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

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.

If experiments as in Bell’s first account are repeated many times, a similar but different track will be photographed each time. Because quantum mechanics deals in probabilities, some tracks may well be more probable than others. Now imagine recording an alpha-particle track by ‘marking’ the corresponding configuration point with ‘paint’. All configuration points that have been ‘illuminated’ in any of the experimental runs will be touched with paint, some many times. Because the instant of radioactive decay cannot be predicted, photographs taken at random will catch tracks of all ‘ages’ – birth, adolescence, middle age, old age. Eventually, many different points will have been touched by paint. A rich structure will have been highlighted. Perhaps the best way to picture this is as innumerable filaments, all emanating from the small region in the configuration space that represents the alpha particle trapped in the radium nucleus while all the cloud-chamber atoms are in their ground states.

It would be quite wrong to suppose that these filaments are so numerous that they fill the configuration space. That comes from confusion with ordinary three-dimensional space. It is always dangerous to take analogies too literally, but if we are going to try to use images, it is better to think of the structure that is formed in the configuration space by the points that have been ‘touched with paint’ as being more like strands of a spider’s web spun out in the reaches of interstellar space with huge gaps between them. Such a structure is then a record of innumerable experiments interpreted in the first ‘crude’ way.

One more comment. So far, we have considered only single tracks. But in modern experiments a single particle colliding with a detector particle can create many secondary particles. These also make tracks simultaneously in the detector. A single quantum event gives rise to many tracks. If a magnetic field is applied the tracks are curved by different amounts depending on the particle masses, charges and energies. Beautiful patterns, representing quite complicated histories, are created (Figure 51). This multitrack process in ordinary space is still represented by one track in configuration space. History, no matter how complicated, is always represented by a single configuration path; records of that history, which may be very detailed and more or less pictorial (actual snapshots), can readily be represented by a single configuration point. A library containing all the histories of the world ever written is just one point in the appropriate configuration space.

We now come to the more sophisticated account of alpha-particle interaction with a cloud chamber. The entire process is treated quantum mechanically – as wave-function evolution in a space of around 10 27dimensions. Initially, before the alpha particle escapes, the wave function (of all the electrons and the alpha particle) is restricted to a rather small configuration region. In the crude collapse picture, alpha-particle escape and track formation is represented as a ‘finger’ of wave function that suddenly emerges from it and rushes through the configuration space like a rocket shooting through the sky.

Figure 51.Multiple tracks of elementary particles created by a single quantum event. The swirls and curved tracks arise from the effect of a magnetic field on the charges of the particles created.

In the new picture, with everything treated quantum mechanically and no collapse, an immense number of wave-function ‘fingers’ emerge almost at once and race in a multitude of directions across the configuration space. Each follows more or less one of the tracks of the scenario with collapse. All the tracks are traced out simultaneously. It is like one of those spectacular fireworks that explodes and shoots out a blazing shower in all directions. This is what we should observe if we could see the wave function bursting out from its original confines into the great open spaces of Platonia.

It is not easy to explain why it behaves like this, but let me try. The most important thing is that a configuration space is not some blank open space like Newton’s absolute space, but a kind of landscape with a rich topography. Think of the wave function pouring forth like floodwater sweeping over a rocky terrain, whose features deflect the water. It will help if you look again at Triangle Land (Figures 3 and 4). It is bounded by sheets and ribs, and is the configuration space for just three particles. The configuration space for 10 27particles is immensely more complicated. Things like the ribs and sheets that appear as boundaries of Triangle Land occur as internal topography in Platonia, which is traversed by all kinds of structures. The rules that govern the evolution of the wave function force it to respond to this rich topography. The wave-function filaments are directed by salient features in the landscape.

Now that we have some idea of how the ‘firework explodes’, we can think about its interpretation. The problem is that we never see configuration space. That is a ‘God’s-eye’ view denied to our senses – but fortunately not to our imaginations. We also never see a solitary alpha particle making many tracks at once: all we ever see is one track. How is this accounted for in the second scenario? By the same device as before – by collapse. In the first scenario, the alpha particle was in many different places in its configuration space simultaneously before we forced it to show itself in one region. This was done by making it interact with an atom. This, most mysteriously, triggered collapse, which was repeated again and again.

In the second scenario, the complete system is, after a time sufficient for the ionization of 1000 atoms, potentially present at many different places in its huge configuration space. The wave function is spread out over a very large area, though concentrated within it, in tiny regions. All the points within any of these regions is like a snapshot of an ionization track, all differing very slightly (and hence represented by different points within a small region). There is an exact parallel between the alpha particle in the first scenario being at many different places before the first collapse-inducing ionization and the state now envisaged for the complete system of cloud chamber and alpha particle. It too is in many different ‘places’ at once.