Philosophy of Space and Time Madingley Hall October 31-Novmber 2, 2008 Mark Hogarth University of Cambridge

1. Philosophy of Space and TimeMadingley HallOctober 31-Novmber 2, 2008Mark HogarthUniversity of Cambridge Mark Hogarth, Girton College

2. This powerpoint will be available on Sunday afternoon at www.markhogarth.net Mark Hogarth, Girton College

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10. Show the movie Mark! Mark Hogarth, Girton College

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12. Roger Penrose Mark Hogarth, Girton College

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

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

15. Key figures John McTaggart Ellis McTaggart 1866-1925 Euclid 325 BC- 265 BC Steven Hawking 1942- Roger Penrose 1931- Albert Einstein 1879-1955 Newton 1643 – 1727 Leibniz 1646-1716 Gauss 1777-1855 Riemann 1826-66 Mark Hogarth, Girton College

16. Key figures Mark Hogarth, Girton College

17. 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

18. Intuition and philosophical ideas Space • Space is a box without sides (Kant) • Space is fixed, immutable (Newton) • Space is infinite Mark Hogarth, Girton College

19. John McTaggart Ellis McTaggart (1866 –1925) “The Unreality of Time” (1908) Mark Hogarth, Girton College

20. 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

21. 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

22. General consensus now is that McT has shown: the A-series is incoherent But time lives on in the B-series Mark Hogarth, Girton College

23. If right then the idea that the past is a sea of dead facts the present is real the future is open Is WRONG Mark Hogarth, Girton College

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

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

26. 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; betwixt that which is opposed to violence, and that which means a negation of necessity and causes. The first is even the most common sense of the word; and as it is only that species of liberty, which it concerns us to preserve, our thoughts have been principally turned towards it, and have almost universally confounded it with the other. David Hume A Treatise of Human Nature Mark Hogarth, Girton College

27. Space is puzzling too Why does a mirror reverse left and right, but not up and down? Mark Hogarth, Girton College

28. 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

29. 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

30. 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

31. Our brains ‘impose’ this structure (‘intuition’) on the world. (As we impose a face on the moon.) Mark Hogarth, Girton College

32. The Fifth Postulate was not so intuitive as the others. Could it be derived from the others? Attempts failed. Mark Hogarth, Girton College

33. 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

34. Following on, Riemann found another geometry. Suddenly there are three geometries on offer! Mark Hogarth, Girton College

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37. Henri Poincaré (1854 – 1912)) Which geometry we choose is a matter of convention; it is like choosing a coordinate system. Mark Hogarth, Girton College

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

39. 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

40. 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

41. 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

42. 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

43. 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

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

45. 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

46. 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

47. 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

48. Einstein Field Equations Mark Hogarth, Girton College

49. Read as Matter=Curvature Mark Hogarth, Girton College

50. 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