The End of Time: The Next Revolution in Physics

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.

It was stimulated by the Russian physicist George Gamow’s theory of radioactive decay, put forward in 1928, in which alpha particles escape from radium nuclei by a process called tunnelling. The only detail we need to know is that Gamow represented an escaping alpha particle by means of an expanding, spherical wave function surrounding a radium nucleus. In accordance with the standard quantum interpretation, there is then a uniform density of the probability for finding the alpha particle all round the nucleus. In my pictorial analogy, blue mist spreads uniformly from the nucleus.

In those days, alpha particles were observed in devices called Wilson cloud chambers through their interaction with atoms, which they ionize by dislodging electrons, leaving the previously neutral atoms positively charged. The alpha particles invariably ionize atoms that lie more or less along a straight line emanating from the radioactive source. The excess positive charge of the ionized atoms stimulates vapour condensation around them, making the tracks visible. If we take Gamow’s theory literally, there is something deeply mysterious about these tracks. If there really is a blue probability mist spreading out spherically all round the radium atom, why are atoms not ionized at random all over the chamber, wherever the blue mist permeates? How come they are ionized only along one line?

Standard quantum mechanics gives two answers, one much cruder than the other. In the crude answer (which is nevertheless very interesting, so I shall take a few pages to discuss it), only the alpha particle is treated in quantum-mechanical terms: the atoms of the cloud chamber are treated as classical external measuring instruments. They are used to ‘measure the position’ of the alpha particle, this being done by the ionization of an atom at some position. In accordance with the standard rules, any position measurement yields a unique position, after which the wave function will be concentrated at that position. The rest of the wave function will be instantaneously destroyed.

Now, atoms actually have a finite diameter, of about 10^–8 centimetres. So the ionization of an atom is not a perfect position measurement, and this has important consequences for the alpha-particle tracks. It is helpful to think in terms of the blue mist. Before the measuring ionization happens, the blue mist is expanding outwards uniformly in all directions. When the first ionization occurs, it is as if a spherical shell has suddenly been placed round the atom. At one point on the shell there is a small hole through which the wave function can pass. This is the point at which the ionized atom is situated. It is only here that the wave function is not totally destroyed and can continue streaming on outwards. In fact, it does so in the form of a jet, which can be very narrow and accurately directed, especially if the alpha particle has a high energy.

At this point it is worth saying something about the diffraction of light. If monochromatic light (light of one wavelength) encounters an opaque screen with an opening, the result depends on its size. If the opening is large compared with the wavelength of the light, the screen cuts off all the light except at the opening and a more or less perfect ‘pencil’ of light – a beam – passes through. The width of the luminous pencil is equal to the width of the opening. However, if the opening is made smaller, diffraction comes into play and the beam of light spreads out, becoming very diffuse for a tiny opening. Diffraction effects are more pronounced for red light, with its longer wavelength, than violet light. Like light, alpha particles have an associated wavelength, which is very short for the ones produced in radioactive decay. Although ionization of the atom creates effectively a very small ‘opening’, the ‘jet of wave function’ that survives the wave-function collapse is narrow and concentrated in a cone with a very small opening angle (much less than a degree). The wave-function jet continues through the cloud chamber like a searchlight beam.

To simplify things, imagine that the cloud-chamber atoms are concentrated on uniformly spaced, spherical concentric shells surrounding the radium atom. The first ionization (quantum measurement and collapse) happens when the alpha particle’s spherical waves reach the first shell. On the second shell, the alpha particle can ionize atoms only where its wave function has non-vanishing value. The atoms that can be ionized are located in the small spot that is ‘lit up’ by the ‘beam’ and hence lie rather accurately on the line joining the radium atom to the ‘opening’ in the first shell. The spot still contains many hundreds or thousands of atoms, any one of which can now be ionized. A second position ‘measurement’ of the alpha particle is about to be made.

The quantum measurement laws now tell us that one and only one of the atoms will be ionized. It is selected by pure chance – it can be anywhere in the spot. Once again, the entire wave function that ‘bathes’ the other atoms is instantly destroyed, and a new narrow beam continues outward from the second ionized atom. The same process of ionization, collapse and ‘jet formation’ is repeated at each successive shell. For an alpha particle with sufficient energy, this may happen hundreds or even thousands of times. A track is formed. It has some important features.

First, although it is nearly straight, there are small deflections at nearly all ionizations. It should not be supposed that the deflection occurs where the kink in the track suggests it did. This subtlety is illustrated in Figure 50. At each ionization and collapse a new cone of the wave function is created. It is not unlil the next ionization occurs that any actual deflection angle is selected. Until then, the complete cone of deflection angles is potentially present. As Heisenberg put it in a famous remark, the track is created solely by the fact that we observe the particle.

Second, quantum mechanics makes no predictions about the individual deflection angles. It merely predicts their statistical distribution, according to a law found by Max Born a few months after Schrödinger had created wave mechanics. Its form is determined by the structure of the atoms on which the scattering (deflection) of the alpha particle occurs. It is normally verified by making experiments with many different alpha particles, the statistical distribution being built up by the repetition of many experiments over time. However, in principle it is possible to test the statistical predictions on a single track, especially if it contains thousands of ionizations.

Figure 50 The creation of an alpha-particle track by successive ionizations. After each ionization a wave-function beam spreads out, but it is not until the next ionization occurs that the ‘kink’ is created.

Third, at each ionization the alpha particle loses a fraction of its energy, typically about one part in ten thousand. Since the energy is related to the particle’s wavelength, it becomes progressively longer along the track. Just as diffraction effects are more pronounced for red than for violet light, this means that the deflection angles get progressively larger along the track. The nature of the track changes along its length – it starts to show quite large zigzags.

Bell comments on this first account of track formation that it ‘may seem very crude. Yet in an important sense it is an accurate model of all applications of quantum mechanics.’ Before we consider the second – infinitely more illuminating – account, we need to draw some conclusions and start to develop new ways of thinking about things, above all history.

THE PREREQUISITES OF HISTORY

The central question of this fifth part of the book is this: whence history?

What light does Bell’s first account cast on this question? What are the essential elements that go into the creation of history? Bell’s analysis promises to give us real answers to these questions, since an alpha-particle track can truly be seen as prototypical history. All the elements are there – a unique succession of events, a coherent story and qualitative change as it progresses. It even models birth – when the particle escapes from the radium atom – and demise – when it finally comes to rest. It literally staggers to its death. The laws that govern the unfolding of history are beautifully transparent. They combine, in an intriguing way, causal development – the forward thrust of the track – with unpredictable twists and turns governed only by probability. History is created by what looks like a curious mixture of classical and quantum mechanics – the continuous track and the twists and turns, respectively.

Three distinct factors together create history in this first account. First, the alpha particle emerges from the radium atom in a state that matches geometrical optics. Its wave function propagates outward in perfectly spherical waves of an extremely regular shape and with a very high frequency and short wavelength. This is a perfect example of a semiclassical solution. Hamilton’s ‘light rays’ are the tracks that run radially outward from the radium atom, always perpendicular to the wave-function crests. Each of these tracks is a good simplified model of the one solitary track that eventually emerges.

I mentioned the ongoing saga of geometrical optics. Schrödinger attempted to create history by superimposing many slightly different semiclassical solutions in a wave packet that mimicked particle motion. We can now see that this attempt was doomed to failure, mainly because it attempted to create particle tracks using the quantum-mechanical properties of just one particle in isolation. The interaction of the particle with the environment played no role in Schrödinger’s attempt, but is crucial in the account just given. We cannot begin to think of a track being formed without the atoms waiting to be ionized. Geometrical optics still plays a vital role because the very special semiclassical state ensures that sharply defined beams are created by the process of ionization and collapse.

We no longer need many semiclassical solutions: one semiclassical solution is now sufficient to create one history. Nevertheless, at least one semiclassical solution remains – and will remain – the prerequisite for history. The core mathematical fact discovered by Hamilton keeps reappearing and being used in different ways. I feel sure that this is the true deep origin of history – we have already seen alpha-particle tracks form before our eyes. Watch a little longer, and even Henry VIII and his six wives will appear.

The second element in Bell’s account is collapse: crude, but effective. Little more needs to be said except that it is hard to believe that nature can behave so oddly. However, Bell’s down-to-earth account does show up the artificiality of the quantum measurement rules. These are formulated for individual observables, and insist that measurement invariably results in the finding of a single eigenvalue of a chosen observable. But in the case of the alpha particle ionizing an atom, no pure measurement results – there is simultaneous measurement of both position and momentum (both with imperfect accuracy, so that the uncertainty relation is not violated).

The third element in the creation of history is low entropy: the initial state of the system is highly special. The alpha particle, which could be anywhere, is inside the radioactive nucleus; the countless billions of cloud-chamber atoms, which could be in innumerable different excited states, are all in their ground states. The only reason we are not amazed by such order is our familiarity with the special. What we have known from childhood ceases to surprise us. But even the experiencing of coherent thoughts is most improbable. Among all possible worlds, the dull, disordered, incoherent states are overwhelmingly preponderant, while the ordered states form a miniscule fraction. But such states, sheer implausibility, must be presupposed if history is to be made manifest – at least it is in the normal view of things.

The initial ordered state creates history and a stable canvas on which it can be painted. The special position of the alpha particle gives rise to its semiclassical state. The thousand or so atoms it ionizes stand out as a vivid track on the un-ionized billions. Photographed before dispersal, the track becomes a record of history. If a large proportion of the atoms were already ionized, such a track could hardly form, let alone stand out. We might claim that history had unfolded, but there would be no evidence of it.

Records are all we have. We have seen one account of their creation. Except for quantum collapse, it does not seem outlandish. But Bell gives a second, fully quantum account in which the monstrously multidimensional configuration space of the cloud chamber is vital. This story of history is amazing. The next section prepares for it.

THE IMPROBABILITY OF HISTORY

The cloud chamber is treated schematically as a collection of hydrogen atoms, each consisting of a nucleus – a single proton – and an electron. We ignore the fact (here not an issue) that all protons are identical, and so are all electrons. It is also reasonable to assume that the protons are at fixed points, and to treat only the electrons and the alpha particle quantum mechanically. The coordinates of each electron can be three mutually perpendicular distances from its proton. A real cloud chamber may contain 10²⁷ atoms. It is daunting to contemplate a space with 3 × 10²⁷ (+ 3 for the alpha particle) dimensions, but we must do our best if we are to get a true feeling for what is going on in quantum mechanics.

The really important thing here is that each configuration point represents one totality of all electron positions in the chamber. If we keep all the electrons fixed except one, which we move, it explores just three of the dimensions. In a much more modest way, there is an analogy here with our existence on the Earth: we live in three dimensions, but are normally restricted to the Earth’s two-dimensional surface and do not normally move far in the third dimension. For the electron, the unexplored dimensions are not one but 3 × 10²⁷.

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.

THE CREATION OF RECORDS: SECOND MECHANISM

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 10²⁷ dimensions. 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 10²⁷ particles 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.

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