Next, we examine the Timeless Theory bag. There are two big differences. First, it contains vastly more triangles (it could, in fact, contain all conceivable triangles). More significantly, there are so many of them that it is quite impossible to arrange them in a continuous sequence. Second, the triangles are present in multiple copies. That is, we might, after a very extensive search, find ten identical copies of one particular triangle, two of another, and ten million of yet another. That is really the complete story. It is all that most people would notice.
I think you will agree that the Current Theory bag does match experience quite closely. The triangles stand for each of the instants you experience, and they follow one another continuously, just as the instants do. By giving them to you in a bag and getting you to lay them out in a sequence, I am giving you a ‘God’s eye’ view of history. All its instants are, as it were, spread out in eternity as if you surveyed them from a mountain-top. In fact, this way of thinking about time has long been a commonplace among Christian theologians and some philosophers, and has prompted them to claim that time does not exist but that its instants all exist together and at once in eternity. My claim is much stronger. I am saying that reality, if we could see all of it, is not at all like the contents of the Current Theory bag with its single sequence of states. It is like the contents of the Timeless Theory bag, in which in principle all conceivable states can be present. Nothing in it resembles our experience of history as a unique sequence of states: that experience is usually explained by assuming that there is a unique sequence of states. I deny that there is such a sequence, and propose a different explanation for the experience that prompts us to believe in it. The only thing the bags have in common with our direct experience of time is the parallel between individual triangles as models of individual instants of time.
Actually, the bags share another property – their contents satisfy a law. Given the sequence of triangles of the first bag, clever mathematicians could deduce that they correspond to the triangles formed by three gravitationally interacting bodies. They could even reconstruct the bodies’ positions in absolute space, and the amount of time that elapses between any two of the triangles in the sequence. With the second bag, mathematicians would discover that the numbers in which the different triangles occur are not random – chosen by chance – but satisfy a law. The numbers vary from triangle to triangle in an ordered fashion. But at first glance at least, this law seems to have no connection with the law that creates the unique sequence of triangles in the first bag. Also, there is nothing like the dual scheme of law and initial condition that creates the sequence of the first bag. In a sense that I shall not yet try to explain, there is just a law, with nothing like an initial condition that has to be added to it.
How is the appearance of time ever going to emerge from the contents of the Timeless Theory bag as just described? Bare triangles lying in a jumbled heap certainly cannot make that miracle happen. Triangles have a structure that is much too simple. This is why I said that rich structure ordered in a special way is an essential element if a notion of time is to emerge. If, when we open the Timeless Theory bag, we find it contains, not triangles, but vastly richer structures, some of which are time capsules in the sense I have defined, my task does not seem quite so hopeless. By definition, time capsules suggest time. But finding just a few time capsules in a vast heap of otherwise nondescript structures will not get me very far.
This is where the assumption that all the structures found in the bag come in multiple copies, and that the numbers of these copies, which can vary very widely, are determined by a definite timeless rule, becomes crucial. Imagine that all the structures for which the numbers of identical copies in the bag are large are time capsules, while there are few copies of structures that are not time capsules. Since the overwhelming majority of possible structures that can exist are certainly not time capsules, any rule that does fill the bag with time capsules will be remarkably selective, creative one might say. If, in addition, you can find evidence that the universe is governed by a timeless law whose effect is to discriminate between structures and which actually selects time capsules with surprising accuracy, then you might begin to take such ideas more seriously. You might begin to see a way in which the Timeless Theory could still explain our experience of time, and could perhaps be superior to the Current Theory.
However, you will probably dismiss such a possibility as the wildest fantasy. Why should Nature go to such contrived lengths simply to create an impression of time and fool poor mortals? To counter this natural reaction, let me give a little more detail about those hints of the non-existence of time that I mentioned in Chapter 1. This may at least persuade you that some dramatic change could be in the offing.
Physics is regarded as the most fundamental science. It is an attempt to create a picture of reality as we should see it if we could, somehow, step out of ourselves. For this reason it is rather abstract. In addition, it often deals with conditions far removed from everyday human experience – deep inside the atom, where quantum theory holds sway, and in the farflung reaches of space, where Einstein’s general relativity reigns. The ideas I want to tell you about have come from attempts during the last forty years to unite these two realms (Box 2). They have produced a crisis. The very working of the universe is at stake: it does not seem to be possible, in any natural and convincing way, to give a common description of them in which anything like time occurs.
Frustratingly little progress has been made. However, in 1967 a possible picture did emerge from a paper by the American Bryce DeWitt. He found an equation that, if his reasoning is sound, describes the whole universe – both atoms and galaxies – in a unified manner. Because John Wheeler, the American physicist who coined the term ‘black hole’, played a major part in its discovery, this equation is called the Wheeler-DeWitt equation. It is controversial in at least three respects. First, many experts believe that the very derivation of the equation is flawed – that it was obtained by an invalid procedure. Second, the equation is not yet even properly defined, as there are still many technical difficulties to be overcome. In fact, it is more properly regarded as a conjecture: a tentative proposal for an equation that is not yet proved. And third, the experts argue interminably over what meaning it might have and whether it can ever be promoted to the status of a bona fide equation. Ironically, DeWitt himself thinks that it is probably not the right way to go about things, and he generally refers to it as ‘that damned equation’. Many physicists feel that a different route, through so-called superstring theory, which it is hoped will establish a deep unity between all the forces of nature, is the correct way forward. That many of the best physicists have concentrated on superstring theory is probably the main reason why the ‘crisis of time’ brought to light by the Wheeler-DeWitt equation has not attracted more attention. However, there is no doubt that the equation reflects and unifies deep properties of both quantum theory and general relativity. Quite a sizeable minority of experts take the equation seriously. In particular, much of the work done by Stephen Hawking in the last twenty years or so has been based on it, though he has his own special approach to the problem of time that it raises.