The End of Time: The Next Revolution in Physics

When, later, I suggest that the quantum universe is timeless in a deeper sense than the classical Machian universe just described, that will be a conjecture. But it is made plausible by the results of this chapter. They are not speculation but mathematical truths. Every phenomenon explained by Newton’s laws, including the beautiful rings of Saturn and the spectacular structure of spiral galaxies, can be explained without absolute space and time. They follow from a simpler, timeless theory in Platonia.

PART 3

The Deep Structure of General Relativity

Now we come to relativity. My aim is not to give an extended account, only to show how its fundamental features relate to the book’s theme. But I have a tough nut to crack. My subject is the non-existence of time, whereas time is almost everything in relativity as it is usually presented. Is relativity Hamlet without the Prince of Denmark?

In fact, the evidence for the non-existence of time in relativity has long been hidden by accidents of historical development, and is far stronger than many people realize. Yet the case is not quite conclusive. We have seen how the space and time of Newton’s theory can be constructed from instants of time as defined in this book. Taking them to be the true atoms of existence, we have shown that no external framework is needed. Einstein’s space-time can also be put together from instants in a strikingly similar way. However, in the finished product they are knit together far more tightly than in Newtonian theory. Explaining the wonderful way in which this happens is the goal now. If the world were classical, no one would try to pull space-time apart into instants. But quantum theory will probably shatter space-time. It is therefore sensible to consider the constituents into which it might shatter. This is what I shall do in Part 3.

I begin by looking at the special theory of relativity, in which gravity plays no role. I then go on to the general theory, in which Einstein found a most brilliantly original way to describe gravity. In both relativity theories time seems to be very real and to behave in baffling ways. But, as became clear only after Einstein’s death, his theory has a deep structure which is revealed only by an analysis of how it works as a dynamical theory. It is this deep structure that is timeless. Quite a large proportion of Part 3 will explain the purely historical accidents that obscured the deep structure of general relativity for so long.

CHAPTER 8

The Bolt from the Blue

HISTORICAL ACCIDENTS

In the whole of physics, nothing is more remarkable than the transformation wrought by a simple question that Einstein posed in 1905: what is the basis for saying that two events are simultaneous? Einstein was not the first to ask it. James Thomson, brother of Lord Kelvin, had in 1883. More significantly, so had Poincaré – a great figure in science – in 1898, in a paper that Abraham Pais, Einstein’s biographer, calls ‘utterly remarkable’. In connection with historical accidents, Poincaré’s paper is very interesting. He identified two problems in the definition of time.

First he considered duration: what does it mean to say that a second today is the same as a second tomorrow? He noted that this question had recently been widely discussed, and he outlined the astronomers’ solution, the ephemeris time described in Chapter 6. However, he then noted a second question, just as fundamental and in some ways more immediate, which had escaped close attention. How does one define simultaneity at spatially separated points? This was the question that Einstein posed and answered seven years later with such devastating effect. I read the subsequent history of relativity as follows. Einstein answered his question – Poincaré’s second – with such aplomb and originality that it eclipsed interest in the question of duration. It is not that duration plays no role in relativity – quite the opposite, it plays a central role. But duration is not derived from first principles. It appears indirectly.

One of the main aims of Part 3 is to redress the balance, to treat duration at the same level as simultaneity. There is, in fact, a beautiful theory of duration at the heart of general relativity, but it is hidden away in sophisticated mathematics. Einstein had no inkling of this. He said of his own theory that no one who had grasped its content could ‘escape its magic’. But the magic was more potent than even he realized. It can, it almost certainly will, destroy time.

BACKGROUND TO THE CRISIS