Science of Discworld III

imply. In 1919 this prediction was confirmed, when Sir Arthur Stanley Eddington led an expedition to observe a total eclipse of the Sun in West Africa. Andrew Crommelin of Greenwich Observatory led a second expedition to Brazil. The expeditions observed stars near the edge of the Sun during the eclipse, when their light would not be swamped by the Sun’s much brighter light. They found slight displacements of the stars’ apparent positions, consistent with Einstein’s predictions. Overjoyed, Einstein sent his mum a postcard: ‘Dear Mother, joyous news today … the English expeditions have actually demonstrated the deflection of light from the Sun.’ the Times ran the headline: REVOLUTION IN SCIENCE. NEW THEORY OF THE UNIVERSE. NEWTONIAN IDEAS OVERTHROWN. Halfway down the second column was a subheading: SPACE ‘WARPED’. Einstein became an overnight celebrity.
    It would be churlish to mention that to modern eyes the observational data are decidedly dodgy – there might be some bending, and then again, there might not. So we won’t. Anyway, later, better experiments confirmed Einstein’s prediction. Some distant quasars produce multiple images when an intervening galaxy acts like a lens and bends their light, to create a cosmic mirage.
    The metric of spacetime is not flat.
    Instead, near a star, spacetime takes the form of a curved surface that bends to create a circular ‘valley’ in which the star sits. Light follows geodesies across the surface, and is ‘pulled down’ into the hole, because that path provides a short cut. Particles moving in spacetime at sublight speeds behave in the same way; they no longer follow straight lines, but are deflected towards the star, whence the Newtonian picture of a gravitational force.
    Far from the star, this spacetime is very close indeed to Minkowski spacetime; that is, the gravitational effect falls off rapidly and soon becomes negligible. Spacetimes that look like Minkowski spacetime at large distances are said to be ‘asymptotically flat’. Remember that term: it’s important for making time machines. Most of our own universe is asymptotically flat, because massive bodies such as stars are scattered very thinly.
    When setting up a spacetime, you can’t just bend things any way you like. The metric must obey the Einstein equations, which relate the motion of freely moving particles to the degree of distortion away from flat spacetime.
    We’ve said a lot about how space and time behave, but what are they? To be honest, we haven’t a clue. The one thing we’re sure of is that appearances can be deceptive.
    Tick .
    Some physicists take that principle to extremes. Julian Barbour, in The End of Time , argues that from a quantum-mechanical point of view, time does not exist.
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    In 1999, writing in New Scientist , he explained the idea roughly this way. At any instant, the state of every particle in the entire universe can be represented by a single point in a gigantic phase space, which he calls Platonia. Barbour and his colleague Bruno Bertottifound out how to make conventional physics work in Platonia. As time passes, the configuration of all particles in the universe is represented in Platonia as a moving point, so it traces out a path, just like a relativistic world-line. A Platonian deity could bring the points of that path into existence sequentially, and the particles would move, and time would seem to flow.
    Quantum Platonia, however, is a much stranger place. Here, ‘quantum mechanics kills time’, as Barbour puts it. A quantum particle is not a point, but a fuzzy probability cloud. A quantum state of the universe is a fuzzy cloud in Platonia. The ‘size’ of that cloud, relative to that of Platonia itself, represents the probability that the universe is in one of the states that comprise the cloud. So we have to endow Platonia with a ‘probability mist’, whose density in any given region determines how probable it is for a cloud to occupy that region.
    But, says Barbour, ‘there cannot be probabilities at different times, because Platonia itself is timeless. There can only be once-and-for-all probabilities for each possible configuration.’ There is only one probability mist, and it is always the same. In this set-up, time is an illusion. The future is not determined by the present – not because of the role of chance, but because there is no such thing as future or present.
    By analogy, think of the childhood game of snakes and