The End of Time: The Next Revolution in Physics

Now we can see the problem. Considered in itself, the pair of triangles is just one thing. Each different relative orientation and time separation we give them depends on our whim. They should not have any effect. Yet each has momentous consequences: they create quite different universes. An exactly analogous problem arises if the universe consists of any number of particles. Two snapshots (the analogues of the two triangles) of the relative configuration of the universe are never quite enough to determine an entire history uniquely.

Before we look at the one possibility that can resolve this puzzle, it is worth considering how the four freedoms that do count show up in practice. We shall then be able to see what a great discovery Newton’s invisible framework was. We start with the twists.

SPACE AND SPIN

When I was a boy, there was only one sport at which I was any good: the high jump. One year I went on a training course at the athletics ground in Oxford. We were introduced to angular momentum and how it could be exploited to improve the jump. As tallest of the young hopefuls, I was chosen to give a demonstration. The instructor made me lie on my side, arms and legs outstretched, on a small bench turntable. He started to rotate it slowly and asked, ‘If you pull yourself into a crouched position, what will happen?’ I knew, I was studying physics: ‘Angular momentum will be conserved, and the turntable will spin faster.’ ‘Right,’ he said, ‘do it.’ Proudly, I pulled in my arms and legs with vigour. The effect was frightening. The turntable whizzed around so fast that I panicked, tried to get off, and was thrown onto the floor. I escaped with bruises. I am still kicking myself, not about the accident, but because I did not stay on another day. I would have seen Roger Bannister run the first four-minute mile.

Angular momentum is a kind of net spin about a fixed axis. To calculate it for the Earth, you multiply the mass of each piece of matter in the Earth by its perpendicular distance from the rotation axis and the speed of its circular motion about the axis. The Earth’s total angular momentum is the sum of the contributions of all the pieces. Clockwise and anticlockwise motions count oppositely. A jet plane flying round the world in the opposite sense to the daily rotation contributes with the opposite sign.

By Newton’s laws, this net spin cannot change for an isolated system. This universal law applies equally to humans and planets. When I pulled in my arms and legs in Oxford, I abruptly reduced the distance of much of my mass from the rotation axis. This inescapably enforced an equally abrupt increase of my rotational speed – with its unfortunate consequences. The same law explains why the Earth’s rotation axis stays fixed, pointing towards the pole star, and why the length of the day, the rotation period, does not change. The rotation speed could change only if the Earth could expand or contract, but, being rigid, it cannot. (Actually, both the axis and the day do change very slowly due to the external influence of the Sun and Moon.) For rigid bodies like the Earth and a top, the effects of angular momentum are rather obvious. However, its effects are far-reaching.

A globular cluster may contain a million stars. It has no rigidity – all its stars move individually in different directions, though gravity holds the cluster together. Its angular momentum is found by choosing three mutually perpendicular axes, and calculating the net spin around each of them. These correspond exactly to the three degrees of freedom to make twists, mentioned in the previous section. However, the three axes can always be chosen in such a way that the spin about two of them is zero, and all the net spin is thus about a single axis. This axis is a kind of arrow that points in a certain direction in space. It and the net spin remain completely unchanged as time passes. In astronomy, time passes in aeons. Since the stars all move in different directions, the bookkeeping exercise that nature performs is remarkable. A deep principle is at work.

The laws of nature are seldom seen to be operating in a pure form, and are hard to recognize. Air resistance and friction distort the basic laws of mechanics. But the greatest difficulty arises because the laws involve time, and we experience only one instant at a time. If only we could see all the instants of time stretched out before us, we could see the effects of the laws of motion directly, as in some of the diagrams earlier in the book.