veritable revolutionary alternative. What innovations did Copernicus introduce in European and World astronomy? In fact, he introduced two innovative schemes in European astronomy, with worldwide ramifications: (a) He was as opposed to Ptolemaic devices, particularly the equant, as Arabic astronomy had been before him. That is why he sought to introduce Arabic mathematical techniques into European astronomy, reminiscent of Urdi, Tusi and (particularly) Ibn Al- Shatir. Whether or not he reinvented these techniques, or plagiarized his Arabic predecessors, is 15 still very much a controversial issue. In any case, he could be considered a continuation of Arabic astronomy, and that aspect of his work could be considered the conservative side of his work. (b) Following his Pythagorean bend, he placed the sun near the centre of the Universe (of motion) and considered it fixed, and transformed the Earth into a mere planet revolving around itself and around the centre of the universe. That is, many of the apparent motions of celestial bodies were reduced and attributed to motions of the Earth. That was indeed the revolutionary side of Copernicus’s work, since it contradicted both common sense and the very essence of Aristotelian physics. What motivated Copernicus to introduce these innovations, and spend almost forty years of hard work to reformulate astromomy on seemingly crazy bases? (a) The spirit of the age (the Rennaissance): It was an age of expansion and discovery. It was also an age of dissatisfaction with past and existing structures. It felt the need to challenge the old and to critique traditional wisdom and knowledge. It was impatient with all authority — a veritable revolutionary age. (b) Copernicus adhered very strongly to the Platonic idea of uniform circular motion in the heavens, and he veheremtly apposed all Ptolemaic deviations from this principle. This motivated both his helio-centrism and revival of Arabic innovations. (c) Ptolemy’s system was too complicated for Copernicus’s aesthetic taste. To him a viable theory should be simple, reflecting the simple beauty of Nature. Besides, he noticed that Ptolemy’s system increased in complexity with time; a good theory ought to move from complexity to simplicity, not the other way around. 16 (d) Related to that is Copernicus’s firm belief that a theory should not be a pile of ad hoc elements, but rather an integrated, coherent, structure. To Copernicus, Ptolemy’s theory lacked coherence and contained too many ad hoc assumptions. That is why he likened it to a monster constructed from incoherent limbs. His ideal was a whole governed by necessity. (e) Copernicus’s Pythagoreanism no doubt drove him to favour the sun at the expense of the Earth. It was only natural for a Pythagorean like himself to consider the sun the centre and source of life and motion. What were the achievements and difficulties of Copernicus’s new theory? Achievements: (a) Copernicus’s system was a powerful comprehensive alternative to Ptolemy’s system. It rivaled the latter in sophistication and was superior to it in explanatory power. (b) It was more coherent, and more of an integrated coherent system, whereby the parts were systematically related to each other. (c) Its explanation of the retrograde motions of the planets was more physical and more natural than its Ptolemaic counterpart. (d) It provided natural explanations for the ad hoc assumptions in Ptolemy’s system. (e) It reduced the number of large epicycles via the Earth’s motion. Difficulties: (a) It did not achieve greater accuracy than Ptolemy’s system. (b) It could not remove all Ptolemaic devices; it had to reintroduce them to achieve a sufficient 17 degree of accuracy, thus reintroducing in itself the complexity it sought to eradicate. (c) Thus, it was a contradictory system with the new features uneasily coexisting with many of the old Ptolemaic features. (d) Copernicus’s theory contradicted both common sense and a very well-established theory of matter and motion—namely, Aristothe’s. It did not offer (and could not possibly have offered) an alternative mechanics. Such a mechanics awaited the genius of Galileo Galilei, in the first third of the 17th century, to crystallize. (e) Copernicus’ theory necessitated the observation of an annual parallax of the fixed stars due to Earth’s motion around the sun. No such parallax was observed. So either the theory was wrong or the stars were at an unimaginably large distance from us. Many could not bring themselves to accept the idea of such an inflated universe, and, thus, had to reject the theory. The Copernicans had to contend with such an absurdly large universe. The conclusive parallax measurement had to await the refinement of astronomical instruments, particularly the telescope, as late as the middle of the 19th century. To start with, the publication of De Revolutionibus did not cause a noticeable stir, as it was a very technical and difficult work. However Copernicus’s theory had enormous far-reaching implications, which could not be ignored for long. Both the scholarly and religious authorities were soon to realize these volcanic implications, and reacted strongly (and, sometimes, violently) to them. What were these implications? In the first place, we have the mind-boggling size of the Copernican 18 universe, even implying the possibility of an infinite universe. And that was precisely the implication drawn by the fiery Italian cleric, Giordano Bruno, who speculated that the Universe was infinite, and populated with an infinite number of planetary systems similar to ours, realizing that the fixed stars were suns similar to our own sun. Secondly, having fixed stars no longer required that they be at an identical distance from us. On the contrary, it is more likely that they are distributed throughout three- dimensional space at varying distances from us, just as Bruno speculated. Thirdly, the Earth was demoted from a fixed solid centre of the universe to a mere moving planet. Thus, there are no qualitative differences between Heaven and Earth. They are of the same ilk. That cast a strong doubt on Aristotle’s cosmology and theory of matter and motion. Fourth, the fact that events on Earth occurred as though it were fixed pointed towards an inertial physics, which completely opposed Aristotle’s mechanics. These great implications were to be developed painstakingly within the next half century, primarily by Kepler and Galileo. 5. Tycho Brahe ( 1546-1601): Tycho was a great observer of the heavens. It could be said that he represented the apex of naked-eye observational astronomy. He had a crucial impact on Kepler’s work. It could even be said that without his discoveries, Kepler would, most likely, not have been able to arrive at his lasting astronomical discoveries. Tycho’s main contributions to astronomy were: 19 (a) He made systematic and regular measurements and observations of celestial objects, particularly Mars. These measurements were unprecedented in precision. They were certainly the most accurate and precise to date. He perfected naked-eye astronomical instruments to such a pitch the he was able to improve celestial measurements many times over. That precision was crucial to Kepler, the great theoretician. (b) In 1572, a supernova appeared in the sky and lasted for several weeks. Tycho conducted extensive measurements on it, and found out that it exhibited no noticeable parallax. That showed not only that the supernova occurred beyond the sphere of the Moon, but that it also belonged to the distant sphere of the stars. This was a clear refutation of Aristothe’s idea that the heavens were unchangeable — eternally fixed and unchanging. It cast a big doubt on Aristotle’s division of the universe into a corrupt Earth and a pure unchanging Heaven. (c) Tycho discovered that comets move beyond the sphere of the moon, and that they cut through a number of the support solid spheres as they orbit the sun. This discovery dealt a heavy blow to the Aristotelian notion of solid spheres and left celestial bodies moving with no tangible support (almost hung in empty space) leaving the door open for field inertial physics. (d) Tycho proposed an alternative model of the Universe to both Ptolemy’s and Copernicus’s models. His model was a compromise between the two, which tried to retain the ―attractive‖ features of both. It tried to adopt Copernicus’s system after plucking the sting (Earth’s motion) out of it. It fixed the Earth at the centre of the Universe, and let the moon, sun and distant stars revolve around it, with the planets revolving around the sun, which carried them with it around the Earth. 20 Physically speaking, it was a very unacceptable repulsive system. 6. William Gilbert ( 1540-1603): This English physician and physicist started the modern science of magnetism with his important book, De Magnete (1600). He showed that the Earth is a huge magnet, and that all magnets are always bipolar. This book had a tremendous impact on both Kepler and Galileo. In Kepler’s case, it triggered the idea of action-at-a-distance or field interactions, and thus the idea of field physics, which Kepler used very effectively as a powerful tool in his astronomy. 6. Pythagoreanism: Two peripheral currents (peripheral in Greek and Arabic antiquity) were strongly revived in the 16th century in Renaissance Europe: pythagoreanism and atomic materialism. Originally, Pythagoreanism stipulated that the Universe, in its inmost structure and reality, was made of numbers and geometric figures, that its secret lay in mathematical relations, and that it was governed by musical ratios, and, thus, could be viewed as a huge musical instrument played by the gods and producing the so-called ―music of the spheres‖. Kepler’s Pythagoreanism, which played a significant role in his scientific methodology, was of a Christian variety. He believed that the Universe was a created entity, that God was a grand mathematician, that He was basically a grand mathematical reason or mind, that He created the Universe according to mathematical principles — i.e., the model of divine creation was mathematical and geometric — and that He constructed it on musical terms. This Pythagorean trend and conviction remained with Kepler throughout his life. 21 7. Materialism: Kepler was a true and passionate Pythagorean, but he was definitely not a materialist. However, he could not escape totally the impact of atomic materialism. In fact, this form of materialism played a significant role in the emergence of modern science. In a sense, it could be said that Bruno, Galileo, Descartes, Gassendi, Boyle, Hooke, Huygens and Newton were atomists of sorts. In his work, Kepler was guided not only by Christian Pythagoreanism. but also by materialism. The tension in his thought reflects the obvious contradiction between the Pythagorean and materialist trends in his methodology. His Pythagoreanism was constantly checked and counterbalanced by his materialism. He viewed celestial objects not as mere divine or Pythagorean symbols, but also as material bodies interacting physically — i.e., he thought about them in physical terms. Without this strong physical intuition, he would never have arrived at his great discoveries, and his work would have belonged wholly to pre-modern times. The dimension of modernity in his thought resided in his materialism and physicalism. Also, his strict adherence to data and precise measurement — i.e., his strict empiricism — was a clear sign of his materialism. His creativity was fired by this intense clash between the antique (pythagoreanism) and the modern (materialism). Kepler imbibed his epistemic heritage, with its variegated elements, at the University of Tübingen in southern Germany. The European Renaissance, with its cultural and commercial vitality, had animated European universities with the intellectual, artistic, scientific and philosophical gems of antiquity, both Greek, Roman and Arabic. Without this process of animating European university life, a Kepler would not have been possible. Kepler became a Copernican at an early stage, during his academic sojourn at Tübingen University, under the 22 direct influence of his astronomy teacher, Michael Maestlin. Whilst still at university, Kepler formed his life-long research project out of his passionate involvement in his astronomical epistemic heritage. His passionate and deep commitment and devotion to this project were phenomernal. They sustained his work under very adverse conditinas and severe hardship. Only a passionately devoted man would work for hours on end working along a very uncertain path, doing laborious calculations, scrapping them several times, and redoing them several times as well. Kepler’s research project could be summarized as follows: (a) Defending the Copernican system and showing its superiority to the other systems. (b) Defending it by resolving its contradictions and eradicating the left-overs of the Ptolemaic system. (c) Explaining the number of the planets; why God created six, and only six, planets. (d) Explaining the distances of the planets from the sun; why God created them with such distances. (e) Finding the relationships between the distances of the planets from the sun and their periods (years) — i.e., how the planets are related to each other and how they constitute an integrated system. (f) Reading the mind of God;how and why God created the Universe in this specific manner, and on what principles. This was the ultimate justification of his endeavours, which would confer meaning on his life and on human life in general. It was the ultimate purpose of his scientific enterprise and of knowledge as such. 23 How did kepler implement his project? He did that through four principal stages, each of which was associated with a major work. (a) The Mysterium Cosmographicum (1596) In this (his first major) work, Kepler spelled out his research project, offered a potent defense of the Copernican system and proposed a Pythagorean theory of the Universe. It is a clear embodiment of Kepler’s Christian pythagoreanism. In it, Kepler looked for the geometric model on which God based his construction of the universe. Also Kepler had the peculiar notion that God projected part of his nature onto the universe. Kepler found the holy trinity reflected in the basic cosmic arrangement of the Copernican system, with the sun representing the Father, the fixed stars representing the son and the intervening space (the planets) representing the Holy Ghost. What was the geometric model proposed by Kepler as the model of divine creation? In fact, it was the five regular Platonic solids: the cube, tetrahedron, dodecahedron, icosahedron, and octahedron. It had been shown b Euclid that whereas there is an infinite variety of two-dimensional regular polygons, there can only be five regular solids. Kepler fitted these five solids between six spheres. The cube, for example, would encase a sphere and would be encased by another sphere; likewise with the other solids. The five regular solids would, thus, give six spheres and, thus, six planets only. Also Kepler was able to reproduce, with this device, the Copernican distances of the planets approximately. That was a moment of great triumph. With one blow, he was able to account for the number and distances of the planets. Kepler would remain a firm believer in this fantastic Pythagorean scheme till the end of his life. 24 And in a sense, he was justified in adhering to it. After all, it could be considered a scientific hypothesis of sorts. Its was a precisely formulated scientific hypothesis, which could be tested. (b) The Astronomia Nova (1609): This is one of the most revolutionary and significant scientific works in the history of astronomy. It was indeed the start of an astronomia nova — a new astronomy. It contained the first two Kepler laws of planetary motion — the first two correct laws of physical astronomy. They are counted among the first correct laws of modern natural science. This work is a clear embodiment of the field physical (materialist) element in Kepler’s thought. That does not mean that Kepler renounced his Christian Pythagoreanism in this work. Not in the least. It was just that for the moment, the materialist element was ascendant. How did Kepler arrive at his two famous laws in his magnum opus? (a) Kepler started by accepting Tycho’s conclusion that the Aristotelian solid spheres do not exist. Instead, he introduced the concept of definite orbits. That was a tremendous revolutionary step, which introduced a basic element of classical physics. It also led him to raise a new question. What moved planets in their definite orbits? (b) In this book, kepler introduced a new approach to astronomy, which he termed physical astronomy. His new approach consisted in viewing the solar system as a physical system of interacting material bodies. Admittedly, his conception of interaction was primitive and qualitative. Yet he was the first astronomer in history to think in this novel way of the Universe. In particular, he considered the sun to be the main source of the field force that moved the planets and animated the solar system. This idea, which could be 25 considered the starting point of classical field physics, guided Kepler in this book in all his subsequent moves. (c) He starting by transferring emphasis from the mean sun (the centre of the planetary orbits) to the sun itself as a material body that exerts field forces on the planets. He refused to relate planetary motions to a mere mathematical point. Instead, he related them and calculated all related parameters in reference to the sun. That was a crucial step forward. (d) In analogy with light, on which Kepler was an expert, he postulated that the field force of the sun diminishes as the distance from the sun increases, and vice versa. Since the sun did not lie at the centre of planetary orbits, this meant that a planet would move quicker as it approached the sun, and slower as it receded from the sun. With this notion, Kepler destroyed the age-old idea that natural motion in the heavens was uniform motion. According to Kepler, celestial motion was of necessity non-uniform, because it depended on distance from the sun. That step and overturning of tables represented a tremendous upheaval in the history of science. Kepler reversed a cherished principle, which had lasted for two millennia. (e) The next question that faced Kepler was: How does the speed of the planet vary as it orbits the sun? To answer this question, Kepler assumed (wrongly, of course) that the field force of the sun obeyed an inverse law ( ) , rather than an inverse square law ( 2 ). Even though the assumption was wrong, it led to a correct result — namely, Kepler’s second law of planetary motion. This law states that the planet sweeps equal areas in equal times. That is , the vector emanating from the sun towards the planet sweeps equal areas in equal times. Thus, Kepler’s second law was actually discovered before the first law, and for circular orbits. 26 (f) Then, Kepler started enquiring about planetary orbits — not yet about their shapes, but about their relationship to the sun and the Ptolemaic devices. He used his physical intuition, and his physical field model, to evaluate the Ptolemaic devices. He decided that the epicycles. were unphysical; why should a planet revolve in uniform circular motion about a mere moving geometric point? Accordingly, he discarded epicycles. Instead, he selected and revived Ptolemy’s equant. That was a truly revolutionary move. After all, for a whole millennium, Arabic astronomers and, later, Copernicus had made their utmost to get rid of the equant. They had considered it the weakest spot in Ptolemy’s system. They had done that on the basis of Aristotelian physics. But, here we find an astronomer (Kepler), who had the audacity to reverse all that, just as he did with the assumption of uniform motion, and assert the equant on the basis of an embryonic field physics, a field materialism if you wish. He realized that Ptolemy’s supposed aberration , his equant, held the key to solving the problem of planetary motion. So, he constructed a model of planetary motion consisting of a circular orbit and an equant. Kepler embarked on matching his model with Tycho’s data for Mars, taking into account Earth’s motion. He tried to specify his model and reconcile it with those data. However, he was left with a discrepancy of 8'. He followed all sorts of ways to remove this discrepancy, but with no avail. Of course, such a tiny discrepancy would have been ignored in the past, because it would have been contained within the margin of error of past data. But, not with Tycho’s unprecedented accurate data. With Tycho’s data, the discrepancy meant some sort of a failure of Kepler’s circular model. And tried as he could, no circular orbit would remove the discrepancy and match Tycho’s data. Of course, Kepler could have artificially removed it by resorting to epicycles. But, he would not. He absolutely rejected epicycles on physical grounds. And he was ready to sacrifice the principle 27 of circular motion rather than to violate his celestial physics. He had to surge forward even if this meant violating a hallowed Platonic principle that had lasted for two whole millennia. Thus, he first attempted an oval orbit, which, of course, did not work. However, from the discrepancy, he was able to deduce a formula, which he later recognized as the formula of an ellipse. The latter proved to be a perfect match to Tycho’s data. Thus, Kepler arrived at his first law of planetary motion, which states that a planet moves around the sun in an elliptical orbit one of whose foci is occupied by the sun. The other (empty) focus was actually the equant. Thus, the circular model with an equant, with which he had started his quest, was actually a first approximation of the elliptical orbit. Ptolemy had intuited that when he invented the equant. So did Kepler when he adopted it despite Arabic astronomers and Copernicus. It was a truly revolutionary move. (c) The Harmonice Mundi or Harmony of the World (1619): When Kepler arrived at his elliptical model on empirical grounds, he did not consider it a refutation of his regular solid Pythagorean model enunciated in his Mysterium Cosmographicum. On the contrary, he felt the need for both models. He was convinced of the truth of both. He was not ready to sacrifice either. Thus, he set himself the task of reconcling the Pythagorean model with the physical empirical model. That task was fulfilled in his 1619 book entitled the Harmonice Mundi (Harmony of the World). However, in this book, he also set himself another task — namely, treating the Universe as an integrated physical system with interlocked elements. He realized that his treatment of planetary motion in the Astronomia Nova had been too disconnected, too unsystemic. He had treated each planet on its own as though it were not part of a solar system or a universe. Thus, he set himself the task of relating 28 planetary motions and illuminating the unity of the Universe and its systemic essence. He fulfilled the first task and resolved the contradiction between the two models by considering the regular solid model (geometric Pythagorean) correct, but insufficient. He convinced himself that God, in creating the Universe, was guided not only by geometry but by other principles as well. In fact, Kepler convinced himself that God was not only a super mathematician, but also a super musician. Had the Universe been static, God would have confined himself to a geometric model, the regular solid model. However, because the Universe was dynamic and fall of motion, God did not confine himself to geometry, but resorted also to the laws of harmony —to music. Kepler convinced himself that he could actually explain his elliptical model with a combination of Pythagorean geometry and Pythagorean music (harmony). The second task led him to thoroughly investigate he relationship between the periods (years) of planets and their distances form the sun. He had already suggested a simple relationship in the Mysterium, but he had realized right from the start that it strongly contradicted the data. This time, however, he was able to come up with a complex relationship that matched the data perfectly. Thus, in the Harmonice Mundi, he announced his third Law of Planetrary Motion, ten years after announcing his first and second laws. The third law states that the square of the perid (year) of a planet is directly proportional to the cube of the mean distance of the planet from the sun. Fifty years after this announcement, Newton was to read the law of universal gravitation in this relationship. (d) Epitome to Copernican Astronomy ( 1621): In the Epitome, Kepler brought his great astronomical work to a conclusion. He applied his discoveries and insights to all 29 the planets and to the whole solar system, corrected past mistakes, removed errors and inconsistencies, tied up loose ends, and combined and reconciled his various principles and ideas. Unfortunately, Kepler’s work was not properly received and appreciated after his death in 1630. In a sense, it was too anachronistic and too advanced for his age. It was too Pythagorean, mystical and obscure on the one hand, and too revolutionary and daring on the other. Only the genius of a Newton could sift through the Keplerian Corpus, and capture the Keplerian gem, with which he could construct his mathematical mechanics. Case II Max Planck (1858-1947) Three events or processes marked the age in which Max Planck was born and moulded: (i) The belated German industrial revolution, which, within two decades, turned Germany into the foremost industrial power in the world. (ii) German unification, which created a powerful imperial state with global ambitions (iii) The emergence of the German university system — a novel rigorous system with powerful links to both government and industry. Max Planck was a distinguished product of this vigorous situation. He was solidly grounded in his epistemic heritage, and endowed with the necessary philosophical, ethical and mathermatical backgrounds and constitutive structures. He was devoted to an ideal of rigor and integrity — to a vision of an ordered cosmos governed by necessity and universality. However, his ultimate loyalty and commitment was to the facts in their theoretical unity. He 30 always tried to save a well-established theory or belief, but he always knew when to withdraw his support. He would vigorously defend a theoretical stance. However, his great expertise would ultimately drive him to realize that there was no way out but to violate it or abandon it. In this respect, he was a thorough empiricist, in the deep sense of the word. Planck was deeply steeped into the solid philosophical, scientific and mathematical traditions of the German academia. His rigor, skill and dedication were a witness to that. His original research project consisted in completing classical physics, tidying it up, clarifying its concepts, and establishing its deep internal interconnections. Planck’s Epistemic Heritage In contrast to Kepler’s epistemic heritage (antique astronomy + Copernicus + Tycho), Planck’s epistemic heritage was the whole of classical physics as it existed in the second half of the nineteenth century. Basically, Classical physics consisted of four major components or theoretical schemes: classical mechanics, electromagnetic theory, thermodynamics, and statistical mechanics (+ gas theory + atomic and molecular theory). 1. Classical Mechanics: The core of classical mechanics is Newtonian mechanics. The main steps in the formation of classical mechanics may be summarized as follows: (a) Kepler, whose contributions we have already discussed in detail. (b) Galileo: His major contributions could be grouped into three classes: (i) Methodological: (1) He initiated a project whereby natural science is a quest for physical quantities, which are determined with mathematics and precise measurement, and their inter- relations. 31 (2) He initiated a new method of thinking of natural processes, whereby one separates the essential from the contingent or peripheral, builds models by abstracting the essential from the peripheral (i.e., idealized models), and creates experimental situations corresponding to these models. This method is an essential feature of all scientific practice. (ii) Astronomical: Galileo was the first scientist to study the heavens systematically with a telescope. He used these studies effectively in devastating antique physics and astronomy, supporting the Copernican system, and establishing a new tradition of astronomical measurement and observation. He discovered with his telescope the materiality of the moon, the sun spots, the phases of Venus, the nature of the Milky way, four moons of Jupiter and other such astronomical phenomena. (iii) Mechanical: (1) He was the first to formulate a law of inertia. With that, he inaugurated inertial physics. However, his formulation was defective, in that he asserted that a body naturally maintained its uniform state of motion as long as it followed a circular path. He thought (wrongly of course) that circular motion entailed no acceleration. His concept of inertia lay in between the correct law of inertia and the Aristotelian notion of natural motion. (2) He was the first to formulate the principle of (Galilean) relativity, which states that, mechanically, all inertial frames of reference are equivalent. That is, we cannot detect absolute velocity, and distinguish between the state of rest and the state of uniform motion, by conducting mechanical experiments in our frames of reference. (3) Galileo discovered the correct law of free fall- namely, that the distance covered by a falling body is 32 directly proportional to the square of the time(s=½gt2) assuming that air resistance is negligible. His law emphasized the contingency of the medium and the importance of acceleration, unlike Aristotle’s law of free fall, which emphasized the necessity of the medium and the importance of velocity. (4) Galileo discovered that a projectile on Earth follows a parabola, not a semi-circle, as had been thought before. This discovery was equivalent to discovering the method of analyzing motion into its components. (5) Galileo was the first to discover the principle of equivalence in its simplest from—namely, that inertial and gravitational masses are exactly equal to each other. Two bodies dropped in a vacuum would reach the ground simultaneously irrespective of their masses. In fact, Galileo laid down the basis of the launching pad of Newtonian mechanics. (c) René Descartes (1596-1650) (1) Descartes discovered analytical geometry (how to translate algebra into geometry and vice versa), which has become an indispensable tool in physics. (2) He was the first to draw a comprehensive materialist program for explaining natural phenomena. He envisaged nature as an infinite material system of colliding particles and ethers. Strict mechanical laws controlled nature. (3) Descartes envisaged the act of divine creation as a one instant affair. God created matter and imparted a fixed and conserved amount of motion (energy, power, force) to it. Thus, after the instant of creation, the Universe would be self- sufficient, and run on its own without divine intervention. In 33 a sense, Descartes marginalized God and made Him redundant and irrelevant. The Universe is basically a self- contained sustainable system of matter. This type of theology led Descartes to a great idea—namely, that the universe is governed by a system of conservation laws. This idea has prevailed in physics ever since. Conservation principles are the basic principles which constrain and govern events. However, Descartes’s proposal for the basic conservation law of nature was erroneous. He erroneously believed that the fundamental conserved quantity is the product of the volume of a body with its speed (Vv). That sparked a controversy as to whether that quantity involved the speed, its square or the velocity. That controversy was resolved only in the second half of the 18th century. (4) Descartes was the first to formulate the law of inertia correctly. He realized that it involved uniform motion in a straight line rather than a circular path. (d) Christian Huygens: (1) Huygens was the first to formulate correctly the law of conservation of linear momentum (mass times velocity) and to explain collisions with it. (2) He was the first to arrive at the correct mathematical expression of the centripetal acceleration (v2/r). However, he wrongly thought that the centripetal force was directed outwards. (e) Isaac Newton: (1) Newton started by identifying significant discoveries in mechanics by his predecessors, and separating them from hazy notions—namely, Galileo’s terrestrial laws of motion and Kepler’s celestial laws of planetary motion. 34 (2) With the idea that uniform circular motion was basically a process of free fall, Newton was able to synthesize Galileo’s terrestrial laws with Kepler’s celestial laws in a universal system of mechanics — a system of universal laws— consisting of the laws of motion and the law of universal gravitation. (3) Newton was the first to tie gravitation with matter as such (irrespective of location and duration( , rather than to Earth only. With Newton, gravitation has become universal. (4) Newton invented a new class of laws—universal mathematized laws, which apply everywhere, at all times, and under any conditions. (5) With his great mathematical invention—the calculus— Newton was able to specify and clarify the concepts of mechanics. (6) By formulating the laws of nature in terms of the calculus, he created a powerful tool of knowledge production out of them. He turned them into a powerful explanatory and predictive tool. (7) He could be considered the founder of theoretical physics. His theory was the first of its kind. It was the first universal mathematized scientific theory in history, and it became a paradigm of subsequent scientific work. (8) With this powerful tool, Newton was able to explain quantitatively all of the phenomena of the solar system hitherto known. (f) Leibniz and Maupertuis: Leibniz highlighted the concept of energy (particularly kinetic energy), which was absent from Newton’s mechanics. Maupertuis introduced the notion of action (energy times time, or momentum times distance) and was able to derive Newton’s laws from an action principle. (g) Lagrange and Hamilton: Lagrange and, later, Hamilton were able to combine all that and generalize the result to a set of very general partial differential equations and action 35 integrals. Their system has survived classical physics and persisted in modern physics — relativity, quantum mechanics and quantum field theory. In a sense, classical mechanics reached its climax and final form in Lagrange and Hamilton. 2. Classical Electrodynamics Between 1750 and 1850, most of the laws of electricity, magnetism and optics were discovered (Coulumb, Oersted, Ampere, Faraday, Young, Fresnel). In 1864, with the aid of Faraday’s concept of field, Maxwell was able to express those laws locally as a set of partial differential equations. Using arguments of symmetry, he was able to complete these equations and use them to deduce the existence of electromagnetic waves and that light is an electromagnetic wave. Later, Oliver Heaviside put these (Maxwell) equations in the new familiar vector form. 3. Thermodynamics Thermodynamics proper started in the 1840’s with the discovery that heat is a form of mechanical motion, followed by the discovery of the principle of conservation of energy (Joule, Meyer, Helmholz). That important principle was considered the first law of thermodynamics. Between 1851 and 1865, Rudolf Clausus formulated the 2 Law of thermodynamics in terms of a new concept — the nd concept of entropy (change in heat divided by temperature). Together, these two fundamental laws constituted the core of the science of thermodynamics. Clausius and others succeeded in expressing the basic laws and concepts of thermodynamics in terms of a set of partial differential equations. 36 4. Statistical Mechanics In the 2nd half of the 19th century, physicists were faced with three general theoretical systems: classical mechanics, electromagnetic field theory and thermodynamics. These systems were deeply related, but looked qualitatively different. The challenge was to integrate them within a unified theoretical framework— i.e., to unity them. Initially, the prevailing mood was mechanical. Mechanics was considered the heart of physics, and physicists sought to base thermodynamics and electromagnetism on mechanics. In fact, they sought to reduce them to mechanics. The first such attempt was atomic gas theory, which was revived by Rudolf Clausius. That attempt consisted in accounting for macroscopic gas properties in terms of molecular motion. Beginning with 1870, Maxwell and, principally, Boltzmann introduced statistics into molecular and atomic dynamics. Boltzmann introduced a highly controversial statistical interpretation of entropy and the 2nd law of thermodynamics. According to that interpretation, the 2nd law was no longer an absolute law, but, rather, a probabilistic law. Max Planck’s Road to the Quantum: Planck started with thermodynamics, focusing on the problem of the 2nd law. In his Ph.D thesis, he dealt with thermodynamics and based himself on Rudolf Clausius’s 37 work. He tried to clarify thermodynamics concepts by reformulating Clausius’s thermodynamics and stating the 2nd law in unambiguous terms. And, indeed, he came up with a statement that has become the standard statement of the 2nd law To him, the 2nd law meant that the entropy of a closed system tends spontaneously to increase, and can never decrease. Next, he realized that the 2nd Law differed in kind (qualitatively) from the 1st Law and the Laws of classical mechanics. Basically, the difference lies in that the 2nd law is irreversible, whereas the 1st law and the laws of classical mechanics are reversible. That is the essence of the difference. Thus his research project consisted in exploring and understanding how the 2nd law is related to classical mechanics— how irreversibility emanated from reversibility. That is, he wanted to understand the 2nd law in mechanical terms despite the apparent contradiction. In a sense, he was looking for ways and means to resolve the contradiction between thermodynamics and mechanics. In the last quarter of the 19th century, there were two competing views of the 2nd law. The first was the energeticist view, which denied the existence of atoms, and molecules, stressed the continuity of matter, believed the 2nd law was an absolute and universal law, and, thus, considered it totally unrelated to mechanics. The 2nd view was Boltzmann’s statistical mechanics, which believed in atoms and molecules, interpreted entropy as a measure of disorder of a molecular system, and considered the 2nd law a probabilistic law rather that an absolute laws, based on mechanics. Planck subscribed to neither view. He considered the 2nd law absolute rather than probabilistic. However, he believed it was deeply related to mechanics and was ultimately based on it and derivable from it. However, he rejected Boltzmann’s statistical atomistic approach, because he simply rejected atomism. Boltzmann’s probabilistic 38 interpretation of the 2nd law was anathema to Planck. He wanted to retain both its absolute character and its mechanical base. He thought this could be done by basing thermodynamics on the mechanics of continuous media, rather than molecular systems. This consideration ultimately led him to black-body radiation. In fact, he interpreted Maxwell’s equations of electromagnetism as mechanical equations of a continuous medium (the ether). Thus, he considered electromagnetic systems perfect systems for achieving his project of deriving irreversibility from reversibility. Black-Body Radiation Black-body radiation is the radiation emitted and absorbed by a perfect black body. The latter absorbs all the radiation that falls on its surface, and its surface is a perfect emitter of radiation. The best example of black-body radiation is the radiation contained in a cavity under conditions of thermal equilibrium (at constant temperature). The challenge that faced physicists at the end of the 19th century was to discover and explain how energy was distributed on the various colors comprising black-body radiation—i.e., how radiation energy density was related to frequency. Planck’s Quantum of Action: To achieve his research project, Planck embarked on working on cavity radiation in 1894. He applied his thermodynamic definitions and Maxwell eqs. to cavity radiation. He thought of the cavity system as a set of field (not corpuscular) resonators interacting with the radiation field. Whilst conducting this theoretical work, an experimental group in Berlin was conducting experimental work on cavity radiation and obtaining important data. 39 The most promising empirical relation between energy density and frequency at that time was Wien’s law. Planck set out to derive it using his thermodynamic apparatus of concepts and equations. In his endeavour to explain the 2nd law and derive Wien’s law, he was to realize that his method was leading him to a dead end, and that he had to introduce Boltzmann’s statistical mechanics in his analysis. That recognition of failure occurred around 1898. Eventually, Planck arrived at a relatively satisfactory derivation of Wien’s law. However, fresh experimental results coming from the Berlin group were soon to reveal the limitations and inaccuracies of Wien’s law. Accordingly, Planck used thermodynamic arguments to modify his basic equations, and to surmise a new radiation law of which Wien’s law was an approximation. This new law agreed perfectly with all know experimental results, and has withstood the test ever since. However, Planck was not wholly satisfied with his great discovery. He aspired to ground it on firmer theoretical grounds—i.e. to derive it from more fundamental principles. To him, theoretical grounding was as important as experimental corroboration. This time he openly resorted to Boltzmann’s so-called combinatorial method. Following Boltzmann, he parceled the radiation energy absorbed and emitted by oscillators into discrete elements, and studied their statistical distribution on oscillators. He found out that this method would lead to his correct radiation equation if he assumed that these elements were physically real (i.e., not mere mathematical ploys), and that each is proportional to frequency: E = hf E = energy f = radiation frequency 40 h = so-called Planck Constant. That is, instead of letting the elements approach zero, and a summation approach an integral, which would have led to an absurd result, he retained the summation and kept the elements finite and dependent on frequency only. That assumption marked the birth of quantum theory, and was subsequently called the quantum hypothesis. It eventually led to one of the greatest upheavals in the history of knowledge—quantum mechanics and quantum field theory. 41

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