Both relativity principles have played important – often decisive – roles in physics. Copernicus and Kepler used kinematic relativity to great effect in the revolution they brought about. Galileo used the other relativity principle to explain how we can live on the Earth without feeling its motion. That was almost as wonderful a piece of work as Einstein’s, nearly three hundred years later. A natural question is this: what is the connection between the two relativity principles? Any satisfactory answer must grapple with and resolve the issue of the distinguished frames of reference. How are they determined? What is their origin? As we have seen, neither Einstein nor Minkowski addressed these questions when they created special relativity, and they have been curiously neglected ever since. This is a pity, since they touch upon the nature of time. We cannot say what time is – and whether it even exists – until we know what motion is.
Poincaré sought to unite the two relativity principles in a single condition on the structure of dynamics, as formulated in the two-snapshots idea. Had he succeeded, he would have derived the empirical fact of Galilean relativity solely on the basis of a natural criterion derived from kinematic relativity. He died without taking this idea any further, but in any case it is doubtful whether the two relativity principles can be fully fused into one. Poincaré formulated his idea in 1902, before the relativistic intermingling of space and time became apparent, and it is hard to see how that can ever be derived from the bare fact of kinematic relativity. It is, however, of great interest to see how far Poincaré’s idea can be taken. We shall come to this when we have seen how Einstein thought about and developed his own relativity principle and thereby created general relativity.
It is important not to be overawed by the genius of Einstein. He did have blind spots. One was his lack of concern about the determination in practice of the distinguished frames that play such a vital role in special relativity – he simply took them for granted. It is true that they are realized approximately on the reassuringly solid Earth in skilfully engineered railway carriages. But how does one find them in the vast reaches of space? This is not a trivial question. Matching this lack of practical interest, we find an absence of theoretical concern. Einstein asked only what the laws of nature look like in given frames of reference. He never asked himself whether there are laws that determine the frames themselves. At best, he sought an indirect answer and got into a muddle – but a most creative muddle.
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.