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

We can now collapse this much larger system by making a ‘measurement’ on it to see where it is. This is often done simply by taking a photograph of the chamber. It catches the chamber in just one of its many possible ‘places’. And what do we find? A chamber configuration showing just one ionization track, corresponding to one of the points within one of the tiny regions on which the wave-function mist is concentrated. We have collapsed the wave function, but this time onto a complete track, not onto one position of one particle.

If such experiments are repeated many times, the tracks obtained are found to be essentially the same as the tracks in the first scenario. There are in principle small differences, which come about because the evolution is not quite the same in the two cases – in the latter case the tracks can interfere to some extent, but in general the final results are more or less the same despite the very different theoretical descriptions.

The reason for this is that seeds of the many different tracks – different histories – are already contained in the initial wave function. A concentrated wave function necessarily spreads, and if this happens in a large enough configuration space under low-entropy conditions it can excite many different configurations that embody records of many different histories. There is a snowball effect. We start with many small snowballs, the different possibilities for the alpha particle at the beginning of the process. Each possibility then becomes associated – entangled – with a different track. This is rather like many different snowballs picking up snow. Subject always to a pervasive quantum uncertainty, a fuzziness at the edges, these are Everett’s many worlds. The distinctness of these different worlds, the different histories, is determined by the extent to which part of the system (the alpha particle in this case) is in the semiclassical (geometrical-optics) regime.

It is the near perfection of the initial semiclassical state of the alpha particle that creates such sharply defined histories and ensures that two such different scenarios give more or less the same results. This is ultimately the reason why the notorious Heisenberg cut – the position at which we suppose the quantum world to end and the external, non-quantum world of classical measuring instruments to begin – can be shifted in such a bewildering manner. As Bell remarks, for practical purposes it does not matter much where we place the cut to determine where collapse occurs, since the end results are much the same. In either case, the appearance of history is created by interaction between the semiclassical part and the remaining, fully quantum system. The resulting correlation forces the quantum system into a very special state.

It is really almost miraculous how the classical histories, latent as very abstract entities within a semiclassical state of the alpha particle when it is considered in isolation, force the wave function of the remainder of the system (the cloud chamber) to seek out with extraordinary precision tiny regions of its vast configuration space. When these regions – or, rather, the points within them – are examined, they turn out to represent configurations that are snapshots of tracks. They are records of histories.

So this is the next twist in the saga. First Hamilton found families of classical, particle-like histories as ‘light rays’ in a regular (semiclassical) wave field. Then Schrödinger tried to mimic particle tracks by superposing many slightly different semiclassical solutions to create just one wave packet – the model of a single particle. It was rather hard and contrived work for a meagre – but still very beautiful – result. However, it immediately slipped through his fingers. But then Heisenberg and Mott showed that quantum mechanics could work far more effectively as the creator of history than Schrödinger had ever dreamed. Now one single semiclassical solution generates (before the final collapse) many histories. Instead of Schrödinger’s contrived

Many semiclassical solutions → One history

we have natural organic growth:

One semiclassical solution → Many records of histories

The Creation of Records: First Mechanism (1)(p. 284) Bell’s paper can be found in his collected publications Speakable and Unspeakable in Quantum Mechanics .

(2)(p. 284) Mott’s paper is reproduced in Wheeler and Zurek (1983). Heisenberg’s treatment is in his Physical Principles of Quantum Theory . I am very grateful to Jim Hartle, who first drew my attention to Mott’s paper. At that time he was considering seriously an interpretation of quantum cosmology that is quite close to my own present position. He has since backed away somewhat, and now advocates an interpretation of quantum mechanics in which history is the fundamental concept. I should also like to express my thanks here to Dieter Zeh. Zeh, who was in this business long before me, also made me realize the importance of Mott’s work, and, crucially, alerted me to Bell’s paper. There are not many physicists who take the challenge of timelessness utterly seriously, but Dieter Zeh and his student Claus Kiefer, from both of whom I have gained and learned much, are two of them.

The story goes on. We have put only the cloud chamber into the quantum mill – can we put the universe, ourselves included, in too? That will require us to contemplate the ultimate configuration space, the universe’s.

You can surely see where this is leading. Now the snowballs can grow to include us and our conscious minds, each in different incarnations. They must be different, because they see different tracks; that makes them different. These similar incarnations seeing different things necessarily belong to different points in the universal configuration space. The pyrotechnics of wave-function explosion out of a small region of Platonia – the decay of one radioactive nucleus – has sprinkled fiery droplets of wave function at precise locations all over the landscape. (What an awful mixing of metaphors – snowballs and sparks! But perhaps they may be allowed to survive editing. The snowballs are in the configuration space, the sparks in the wave function. This is a dualistic picture.)

And now to the great Everettian difference: collapse is no longer necessary. Nothing collapses at all. What we took to be collapse is more like waking up in the morning and finding that the sun is shining. But it could have been cloudy, or cloudy and raining, or clear and frosty, or blowing a howling gale, or even literally raining cats and dogs. When we lay down to sleep in bed – when we set up the alpha-particle experiment – we knew not what we should wake to. What we take to be wave-function collapse is merely finding that this ineffable self-sentient something that we call ourselves is in one point of the configuration space rather than another. When we observe the outcome of an experiment, we are not watching things unfold in three-dimensional space. Something quite different is happening. We are finding ourselves to be at one place in the universal configuration space rather than another. All observation, which is simultaneously the experiencing of one instant of time, is ultimately a (partial) locating of ourselves in Platonia. Each of our instants is a self-sentient part of a Platonic form.

The coherence of this picture hangs on the ability of the universal wave function to seek out time capsules in Platonia that tell a story of organic growth. All stories are in Platonia, some bizarre beyond the dreams of Hieronymus Bosch or modern surrealists. The history that we experience may have its horrors, but it is extraordinarily coherent and self-consistent. The first task of science is to save the appearances. So, first and foremost, we need to find a rational explanation for the habitual miraculous experiencing of time capsules, these freighters of history. This is where the probability density of the wave function, its shimmering blue mist, plays such a crucial role. Because apparent records of all histories – and a mind-numbing multitude of non-histories – are present in Platonia, we shall not have an explanation of the appearances worthy of the name unless the blue mist shines brightly over time capsules of the kind we know so well from direct experience. And it should not shine brightly anywhere else. We shall then have a theory that does truly save the appearances. Bell’s analysis hints that universal quantum cosmology might be that theory.