Julian Barbour - The End of Time - The Next Revolution in Physics

To see why, it is helpful to trace the development of his thinking – a fascinating story in its own right. As an extremely ambitious student, he read Mach’s critique of Newton’s absolute space. This made him very sceptical about its existence. Simultaneously, he was exposed to all the issues related to the aether in electrodynamics. Lorentz, in particular, had effectively identified absolute space with the aether, in the form of an unambiguous state of rest. But, writing to his future wife Mileva in August 1899, Einstein was already questioning whether motion relative to the aether had any physical meaning. This would develop into one of the key ideas of special relativity. If it is impossible to detect motion relative to it, the aether cannot exist. It was natural for Einstein to apply the same thought to absolute space.

His 1905 paper killed the idea that uniform motion relative to any kind of absolute space or aether could be detected. But Newton had based his case for absolute space on the detection not of uniform motion, but of acceleration. In 1933, Einstein admitted that in 1905 he had wanted to extend the relativity principle to accelerated as well as uniform motion, but could not see how to. The great inspiration – ‘the happiest thought of my life’ – came in 1907 when he started to consider how Newtonian gravity might be adapted to the framework of special relativity. He suddenly realized the potential significance of the fact, noted by Galileo and confirmed with impressive accuracy by Newton, that all bodies fall with exactly the same acceleration in a gravitational field.

Most physicists saw this as a quirk of nature, but Einstein immediately decided to elevate it to another great principle and exploit it as he had the relativity principle. Unable to divine new laws of gravitation straight off, he formulated the equivalence principle , according to which processes must unfold in a uniform gravitational field in exactly the same way as in a frame of reference accelerated uniformly in a space free of gravity. He argued that pure acceleration could not be distinguished from uniform gravitation. Suppose that you awoke from a deep narcotic sleep in a dark bedroom to find that gravity was mysteriously stronger. There could be two different causes. You might have been transported, bedroom and all, to another planet with stronger gravity. But you might still be on the Earth but in an elevator accelerating uniformly upward. No experiments you could perform in your bedroom would enable you to distinguish between these alternatives.

Einstein saw here a striking parallel with the relativity principle. The relativity principle prevented an observer from detecting uniform motion. In its turn, the equivalence principle prevented an observer from detecting uniform acceleration – observed acceleration could be attributed either to acceleration in gravity-free space or to a gravitational field. Einstein recognized the immediate short-term potential of his new principle. He knew how processes unfolded in gravity-free space. Mere mathematics showed how they would appear in an accelerated frame, but by the equivalence principle it was possible to deduce that these same processes must occur in a uniform gravitational field. Once again, Einstein’s inspired selection of a simple universal principle – all bodies fall in the same way – enabled him to perform a startling conjuring trick. He showed that the rate of clocks must depend on their position in a gravitational field. Clocks closer to gravitating bodies must run slow relative to clocks farther away.

This fact is often said to show that ‘time passes more slowly’ near a gravitating body. However, objective facts within relativity can seem utterly mysterious and logically impossible if we imagine time as a river. Such a time does not exist. Relativity makes statements about actual clocks, not time in the abstract. It is easy to imagine – and physicists now find it comparatively easy to verify – that otherwise identical clocks run at different rates at the top and bottom of a higher tower. Incidentally, the ‘time dilation’ effect in gravity is much easier to accept than the similar effect associated with motion. There is no reciprocal slowing down. Thus, observers at the top and bottom of the tower both agree that the clock at the top runs faster.

By 1907 Einstein was also able to show that gravity must deflect light. Both his early predictions, made precise in his fully developed theory, have been confirmed with most impressive accuracy in recent decades. However, Einstein saw his early predictions merely as stepping stones to something far grander. The equivalence principle persuaded him that inertia (i.e. the tendency of bodies to persist in a state of rest or uniform motion) and gravity, which Newton and all other physicists had regarded as distinct, must actually be identical in nature. He started to look for a conceptual framework in which to locate this conviction. At the same time, he saw a great opportunity to abolish not only the aether but also all vestiges of absolute space. So far he had managed to achieve two steps in this process by showing that uniform motion and uniform acceleration could not correspond to anything physically real in the world. However, much more general motions could be imagined. Einstein aimed to show that the laws of nature could be expressed in identical form whatever the motion of the frame of reference.

The relativity he had so far established was very special. What he wanted was complete general relativity . This idea, nurtured and developed over eight years and involving intense and often agonizing work during the last four, explains the name he gave to his unified theory of gravitation and inertia that finally emerged in 1915. Viewed in the light of the ancient debate about absolute and relative motion, Einstein’s approach was very distinctive and somewhat surprising since he made no attempt to build kinematic relativity directly into the foundations of his theory. Unlike Mach and many other contemporaries, he did not insist that only relative quantities should appear in dynamics. He went at things in a roundabout way, mostly because of his preference for general principles. However, I think it was also a result of the way he thought about space and time.

As far as I can make out, Einstein did conceive of space-time as real and as the container of material things – fields and particles. However, he recognized that all its points were invisible and that they could be distinguished and identified only by observable matter present at them. Since space-time was made ‘visible’ by such matter, he supposed he could lay out coordinate grid lines on space-time and express the laws of nature with respect to them.

Now came the decisive issue. Einstein saw space-time without any matter in it as a blank canvas. Nothing about it could suggest why the coordinate grid lines should be drawn in one way rather than another. Any choice would be arbitrary and violate the principle of sufficient reason. Einstein found this intolerable. That is no exaggeration: his faith in rationality of nature – as opposed to human beings – was intense. The only satisfactory resolution was general relativity. In truth, there can be no distinguished coordinate systems. It must be possible to express the laws of nature in all systems in exactly the same form.

The only justification for the distinguished systems that appeared in Newtonian dynamics and special relativity was the law of inertia. But the equivalence principle had opened up the possibility of unifying inertia and gravity. This insight sustained Einstein in his long search for general relativity. His contemporaries would all have been content simply to find a new law of gravity. He was after something sublime.

It is suggestive that both Poincaré and Einstein – the old and young giants – began their attack on absolute space from the principle of sufficient reason. The difference between their approaches is interesting. Working within the traditional dynamical framework, Poincaré said that only directly observable quantities – the relative separations of bodies and their rates of change – should be allowed as initial data for dynamics. In such a theory, we may say that perfect Laplacian determinism holds (it doesn’t hold in Newtonian theory, which uses invisible absolute space and time). Einstein had a more general approach. He merely insisted that there should be no arbitrary choice of the coordinate systems used to express the laws of nature.