The End of Time: The Next Revolution in Physics

We can now think about representing an ionization track. The electron of a hydrogen atom has a characteristic probability distribution of diameter 10⁻⁸ centimetres around its proton. In quantum mechanics it is difficult to be certain about anything, but if we find a proton with no electron near it, this can indicate ionization – the electron has been torn away by the alpha particle. Imagine that we find a state of the chamber in which 1000 protons have no electrons near them; that these 1000 electron-less protons all lie more or less on a line between the decayed radium nucleus and the alpha particle; and that the statistics of the kinks along the line match Born’s predictions for small-angle scattering. Naturally we should say that this is an alpha-particle track. It has all the appearances of recording quantum evolution with intermittent collapse. This state of the chamber, interpreted as an ionization track, is a perfect time capsule. Purely mathematically, it is a single point in a space. But the one point stands for a distribution of a huge number of electrons. As such, it is extraordinarily special – it is like a snapshot of history itself. If it could think, it would say, ‘I am the track of an alpha particle moving in space and time through a cloud chamber.’

If the configuration space has innumerable dimensions, how much vaster is the number of its points. The overwhelming – hugely overwhelming – majority of the distributions they represent correspond to nothing interesting or striking. Sprinkled very thinly through this immense space are the distributions in which 1000 proton nuclei have no electrons near them. There are an incredible number of such distributions, but they are still much more thinly distributed than the stars in the sky. Within this already very thin company with 1000 ionizations are those for which the ionizations are all more or less on the line between the radium nucleus and its escaped alpha particle. But still these are not yet alpha-particle tracks. There is one more sieve – the scattering angles of the kinks must match Born’s statistical distribution.

This piling of improbability upon improbability may seem pedantic, but I do want to bring home the sheer improbability of history. What immense creative power makes it? In addition, I am preparing the next step in the story of geometrical optics. For this, as I suggested earlier, it is helpful to start thinking of historical records as exceptional, specially structured points in configuration space: time capsules. Of course, if you look hard enough you can find not only them but all sorts of other things – pictures of Marilyn Monroe, more or less anything you like – but all such ‘interesting pictures’ are terribly thinly distributed. It is amazing that anything ‘ferrets them out’. But causal quantum mechanics coupled with the incongruous collapse mechanism and a benign low-entropy environment can do the trick.

Before taking the next step, jettisoning collapse, we can add some refinements. In the collapse picture, we can not only mark (with ‘paint’) the configuration point that is the time capsule of the complete track. We can imagine a snapshot taken when only, say, 557 atoms have been ionized. The configuration point captured by it will also be a time capsule, and we can mark it too. If we mark in this manner all the stages – from no ionizations to all ionizations – all the corresponding time capsules will be different points in the configuration space. That is because they tell different stories, some of which only reach, say, the track’s ‘adolescence’ or ‘middle age’. Different configuration points necessarily represent different stories. However, they are joined up more or less continuously in a path, which represents an unfolding process.

If, like the god I imagined come to look at Platonia and its mists, we could ‘see’ the configuration space and the wave function sweeping over it, then in Bell’s ‘crude’ account we should see a patch of wave function jigging its way along a track. The points along it are the complete cloudchamber configurations with successively more ionizations. This configuration track is quite unlike the track that represents a history in Newtonian dynamics. For a single alpha particle, that is a track in three-dimensional space and the points along it, defined by three numbers, cannot possibly record history. In contrast, each of the points traced out in the big configuration space looks like a history of the three-dimensional track up to some point along it. An analogy may help. Doting parents take daily snapshots of their child and stick them day by day into a progress book. The progress book after each successive day is like each successive point along the track in the big configuration space: it is the complete history of the child up to that date. Similarly, a point along the track does not show the alpha particle at an instant of time, but its history up to that time.