Philosophy of Space and Time Madingley Hall October 31-Novmber by yantingting

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									Philosophy of Space and Time
       Madingley Hall
       April 8-10, 2011

      Mark Hogarth
  University of Cambridge




        Mark Hogarth, Girton College
This powerpoint will be available on Sunday
  afternoon at

        http://web.mac.com/mhogarth




                  Mark Hogarth, Girton College
Keep in mind throughout that

     much of the world is not as it seems…




                  Mark Hogarth, Girton College
Mark Hogarth, Girton College
Mark Hogarth, Girton College
Mark Hogarth, Girton College
Mark Hogarth, Girton College
Mark Hogarth, Girton College
http://www.youtube.com/watch?v=vJG698U2M
                     vo




               Mark Hogarth, Girton College
Mark Hogarth, Girton College
   Roger Penrose
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‘Philosophy’ of space and time, but the
  philosophy is shaped by science, particularly
  modern science




                   Mark Hogarth, Girton College
Experiment escorts us last -
His pungent
company
Will not allow an Axiom
An
Opportunity –




Emily Dickinson


                  Mark Hogarth, Girton College
                                 Key figures                              John McTaggart
                                                                          Ellis McTaggart
                                                                          1866-1925



Steven
                 Roger Penrose
Hawking
                 1931-                            Albert Einstein 1879-
1942-
                                                  1955

Euclid 325 BC-
   265 BC
                  Newton 1643 –
                  1727        Leibniz 1646-1716             Gauss 1777-
                                                            1855




                                                                            Riemann 1826-
                                                                            66
                                  Mark Hogarth, Girton College
Key figures




 Mark Hogarth, Girton College
Philosophy without science can be a rather blunt
  tool…




                  Mark Hogarth, Girton College
  Intuition and philosophical ideas
                         Time
• "What then is time? If no one asks me, I know
  what it is. If I wish to explain it to him who
  asks, I do not know.” (St. Augustine)

• Time passes; time flows

• Time is universal, absolute
                   Mark Hogarth, Girton College
  Intuition and philosophical ideas
                     Space
• Space is a box without sides (Kant)

• Space is fixed, immutable (Newton)

• Space is infinite



                      Mark Hogarth, Girton College
John McTaggart Ellis McTaggart (1866 –1925)




        “The Unreality of Time” (1908)
   This is a ‘purely philosophical’ argument

                Mark Hogarth, Girton College
We can think of ‘time’ in two ways
• The A-series: "..the series of positions running
  from the far past through the near past to the
  present, and then from the present to the
  near future and the far future..”

• The B-series: "The series of positions which
  runs from earlier to later..”


                   Mark Hogarth, Girton College
McT’s argument is:

There is change in the world
Only the A-series time can account for change
The A-series is incoherent
Therefore there is no time



                  Mark Hogarth, Girton College
General consensus now:

 the A-series is incoherent

 but change can occur in the B-series

 and time lives on in the B-series

                   Mark Hogarth, Girton College
If right then the idea that there is a ‘moving
   now’ is wrong.

Ditto:   the past is a sea of dead facts
         the present is real
         the future is open



                    Mark Hogarth, Girton College
Where’s free will gone?




      Mark Hogarth, Girton College
David Hume (1711 –1776) has the answer…




                Mark Hogarth, Girton College
      Two ways to think about free will

“Few are capable of distinguishing betwixt the
liberty of spontaniety, as it is called in the
schools, and the liberty of indifference”




                                     David Hume A Treatise of Human Nature
                 Mark Hogarth, Girton College
          Space is puzzling too

Why does a mirror reverse left and right, but not
 up and down?




                   Mark Hogarth, Girton College
                          Euclid
• Any two points can be joined by a straight line.
• Any straight line segment can be extended indefinitely
  in a straight line.
• Given any straight line segment, a circle can be drawn
  having the segment as radius and one endpoint as
  center.
• All right angles are congruent.
• Parallel postulate. If two lines intersect a third in such
  a way that the sum of the inner angles on one side is
  less than two right angles, then the two lines inevitably
  must intersect each other on that side if extended far
  enough.

                       Mark Hogarth, Girton College
Parallel postulate (another version)

Exactly one line can be drawn through any point
  not on a given line parallel to that line




                   Mark Hogarth, Girton College
              Immanuel Kant
That space is Euclidean is synthetic a priori

Synthetic – roughly, not true by definition

A priori – not based on experience




                   Mark Hogarth, Girton College
Our brains ‘impose’ this structure (‘intuition’)
 on the world.



(As we impose a face on the moon.)




                  Mark Hogarth, Girton College
The Fifth Postulate was not so intuitive as the
  others.

Could it be derived from the others?

Attempts failed.



                   Mark Hogarth, Girton College
                      1830s
                    János Bolyai
          Nikolai Ivanovich Lobachevsky
                 dropped the Fifth
           to produce a new geometry



(Actually Karl Friedrich Gauss had done this much
  earlier)

                   Mark Hogarth, Girton College
Following on, Riemann found another geometry.

 Suddenly there are three geometries on offer!




                  Mark Hogarth, Girton College
Mark Hogarth, Girton College
Mark Hogarth, Girton College
Henri Poincaré (1854 – 1912))

Which geometry we choose is a matter of
 convention; it is like choosing a coordinate
 system.




                   Mark Hogarth, Girton College
He argues using a thought experiment about a
 2d “disk world”




                 Mark Hogarth, Girton College
           Think in 4 dimensions
• No mystery in this: space has 3 dimensions, time 1, so
  4 numbers (coordinates) specify the position of any
  event in space-and-time=spacetime.
• Don’t’ say ‘Time is the forth dimension’.
• Say : ‘Space and time can be considered as parts of a
  single entity: spacetime’, which is 4-dimensional.




                      Mark Hogarth, Girton College
• Event: an occurrence in the world with no extension in space or time, e.g.
  the explosion of a fire-cracker. Events are represented by points.

• Worldline: the path through time of a body with no spatial extension.

• Inertial observer: an observer unaffected by any external forces.

• Inertial frame: a frame of reference (a map or coordinate system if you
  like) in which any inertial observer moves in a straight line.

• According to Newton, there is one special inertial frame: it represents
  absolute space. It is at (absolute) rest, while the other inertial frames
  move at constant velocity w.r.t. this frame.




                               Mark Hogarth, Girton College
 The story of spacetime prior to Einstein (1905)

• According to Newton’s theory only acceleration, and not velocity,
  could be detected relative to absolute space (through a conspiracy
  of nature).

• Formally this is the Principle of Relativity (PR, due to Galileo): all
  inertial frames are equivalent. Illustrated by his Ship Argument.

• But Newtonian physics, which embodies the PR, can work without
  absolute space: just make all inertial frames equivalent. This arena
  is called Neo-Newtonian spacetime.




                             Mark Hogarth, Girton College
• Maxwell’s theory of electromagnetism (circa 1870) predicted that
  the speed of light has a fixed value c.

• Relative to what? Again, absolute space (this time called the aether
  ) seemed to be required, and a violation of PR seemed inevitable.

• But ‘round-trip’ experiments detect no change in light speed from
  inertial frame to inertial frame. So no evidence for the
  aether=absolute space.

• Lorentz suggested a ‘compensatory theory’ to account for
  negative results: the material of rod and clocks is being distorted
  against a background of absolute space.



                           Mark Hogarth, Girton College
•   Einstein instead suggests two postulates:
•
•   (1) Galilean relativity
•
•   (2) Universality of the speed of light (Einstein)
•
•   (1) and (2) leads to Special Relativity (SR).
•
•   The spacetime of special relativity is called Minkowski.
•
•   First let’s adopt new units. Measure time in meters: one meter of time is
    time taken for light to travel one meter.
•
• Speed of light c =1


                                 Mark Hogarth, Girton College
• Intuitive argument why (1)+(2) implies ‘time
  dilation’
In train frame, 2t is the round trip time for light
  beam




                    Mark Hogarth, Girton College
Einstein next sought a relativistic theory of
  gravity.

He is aware that Newton’s theory can’t explain
 the perihelion of Mercury.

In 1915 he published his general theory of
  relativity.
                   Mark Hogarth, Girton College
         A new theory of gravity, based on SR

•   According to Newton gravity is a force. The force F between a particle A
    with mass mA and a particle B with mass mB separated by a distance r is
    given by
•
• F = product of the masses/square of distance between them
•
• Idea is that particles A and B are compelled by F to deviate from the
  inertial world lines (geodesics).
•
• Radical proposal: suppose there is no force of gravity. Suppose instead
  that gravity manifests itself as spacetime curvature, and that A and B are
  simply moving on geodesics (of a curved spacetime).
•
• This would explain Galileo’s claim: all bodies fall at the same rate,
  irrespective of their mass.


                              Mark Hogarth, Girton College
              Clues from Riemann


Realising that curved geometries might hold the
 key to gravity, Einstein consulted the works of
 Riemann.

Riemann’s theory is a generalised version of
  Gauss’s theory of surfaces: a Riemannian
  space is locally a Euclidean space but globally
  can be more complex.

                   Mark Hogarth, Girton College
Einstein Field Equations




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Read as




   Matter=Curvature

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In 1919 Eddington measured the bending of star
  light during a solar eclipse.

Einstein’s theory predicted 1.75 arc seconds

The experimental result was…



                  Mark Hogarth, Girton College
1.61 +/- 0.30 arc seconds




       Mark Hogarth, Girton College
                  Black Hole

This is formed after a star has exhausted its
  supply of nuclear fuel and collapsed
  completely.

Strong evidence that black holes exist (Signus X-
  1 is a likely candidate).



                   Mark Hogarth, Girton College
Mark Hogarth, Girton College
Mark Hogarth, Girton College
In the 1960s Roger Penrose developed a neat
  way of representing spacetimes – the Penrose
  diagram.




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Black hole: 2 representations




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Another kind of black hole




  Here lots of universes are connected by ‘wormholes’


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 What is the whole of spacetime like?
One of these two:




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Or in the Penrose representation




                   Mark Hogarth, Girton College
  But all these spacetime models are
simplifications: e.g. we expect colliding
   black holes, but have no model




        Jets from the core of the radio galaxy NGC 326

                      Mark Hogarth, Girton College
 Some models in GR allow time travel
But what is time travel?

‘Time travel’ sometimes refers to this kind of
  (‘Wellsian’) discontinuous travel. Doctor
  Who?




                   Mark Hogarth, Girton College
Logically possible but surely physically
impossible. (And can we count both bits as
same Fred?) I will ignore Wellsian TT.

Kurt Gödel (1906-78) had a better
idea (1949).




                         Mark Hogarth, Girton College
Gödel’s Universe
 This universe contains ‘temporal loops’




        Mark Hogarth, Girton College
•   The paradoxes of TT
•
•   You say that TT is physical possible but surely it’s just logically impossible.
•
•   Here’s the canonical argument:
•
•   If time-travel is possible then I could go back and kill my paternal
    grandfather before he sired my Dad, which means I would not be born.
    Contradiction. Ergo time-travel is impossible.
•
•
• One thing at a time. Let’s put sentient beings with their alleged free-will
  to one side.




                                Mark Hogarth, Girton College
• Paradox: Bullet destroys gun, therefore no bullet in first
  place.

• Resolution: what the words of the paradox show is not that
  loops are somehow logically flawed (as if it could be: we
  have a sound mathematical description) but that loops
  place constrain what is allowed to happen.
•
• This is not strange. Containers place constraints on the
  objects they contain. Anything in a mouse-sized box must
  be no bigger than a mouse. Elephants are out.
•


                         Mark Hogarth, Girton College
                        So…
Guns capable of shooting themselves are not
 compatible with loops.

But there are scenarios that are compatible…




                  Mark Hogarth, Girton College
   And the grandfather paradox?

Stories involving humans cannot be made to
  unravel so that the story is consistent over a
  closed loop.




                   Mark Hogarth, Girton College
                   Finally…
The Doomsday Argument is much discussed
  currently in the philosophy literature.

If the argument is right, we are doomed – all of
   us, and soon.




                   Mark Hogarth, Girton College
Suppose

(1)the world will one day end
(2)Human population growth is such that any
  generation contains more people than all the
  previous generations put together
  (2,4,8,16,32,…)


                  Mark Hogarth, Girton College

								
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