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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 Mark Hogarth, Girton College ‘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 Mark Hogarth, Girton College Read as Matter=Curvature Mark Hogarth, Girton College 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. Mark Hogarth, Girton College Black hole: 2 representations Mark Hogarth, Girton College Another kind of black hole Here lots of universes are connected by ‘wormholes’ Mark Hogarth, Girton College What is the whole of spacetime like? One of these two: Mark Hogarth, Girton College 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