The End of Time: The Next Revolution in Physics

Classical physics before general relativity ‘explained’ the world by assuming it to be a four-dimensional history of such relative configurations located in a rigid external framework of absolute space and time. Such a world is supposed to have evolved from certain initial conditions to the state we now observe by means of the laws of classical dynamics, in which the framework of space and time play a significant role. These laws provide all the explanation of which classical physics is in principle capable. In Part 2 I showed how the external framework can be dispensed with. It does not need to be invoked to formulate the laws of dynamics, nor even to visualize how things are located in space and time. Schrödinger’s Kantian appeal to space and time as the ineluctable forms of thought was unnecessary. We can form a clear conception of structured things that stand alone. We have seen how this is also true of general relativity, in which space-time is ‘constructed’ by fitting together 3-spaces in a very refined and sophisticated way.

So, then, what does the Wheeler-DeWitt equation tell us can happen in a rational universe? The answer is ironic. Nothing! The quantum universe just is. It is static. What a denouement. This is a message that needs to be shouted from the rooftops. But how can this seemingly bleak message reverberate around a static universe? How can we bring dead leaves to life? The poet Shelley called on the wild west wind to carry his thoughts over the universe. What can play the role of the wind in static quantum Platonia?

CHAPTER 18

Static Dynamics and Time Capsules

DYNAMICS WITHOUT DYNAMICS

DeWitt already clearly saw the problem posed at the end of the last chapter – the crass contradiction between a static quantum universe and our direct experience of time and motion – and hinted at its solution in 1967. Quantum correlations must do the job. Somehow they must bring the world alive. I shall not go into the details of DeWitt’s arguments, since he saw them only as a first step. However, the key idea of all that follows is contained in his paper. It is that the static probability density obtained by solving the stationary Schrödinger equation for one fixed energy can exhibit the correlations expected in a world that does evolve – classically or quantum mechanically – in time. We can have the appearance of dynamics without any actual dynamics.

It may surprise you, but it was about fifteen years before physicists, and then only a few, started to take this idea seriously. The truth is that most scientists tend to work on concrete problems within well-established programmes: few can afford the luxury of trying to create a new way of looking at the universe. A particular problem in everything to do with quantum gravity is that direct experimental testing is at present quite impossible because the scales at which observable effects are expected are so small.

Something like a regular research programme to recover the appearance of time from a timeless world probably began with an influential paper by Don Page (a frequent collaborator of Stephen Hawking) and William Wootters in 1983. This was followed by several papers that concentrated on an obvious problem. In ordinary laboratory physics, the fundamental equation used to describe quantum phenomena is the time-dependent Schrödinger equation. It undoubtedly holds to an extraordinarily good accuracy for all ordinary physics: we could not even begin to understand, for example, the radiation of atoms without this equation. But if the universe as a whole is described by a stationary Schrödinger equation and time does not exist at all, how does a Schrödinger equation with time arise? This question seems to have been first addressed by the Russians V. Lapchinskii and V. Rubakov, but a paper in 1985 by the American Tom Banks did more to catch the imagination of physicists. This was followed in 1986 by a paper treating the same problem by Stephen Hawking and his student Jonathan Halliwell. Further papers on the subject appeared in the following years. The whole associated research programme has become known as the semiclassical approach, for a reason I shall explain later. The basic idea is easy to grasp.