Another problem actually killed the proposal. Although wave packets do travel as if they were a particle, they do spread. This was the one effect that Schrödinger failed to grasp initially. He actually did detailed and beautiful calculations for one special case – the two-dimensional harmonic oscillator, or conical pendulum. If a lead bob suspended on a weightless thread is pulled to one side and released, it will swing backwards and forwards like an ordinary pendulum. However, if it is given a sidewise jolt as well it will trace out an ellipse.
Schrödinger was able to show that for the quantum states corresponding to large ellipses it is possible to form wave packets that do not spread at all – the wave packets track round the ellipse for ever. This was a truly lovely piece of work, but misleading. Murphy’s law tripped up Schrödinger. The harmonic oscillator is exceptional and is essentially the only system for which wave packets hold together indefinitely. In all other cases they spread, doing so rapidly for atomic particles. This doomed the idea of explaining particle-like behaviour by the persistence of wave packets, as Heisenberg noted with some satisfaction. (Most of the founding fathers of quantum mechanics defended their own particular directions with great fervour. Schrödinger hated quantum jumps, and found the extreme abstraction of Heisenberg’s matrix mechanics ‘positively repulsive’.)
However, the notion of a wave packet is beautiful and transparent, and has been widely and effectively used. This has tended to make people think that Schrödinger’s original idea was still to a large degree right, and does explain why classical particle-like behaviour (restricted in its accuracy only by the Heisenberg uncertainty relation) is so often observed, especially in macroscopic bodies. There is one great difficulty, though. We can construct wave packets with strongly expressed particle-like properties, but we have to superimpose many different semiclassical solutions in just the right way. There must be a relatively small range of directions and wavelengths, adjustment of the wave amplitudes and, above all, coincidence of the phases of all waves at one point. Nothing in the formalism of quantum mechanics explains how this miraculous pre-established harmony should occur in nature. A single semiclassical solution might well arise spontaneously and naturally. But that will be associated with a whole family of classical trajectories, which exist only as formal constructions – they are at best latent histories. Quantum mechanics generally gives a wave function spread out in a uniform regular manner. Even if by some miracle we could ‘manufacture’ some wave packet, it would inevitably spread. Some further decisive idea is needed to explain how a universe described by quantum mechanics appears so classical and unique.
CHAPTER 20
The Creation of Records
HISTORY AND RECORDS
In Newtonian physics the notion of history is clear cut. It is a path, a unique sequence of states, through a configuration space. This picture is undermined in relativity and severely threatened in quantum mechanics, since the wave function in principle covers the complete configuration space. Almost all interpretations of quantum mechanics seek to recover a notion of history by creating or identifying in some way paths through the configuration space which are then candidates for the unique history that we seem to experience. This is a difficult and delicate exercise, since such paths simply do not belong to the basic quantum concepts. The methods used are quite varied, but they come in four main categories: the basic equations of quantum mechanics are modified (by ad hoc collapse of the wave function in the Copenhagen interpretation and by spontaneous physical collapse in some other interpretations); the equations are not changed but very special solutions are constructed (as Schrödinger attempted); extra elements are added to the quantum formalism (in so-called hidden-variable theories); or the equations and their solutions are accepted in full but it is asserted that the solutions in reality represent many parallel histories (Everett’s many-worlds interpretation). None of these approaches is free of severe problems, some of which I have mentioned.
I suspect that the main difficulties arise because an important aspect of history has been ignored. Even if history is a unique succession of instants, modelled by a path in configuration space, it can be studied only through records, since historians are not present in the past. This aspect of history is not captured at all by a path. All the solutions of a Newtonian system correspond to unique paths, but they very seldom resemble the one history we do experience, in which records of earlier instants are contained in the present instant. This simply does not happen in general in Newtonian physics, which has no inbuilt mechanism to ensure that records are created. It is a story of innumerable histories but virtually no records of them. (1 discussed this at the end of Chapter 1.)
In thinking about history, I believe we should reverse the priorities. Up to now the priority has been to achieve successions of states and to assume that records will somehow form. But nothing in the mechanisms that create successions ensures that records of them will be created. Now a record is a configuration with a special structure. Quantum mechanics, by its very construction, makes statements about configurations: some are more probable than others. This is especially apparent in the quantum mechanics of the stationary states of atoms and molecules. It determines their characteristic structures. In contrast, there is no way that quantum mechanics can be naturally made to make statements about histories. It is just not that kind of theory.
It is also interesting that classical physics makes only one crude distinction. Either a history is possible because it satisfies the relevant laws, or it is impossible because it does not. The possible continuous curves in the configuration space are divided into a tiny fraction that are allowed and the hugely preponderant fraction that are not. It is yes or no. Quantum mechanics is much more refined: all configurations are allowed, but some are more probable than others. By its very nature, quantum mechanics selects special configurations – those that are the most probable. This opens up the possibility that records, which are special configurations by virtue of their structure, are somehow selected by quantum mechanics. This is the possibility I want to explore in this and the following chapter. The aim is to show that quantum mechanics could create a powerful impression of history by direct selection of special configurations that happen to be time capsules and therefore appear to be records of history. There will be a sense in which the history is there, but the time capsule, which appears to be its record, will be the more fundamental concept.
THE CREATION OF RECORDS: FIRST MECHANISM
In the same conference in Oxford in 1980 at which Karel Kuchař spoke about time in quantum gravity, John Bell gave a talk entitled ‘Quantum mechanics for cosmologists’. Among other things, he considered how records arise. This led him to describe a cosmological interpretation of quantum mechanics in which there are records of histories but no actual histories. Perhaps not surprisingly he rejected this as too implausible, but his account of how records arise is most illuminating. I shall reproduce it here in somewhat different terms, and then use it to propose an interpretation that is quite close though not identical to his, since Bell still assumed that the wave function of the universe would evolve with time. If this assumption is removed, as I believe it must be, Bell’s interpretation becomes less implausible.
Bell illustrated how records are created in quantum mechanics by showing how elementary particles make tracks in detection devices. The essential principles had already been published, by Nevill Mott in 1929 and Heisenberg in 1930. As far as I am concerned, their work is more or less the interpretation of quantum mechanics, but surprisingly few people know about it.