The End of Time: The Next Revolution in Physics

The decisive element in this picture is the seed – or rather, seeds – from which these stories can all grow by the penetration of the wave function into the nooks and crannies in Platonia where the configurations are coherent stories. The wave function can be present there only if it is entangled with the latent histories of a semiclassical wave function established at least somewhere in Platonia. These are the Hamiltonian ‘light rays’ from which everything must ‘grow’. Where are they likely to run, and what will their properties be? This is where the shape of Platonia must become decisive. The points in Platonia near Alpha containing Wagner and kingfishers are simply not visited by the blue mist, since Platonia as a whole lays out the latent histories in patterns that do not get entangled with such points.

Modern classical cosmology gives some hints as to where the latent histories might run. The simplest Big Bang cosmological solutions of Einstein’s equations, first discovered by the Russian mathematician Alexander Friedmann in the early 1920s, have the maximum degree of symmetry and therefore ascend the central line in Figure 53. This is the history distinguished in cosmology by the universe’s contents, despite the relativity of simultaneity. The universe explodes out of the singular state of zero volume, expands to a maximum volume and then recon-tracts to zero volume, gravity having halted and then reversed the initial, very rapid expansion. As shown schematically in Figure 55 (see p. 321), the universe ends in a Big Crunch. In other cosmological models, which normally require the universe to be spatially infinite, the expansion is so violent that the expansion is never halted.

In reality the universe is not completely symmetric, and the path out from Alpha is not exactly retraced, as shown in Figure 55, in which the rays emanating from Alpha are a measure of the relative ‘irregularity’ of the spatial configurations of the universe. Up the vertical ray, the universe is perfectly smooth, but on the rays that fan out at progressively larger angles the relative irregularity increases. The diagram shows one classical history which, at one end, starts in an almost perfectly smooth state but then becomes more and more irregular, due to the formation of galaxies, stars, black holes, planets and even human beings. This history reaches maximum expansion, turns round and recontracts, becoming more irregular all the time. It returns to the state of very small volume at a different point of Platonia, since although the volumes are small in both cases there are many additional variables that describe the structure of the state. Thus Alpha, the ‘end of Platonia’, is not a true point but actually a huge space of different possibilities, all with vanishingly small volumes.

Regarded purely as a path through Platonia, we cannot say that one end of this history is its beginning and the other is its end. I have lapsed into conventional talk. Such a priori notions do not belong in a timeless theory. Nevertheless, the two ends of the path are very different in nature, and it is tempting to say that, if our own existence is associated with such a path, its smooth end is what we would call the past and the irregular end the future. This would be very much in the tradition, initiated by Boltzmann, of suggesting that our sense of the forward flow of time, its arrow, is grounded solely in the increase in disorder that virtually all classical trajectories must exhibit if they pass through an exceptionally ordered region. Normally there are trajectories that both enter and leave such regions, and the entropic explanation of the arrow of time suggests that time will seem to flow forward in both directions out of these regions. In the present example, the exceptional region is on the frontier of Platonia, so the path truly ends there. This is beginning to look quite promising as the basis for a total explanation of time, but several conditions must be met. Before we address them, it is worth saying a little about gravity and thermodynamics.