The End of Time: The Next Revolution in Physics

The fact is that we live in a very special location. Only the tiniest fraction of matter in the solar system, let alone the universe, is in solid form. Imagine that we lived in an environment much more typical of the universe – in space. To simplify things, let there be only a finite number of objects, all in motion relative to one another. At any instant there are certain distances between these other objects and us. There is nothing else. In these circumstances, what would be the natural way to answer what is always a fundamental question: where are we? We have no other means of saying where we are except in terms of our distances to other objects. What is more, it would be artificial to choose just a few of them to locate ourselves. Why these rather than those? It would be much more natural to specify our distances to all objects. They define our position. This conclusion is very natural once we become aware that nothing is fixed. Everything moves relative to everything else.

Taking this further, thinking about the position and motion of one object is artificial. We are part of Mach’s All, and any motion we call our own is just part of a change in the complete universe. What is the reality of the universe? It is that in any instant the objects in it have some relative arrangement. If just three objects exist, they form a triangle. In one instant the universe forms one triangle, in a different instant another. What is to be gained by supposing that either triangle is placed in invisible space? The proper way to think about motion is that the universe as a whole moves from one ‘place’ to another ‘place’, where ‘place’ means a relative arrangement, or configuration, of the complete universe.

An arena is the totality of places where one can go in some game. But who is playing the game and where? In Newton’s game, individual objects play in absolute space. In Mach’s game, there is only one player – the universe. It does not move in absolute space, it moves from one configuration to another. The totality of these places is its relative configuration space: Platonia. As the universe moves, it therefore traces out a path in Platonia. This captures, without any redundant structure, the idea of history. History is the passage of the universe through a unique sequence of states. In its history, the universe traces a path through Platonia.

However, such language makes it sound as though time exists. I may have inadvertently conjured up an image in your mind of the universe as a lone hiker walking the fells in northern Platonia. Properly understood, the Machian programme is much more radical. For no Sun rises or sets over that landscape to mark the walker’s progress. The Sun, like the moving parts of any clock, is part of the universe. It is part of the walker. Of course, to say that time has passed, we must have some evidence for that. Something must move. That is the most primitive fact of all. In the Newtonian picture, as in Feynman’s quip, time can pass without anything happening. If we deny that, the grandstand clock must go. There is nothing outside the universe to time it as it goes from one place to another in Platonia – only some internal change can do that. But just as all markers are on an equal footing for defining position, so are all changes for the purposes of timing. We must reckon time by the totality of changes. But changes are just what takes the universe from one place in Platonia to another. Any and all changes do that. We must not think of the history of the universe in terms of some walker on a path who can move along it at different speeds. The history of the universe is the path. Each point on the path is a configuration of the universe. For a three-body universe, each configuration is a triangle. The path is just the triangles – nothing more, nothing less.

With time gone, motion is gone. If you saw a jumbled heap of triangles, it would not enter your head that anything moved, or that one triangle changed into another. When Newton’s superstructure is removed, Newtonian history is like that jumbled heap of triangles, except that it is a special heap. If you picked up each triangle – I call that picking up an instant of time – and marked its position in Triangle Land, you would find that the marks of the triangles form a continuous curve.