The End of Time: The Next Revolution in Physics

If the wave function of the universe is static, quantum cosmology reduces to the question of how its values are distributed in Platonia. For the moment, I shall simply give you my guess; arguments for it come later. My guess is a special distribution closely similar to the cloud-chamber one described by Bell. In most of Platonia the wave function has extremely small values – the blue mist has negligible intensity. However, in a few special regions, distributed over a large area, the blue mist’s intensity is, relatively, hugely higher. These regions correspond to some arrangement of the swarms, determined by the horizontal position, and to the detailed positions within them, determined by the vertical positions. It is in the probabilities for these detailed positions that the blue mist is extraordinarily selective. The probabilities for the horizontal positions are relatively uniform over quite large regions. By themselves, they represent a dull state of affairs. The situation is transformed by the configurations that specify the fine details within the swarms. At the very rare configurations where the blue mist shines brightly, the fine details look like records of a history of the swarms as complete units. They suggest that the swarms have moved in a classical history from some past up to a present instant, in the position they now occupy.

This is illustrated in Figure 52, in which the points X and Y in Platonia have large-scale positions B and D. The fine details at X and Y seem to represent records of how the swarms have moved from earlier configurations A and C along curves AB and CD in the large-scale (horizontal) configuration space. They seem to be records of these large-scale histories. The blue mist has a high intensity not only at X and Y but also, for example, at P and Q, at which points the fine details suggest they represent records up to the intermediate stages E and F in the histories AB and CD.

By no means all details need represent history. Footprints in the sand on a wide beach record the movements of people who have walked on it, but over much of the beach there need be no apparent records. Think again of the number of atoms in a pea. A tiny fraction of them can easily record the pea’s history up to its current present. The huge numbers we confront in physics explain why we may have wrong ideas of what history actually is. We may have jumped to a conclusion too quickly.

In the Newtonian picture, in which history is a curve in configuration space, it is extremely hard to understand how records arise. Even if a single curve is realized, any point on it could have any number of histories passing through it. How can one instantaneous configuration of particles suggest the motions that they have? However, if we keep an open mind about the laws that determine things, a fraction of a pea’s atoms may well seem to record a history of its large-scale features. This does not mean that all its atoms had a unique history. Without change in the pea’s large-scale structure, the same large-scale history could be coded in innumerable different ways by only a tiny fraction of its atoms. In the imagery of Figure 52, there will be a whole cloud of points X in the configuration space that correspond to the same large-scale configuration and to the same history up to it. The different points in the cloud simply code the same history in different ways. What is more, for each point along the large-scale history AB there will be a corresponding cloud of points that record the same history up to that point in different ways. There will be a ‘tube’ of such points in the configuration space. No continuous ‘thread’ joins up these points in the tube into Newtonian histories. The points are more like sand grains that fill a glass tube. Each grain tells its story independently of its neighbours. In any section of the tube, the grains all tell essentially the same story but in different ways, though some may tell it with small variations.

Figure 52 The division of Platonia. The horizontal dimensions represent the large-scale configuration space, and the single vertical dimension represents the small-scale space. The ‘horizontal curves’ (AEB and CFD) represent histories of the large-scale features. Each point like A represents, say, the overall position and size of a swarm of bees. In contrast, each of the points Q, P, X, V on the vertical lines represents the huge number of small-scale details.

I think this is the way to think about history in quantum stasis. Could we but see the picture – all Platonia with its misty crannies – we should see it as it is: the lawful definite world for which Einstein, like so many physicists, longed. But it is a timeless book full of different stories that tell of time. Quantum mechanics can create the appearance of multiple histories. However, will it in quantum cosmology? Its conditions are not quite Mott and Heisenberg’s conditions.

CHAPTER 22