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.
THE CRISIS OF TIME
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.
For now, all I want to say about the Wheeler-DeWitt equation is that if one takes it seriously and looks for its simplest interpretation, the picture of the universe that emerges is like the contents of the Timeless Theory bag. For a long time, physicists shied away in distrust from its apparently timeless nature, but during the last fifteen years or so a small but growing number of physicists, myself included, have begun to entertain the idea that time truly does not exist. This also applies to motion: the suggestion is that it too is pure illusion. If we could see the universe as it is, we should see that it is static. Nothing moves, nothing changes. These are large claims, and the bulk of my book will discuss the arguments from physics (presented as simply as I can) that lead me and others to such conclusions. At the end, I shall outline, through the notion of time capsules, a theory of how a static universe can nevertheless appear to teem with motion and change.
Now I want to give you a better feel for what a timeless universe could be like. What we need first is a proper way to think about Nows.
THE ULTIMATE ARENA
One issue that runs through this book is this: what is the ultimate arena of the universe? Is it formed by space and time (space-time), or something else? This is the issue raised by Dirac’s sentence I quoted in the Preface: ‘This result has led me to doubt how fundamental the four-dimensional requirement in physics is.’ I believe that the ultimate arena is not space-time. I can already begin to give you an idea of what might come in its place.
I illustrated the Newtonian scheme by a model universe of just three particles. Its arena is absolute space and time. The Newtonian way of thinking concentrates on the individual particles: what counts are their positions in space and time. However, Newton’s space and time are invisible. Could we do without them? If so, what can we put in their place? An obvious possibility is just to consider the triangles formed by the three particles, each triangle representing one possible relative arrangement of the particles. These are the models of Nows I asked you to contemplate earlier. We can model the totality of Nows for this universe by the totality of triangles. It will be very helpful to start thinking about this totality of triangles, which is actually an infinite collection, as if it were a country, or a landscape.
If you go to any point in a real landscape, you get a view. Except for special and artificial landscapes, the view is different from each point. If you wanted to meet someone, you could give them a snapshot taken from your preferred meeting point. Your friend could then identify it. Thus, points in a real country can be identified by pictures. In a somewhat similar way, I should like you to imagine Triangle Land. Each point in Triangle Land stands for a triangle, which is a real thing you can see or imagine. However, whereas you view a landscape by standing at a point and looking around you, Triangle Land is more like a surface that seems featureless until you touch a point on it. When you do this, a picture lights up on a screen in front of you. Each point you touch gives a different picture. In Triangle Land, which is actually three-dimensional, the pictures you see are triangles. A convenient way of representing Triangle Land is portrayed in Figures 3 and 4.
I have gone to some trouble to describe Triangle Land because it can be used to model the totality of possible Nows. Like real countries, and unlike absolute space, which extends to infinity in all directions, it has frontiers. There are the sheets, ribs and apex of Figure 4. They are there by logical necessity. If Nows were as simple as triangles, the pyramid in Figure 4 could be seen as a model of eternity, for one notion of eternity is surely that it is simply all the Nows that can be, laid out before us so that we can survey them all.
Figure 3 The seven triangles represent several possible arrangements of a model universe of three particles A, B, C. Each triangle is a possible Now. Each Now is associated with a point (black diamond) in the ‘room’ formed by the three grid axes AB, BC, CA, which meet at the corner of the ‘room’ farthest from you. The black diamond that represents a given triangle ABC is situated where the distance to the ‘floor’ is the length of the side AB (measured along the vertical axis), and the distances to the two ‘walls’ are equal to the other two sides, BC and CA. The dash-dotted lines show the grid coordinates. In this way, each model Now is associated with a unique point in the ‘room’. As explained in the text, if you ‘touched’ one of the black diamonds, the corresponding triangle would light up. However, not every point in the ‘room’ corresponds to a possible triangle – see Figure 4.