The End of Time: The Next Revolution in Physics

This was the decisive picture that crystallized in my mind about 1971. At that stage I had no thought of applications to quantum mechanics, and no inkling that it might lead to the replacement of one clearly delineated path through Platonia by a mist that hovers over the same timeless landscape. We had a blackboard in our kitchen in College Farm, and I wrote at the top it it: The history of the universe is a continuous curve in its relative configuration space.’ My wife, perhaps understandably, was rather sceptical about the progress I was making. After all, fourteen words were not much to show for seven years of thought. But the clear formulation of the concept of Platonia was the important thing. It shifts attention from the parts of the universe to the universe itself. It shows that time is not needed as an extra element, the Great Timekeeper outside the universe. The universe keeps track of itself. In one instant it is where it is, in another it is somewhere else. That is what a different instant of time is: it is just a different place in Platonia. Instants of time and positions of the objects within the universe are all subsumed into the single notion of place in Platonia. If the place is different, the time is different. If the place is the same, time has not changed. This change of viewpoint is made possible only because the universe is treated as a single whole and time is reduced to change.

I think the reason why I take the possibility of a completely timeless universe more seriously than almost all other physicists is this background that came from thinking about Mach’s principle. As we shall see, Platonia is the natural arena for the realization of that idea. Many years after I had first recognized that Platonia would provide the basis for the solution to the Machian problem, I began to see that it had deep relevance in the quantum domain too. The problems of the origin of inertia and of quantum cosmology form a seamless whole.

CHAPTER 5

Newton’s Evidence

THE AIMS OF MACHIAN MECHANICS

Merely changing the framework in which one conceives of the universe does nothing, but it is still very illuminating to look at some fundamental facts of mechanics in the alternative arenas of absolute space and Platonia. This exercise brings out the strengths of Newton’s position, and at the same time shows what a Machian approach must achieve. The following discussion is based on penetrating remarks made in 1902 by the great French mathematician Henri Poincaré. More clearly than Mach, he demonstrated what is required of a theory of relative motion. Unfortunately, his remarks were overshadowed by Einstein’s discovery of relativity and did not attract the attention they deserved – and still deserve.

You may find that this chapter requires more reflection than all the others. You certainly do not need to grasp it all, but I hope that you will be able to change from a way of thinking to which we have been conditioned by the fact that we evolved on the stable surface of the Earth to a more abstract way of thinking that would have been forced upon us had we evolved from creatures that roamed in space between objects moving through it in all directions. We have to learn how to find our bearings when the solid reassuring framework of the Earth is not there. This is the kind of mental preparation you need to understand the ideas Poincaré developed. In this respect, he was smarter than Einstein.

Poincaré simply asked, rather more precisely than anyone before him, what information is needed to predict the future. Another French mathematician, Pierre Laplace, had already imagined a divine intelligence that at one instant knows the positions and motions of all bodies in the universe. Using Newton’s laws, the divinity can then calculate all past and future motions – it can see, in its mind’s eye, all of history laid out for the minutest inspection. As an alternative to the standard representation in Newton’s absolute space, it will help to see this miracle performed in Triangle Land, the simplest Platonia. This will reveal a curious defect in Newtonian mechanics.