The End of Time: The Next Revolution in Physics

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.

THE MAIN ADVANCES