The End of Time: The Next Revolution in Physics

The first idea Bruno and I developed had several interesting and promising properties. Above all, it showed that a mechanics of the complete universe containing only relative quantities and no extra Newtonian framework could be constructed. Hitherto, most people had thought this to be impossible. Just as Mach had suspected, the phenomenon that Newton called inertial motion in absolute space could be shown to arise from motion relative to all the masses in the universe. We also showed that an external time is redundant. However, besides the desirable features we obtained effects which showed that the theory could not be right. While the universe as a whole could create the experimentally observed inertial effects that we wanted, the Galaxy would create additional effects, not observed by astronomers, that ruled out our approach.

The idea that Bruno and I first developed seemed so natural it surprised us that no one had thought of it earlier. However, I learned quite recently that something similar was proposed in 1904 (in an obscure booklet by one Wenzel Hofmann), and then rediscovered in 1914 by the physicist Hans Reissner and again in 1925 by none other than Schrödinger, just before he discovered wave mechanics. This was especially ironic since Bruno had been Schrödinger’s student. I think the main reason why these papers got overlooked was that they were completely overshadowed by Einstein’s general relativity and the excitement of the discovery of quantum mechanics in 1925/6. There is also an undoubted tendency for physicists to work within a so-called paradigm (the American philosopher of science Thomas Kuhn’s famous expression), and pay at best fleeting attention to ideas that do not fit within the existing established patterns of thought.

I mention these things because the next idea that Bruno and I tried seems to me just as natural as our first idea, if one approaches the problems of describing motion and change with an open mind. It does, however, seem very different from the present paradigm, which has become deep-rooted with the long hegemony of Newtonian ideas, which were only partly changed by Einstein. Although, as we shall see, our second idea is actually built into Einstein’s theory at its very heart, within the context of classical physics it merely provides a different perspective on that theory. However, for the study of quantum effects it does represent a genuine alternative, and the attempt to create a quantum theory of the universe may force its adoption, alien though it may appear to many working scientists.

EXPLORING PLATONIA

Let me now explain this second idea. So far, I have explained only what the points of Platonia are. Each is a possible relative arrangement, a configuration, of all the matter in the universe. If there are only three bodies in it, Platonia is Triangle Land, each point of which is a triangle (Figures 3 and 4). Can we somehow say ‘how far apart’ any two similar but distinct triangles are? If so, this will define a ‘distance’ between neighbouring points in Triangle Land, and just as mathematicians seek geodesics using ordinary distances on curved surfaces, we can start to look for geodesics in Platonia. If we can find them, they will be natural candidates for actual histories of the universe, which we have identified as paths in Platonia. They will be Machian histories if the ‘distance’ between any two neighbouring points in Platonia is determined by their structures and nothing else, and we shall not need to suppose that they are embedded in some extra structure like absolute space.

There is such a simple and natural solution to the problem of finding geodesics in Platonia that I would like to spell it out. The fact that it does seem to be used by nature is one of the two prime pieces of evidence I have for suggesting that the universe is timeless. (The second, equally simple in its way, comes from quantum mechanics.) How it works out for the simplest example of a universe of three bodies is described in Box 8.

BOX 8 Intrinsic Difference and Best Matching

In Figure 21, triangle ABC is one point in Triangle Land, and the slightly different triangle A*B*C* is a neighbouring point. A ‘distance’ between them can be found in many ways, but one of the simplest is the following. Imagine that ABC is held fixed, and A*B*C* is placed in any position relative to it. This creates ‘distances’ AA*, BB*, CC* between the corresponding vertices, at which we suppose there are bodies of masses a, b, c. We form a ‘trial distance’ d by taking each mass and multiplying it by the square of the corresponding distance, adding the results and taking the square root of the sum. Thus