The End of Time: The Next Revolution in Physics

First, you notice that it contains triangles of all different sizes. There is a smallest triangle, very tiny; then another very like it, but a little larger and with a slightly different shape; and so on. In fact, you soon realize that you can lay out all the triangles in a sequence. The order in which they should go is clear because each successive triangle differs only slightly from its predecessor. Their increasing size makes the ordering especially easy. Of course, a real bag can contain only finitely many triangles, but I shall suppose that there are infinitely many and that the sequence is endless, the triangles getting ever larger.

Such a sequence of triangles is like the sequence of experienced instants that I suggested ‘photographing’. It is also like the succession of Newtonian instants from the moment God decided to create the universe, or the succession of states of the universe expanding out of the Big Bang, represented by the smallest triangle. In fact, the contents of Current Theory correspond to the simplest Newtonian universe that can begin to model the complexity of the actual universe: three mass points moving in absolute space and time, as in Figure 1. Initially very close to each other, they move apart so rapidly that gravity cannot pull them back, and they fly off to infinity.

According to Newton, the three mass points are, at all instants, at certain positions in absolute space and form certain triangles. The triangles tell us how the points are placed relative to one another, but not where they are in absolute space. It is such triangles, represented in cardboard, that I imagine have been put into the Current Theory bag. Since we cannot experience absolute space and time directly, I have tried to match the model more closely to our actual experience. The sequence of triangles corresponds to one possible history. There could be many such histories that match the dual scheme of laws and initial conditions. But we find only one in the Current Theory bag.

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.