Julian Barbour - The End of Time - The Next Revolution in Physics

The scheme is realist because the structure of an external, objectively existing real thing is being proposed as the explanation of the structure experienced within a perceptual instant. What we experience in subjective instants reflects, through psychophysical parallelism, physical structure in external things: configurations of the universe. Their actual nature is a matter for ongoing research. The notion has been illustrated by configurations of mass points in Euclidean space, by island-type distributions of fields of Faraday-Maxwell type in Euclidean space, and by closed Riemannian 3-geometries (which may also have fields defined on them). It is at the last level that I believe satisfactory explanations can in principle be obtained for many of the known facts of physics and cosmology. However, some further development, very possibly associated with the notions of superstrings and supersymmetry, may well be needed to explain the actual cocktail of forces and particles that pervades the universe.

What is important about relative configurations is that they are intrinsically defined – they are self-contained things – and that the rule that defines one thing simultaneously defines many. Moreover, they can all be arranged systematically in a relative configuration space: Platonia, as I have called it.

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?

(p. 255) On the subject of the aims and methods of science, I strongly recommend David Deutsch’s The Fabric of Reality .

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.

Imagine yourself on a wide sandy beach on which the receding tide has left a static pattern of waves. As you are a free agent, nothing can stop you from laying out a rectangular grid on the beach and calling the direction along one axis ‘space’ and that along the perpendicular axis ‘time’. For each value of the ‘time coordinate’, you can examine the wave pattern along the one-dimensional line of ‘space’ at that ‘time’. When you move to the neighbouring line on the beach corresponding to ‘space’ at a slightly later ‘time’, you will find that the wave pattern has changed. Simply by laying out your grid and calling one direction ‘space’ and the other ‘time’, you have transformed – in your mind’s eye – a two-dimensional static picture into wave dynamics in one dimension. This can be done with wave patterns in spaces of any dimension N . One direction can always be called ‘time’, and this automatically creates ‘evolution’ in the remaining N – 1 dimensions.

Of course, if the original wave pattern is ‘choppy’ and has not been created by some rule, the choice of the ‘time’ direction will be arbitrary. Any choice will create the impression of evolution in the remaining N – 1 dimensions, but it will not obey any definite and simple law. In the semiclassical approach, there are two decisive differences from the arbitrary situation. First, the static wave pattern is the solution of a definite equation. Second, it is a somewhat special solution – called a semiclassical solution – in that it exhibits a more or less regular wave pattern. This assumption will be considered later. However, if the wave pattern satisfies the assumption, it automatically selects a direction that it is natural to call time . With respect to this direction, a genuine appearance of dynamics arises in a static situation (Box 14). The result is this. Two static wave patterns (in a space of arbitrarily many dimensions) can, under the appropriate conditions, be interpreted as an evolution in time of the kind expected in accordance with the time-dependent Schrödinger equation. The appearance of time and evolution can arise from timelessness.