The End of Time: The Next Revolution in Physics

CHAPTER 21

The Many-Instants Interpretation

MANY HISTORIES IN ONE UNIVERSE

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.

It is time to take stock once more. First, we muster the interpretations of quantum mechanics. How do they look in the light of Bell’s analysis? What appearances do they save and how well do they do it? There are two minimum requirements of an interpretation – it must explain why we see just one world (Einstein’s Moon problem) and it must explain why we think it has a history. The latter is the harder task. However, it may be important not to ask for too much. To save the appearances, we do not have to create a unique history: we need only explain why there seems to be a unique history. That was Everett’s insight. If we can stand back from our parochial prejudices, a theory which can achieve that is already little short of miraculous.

Except for many-worlds variants, all the interpretations strive for the severe criterion of only one history. They were created for that and all achieve it by brute force. History is created by repeated strangling of the wave function (Copenhagen and physical collapse) or by adding incongruous extras: the so-called hidden variables. The German doppelt gemoppelt means messing things up by doing them twice over. In their anxiety to recover a unique history, the proponents of these interpretations crudely impose one history on a theory that can already create many histories which are autonomous – and hence each unique in our experience – by a beautiful natural mechanism. Hamilton’s discovery makes it inescapable that histories are latent in the quantum formalism. It is just a matter of coaxing them out into the open.

BELL’S ‘MANY-WORLDS’ INTERPRETATION

From his discussion of alpha-particle tracks, Bell turned to a remarkable cosmological interpretation of quantum mechanics. It makes essential use of the notion of time capsules and is therefore very similar to the interpretation I shall present in the final chapter. Bell saw it as a way of retaining Everett’s idea that the wave function never collapses without proliferating worlds.

Bell claimed that the really novel element in Everett’s theory had not been identified. This was ‘a repudiation of the concept of the “past”, which could be considered in the same liberating tradition as Einstein’s repudiation of absolute simultaneity’. Obviously, something exciting is in prospect, and Bell does not disappoint. He looked for the quantum property that enabled Everett to make his many-worlds idea plausible, and pointed out that the accumulation of mutually consistent records is a vital part of it. This recognition had led Bell to his analysis of the formation of alpha-particle tracks, which have the obvious interpretation that they are records of alpha-particle motion. He showed that ‘record formation’ is a characteristic quantum property. At least under cloud-chamber conditions, the wave function concentrates itself at configuration points that can be called records. Although Bell did not use my term, such points are manifestly time capsules. He noted that Everett’s interpretation could not even be formulated were it not for the wave function’s propensity to find them.

He then attacked head-on the conventional notion of history inherited from classical physics as a continuous path through configuration space. This might make sense if, god-like, we could see all time and the configuration space with history highlighted as a path in it by a ‘thread’ or ‘paint’. But our only access to the past is through records. As Bell says, ‘We have no access to the past. We have only our “memories” and “records”. But these memories and records are in fact present phenomena.’ Our only evidence for the past is through present records. If we have them, the actual existence of the past is immaterial. It will make no difference to what we know. Hence ‘there is no need whatever to link successive configurations of the world into a continuous trajectory’.

His ‘Everettian’ interpretation is this: time exists, and the universal wave function ψ evolves in it without ever collapsing. Because ψ has the propensity to seek out time capsules, it will generally be concentrated on them. Real events are actualized as follows. At each instant of time, ψ associates a definite probability (the intensity of the blue mist in my analogy) with each configuration. At any instant, just one event is actualized at random in accordance with its relative probability. The higher the probability, the greater the chance of actualization. Since time capsules have the highest probabilities, they will generally be selected.

Sentient beings within them will possess memories and records that convince them they are the product of history. But this will be an illusion. In reality, the points realized at successive instants of time are chosen randomly and jump around in a wildly unpredictable manner in the configuration space. The sentient beings within the actualized points have memories of quite different histories. It is all very bizarre, though within each randomly selected time capsule the memories and records tell a most consistent story. Bell rejected his ‘many-worlds’ interpretation as too absurd:

Everett’s replacement of the past by memories is a radical solipsism – extending to the temporal dimension the replacement of everything outside my head by my impressions, of ordinary solipsism or positivism. Solipsism cannot be refuted. But if such a theory were taken seriously it would hardly be possible to take anything else seriously. So much for the social implications. It is always interesting to find that solipsists and positivists, when they have children, have life insurance.

This is all very entertaining – and I too have children and life insurance – but these are just the kind of ad hominem quips that were tossed at Copernicus and Galileo. I do believe that Bell came close to a viable cosmological interpretation of quantum mechanics, and should have kept faith with his title (‘Quantum mechanics for cosmologists’). But he left the cosmologists with nothing. Later he gave warm support to one of the theories in which wave-function collapse is a real physical process. In it, the propensity of the quantum-mechanical wave function to find time capsules plays no role. History is created by a succession of actually realized states. It is there with or without any record of it.

From the way Bell wrote in 1980, either he was unaware of the Wheeler-DeWitt equation and the possibility that the universal wave function is static, or he dismissed this without mention. It would be interesting to know how he would have reacted to the idea – he seems to have had a somewhat Newtonian notion of time. Sadly, he died several years ago, so we cannot ask him. I regret this especially since his 1980 proposal is very close to mine in two of its three main elements. He may have believed in time, but his emphasis on memories and records and their rather natural occurrence in the quantum context are valuable support for me. So are his views on ontology and psychophysical parallelism. This is the third common element.

In discussing Everett’s theory, I mentioned the so-called preferred-basis problem. This arises from transformation theory: a quantum state simultaneously encodes information about mutually exclusive properties. Viewed one way, it gives probabilities for particle positions; viewed another, it gives probabilities for their momenta. It is impossible to extract this information simultaneously and directly by, so to speak, ‘looking at the system’. We must let the system interact with instruments. Depending on how the instruments are arranged, we can extract information about either the positions or the momenta, but not both at once. The ambiguity becomes especially acute if the instruments are treated quantum mechanically. We cannot say what state they are in or what they are measuring.

Bell advocated a simple and robust answer to this in many of his writings, including his 1980 paper: the complete system formed by the particles and the instruments measuring them is always defined in the last resort by positions. In any quantum state, different sets of positions are present simultaneously, but it is always positions that are present. The different kinds of quantum measurement, giving alternatively position-type and momentum-type outcomes, arise because the same sets of positions of the measured system are made to interact with characteristically different sets of instrument positions. Everything is ultimately inferred from positions. This is exactly my position. Platonia is the universal arena. To Bell’s arguments – and gut conviction – for this standpoint I would add the impossibility of obtaining a satisfactory theory of inertia and time unless positions are fundamental.

Now, what did Bell regard as the physical counterpart of psychological experience? Is it in the wave function, as Everett and many others have assumed, or in matter configurations? Bell, like myself, opts for the latter: ‘It is ... from the xs [the configurations], rather than from ψ, that in this theory we suppose “observables” to be constructed. It is in terms of the xs that we would define a “psycho-physical parallelism” – if we were pressed to go so far.’ Although Bell does not spell out his parallelism too explicitly – he does not seem to want to be ‘pressed’ too far – it is clear from the way he makes memories and records responsible for our idea of the past, rejecting any ‘thread’ connecting configurations at different times, that subjective awareness of both positions and motions of objects must be derived from the structure in one instantaneous configuration. The self-sentient configurations must be time capsules. Not only the kingfisher but also the appearance of its flight must be in one configuration, for nothing else would be logically consistent. The main lessons I draw from Bell’s paper are incorporated in the many-instants interpretation that I favour.

THE MANY-INSTANTS INTERPRETATION

This is based on a conjecture that I shall try to justify in the next chapter. Here I simply assume it. It is that the universe is described by an equation of Wheeler-DeWitt type, which may have one or many solutions, and that each of its well-behaved solutions concentrates its probability density on time capsules. Bell showed that this does happen if time exists, and if evolution is real and commences from a low-entropy state. Since I deny time, I cannot appeal to a special initial state. There is only one state and no evolution. That is the problem for the next chapter; here I want to describe the kind of state I conjecture and how it must change our view of history.

Most important is a distinction between two different kinds of variable. Bell showed how the alpha-particle semiclassical state contains latent histories which then become entangled with the cloud-chamber electrons. The electrons could be in a huge number of different configurations, but in the Mott-Heisenberg solution the only configurations with high probability are those that look like alpha-particle tracks. Something similar must happen in cosmology, but there is a difference.

Imagine a swarm of 5000 bees. Its configuration space has 15,000 dimensions. However, from a distance we cannot see the individual bees, only the overall position of the swarm and, say, its size (radius). These are four dimensions of the configuration space. In such situations a few of the configuration-space dimensions describe the system’s large-scale properties, and the remaining, much more numerous dimensions describe the fine details. The corresponding large-scale and small-scale configuration spaces are illustrated in Figure 52.

Any point in Figure 52 represents a possible position of all the bees. Horizontal motion from a point changes the swarm’s position and size without changing the relative position of the bees within it. Vertical displacement leaves the swarm’s position and size unchanged but rearranges the bees. Since this can happen in so many ways, each vertical point actually represents multitudinous possibilities. Alas, we have only the vertical to represent them. Also, to make even a moderately realistic model of the universe, the horizontal positions should represent the positions of not just one swarm but many. Imagine, say, 100 swarms. Each horizontal position then represents one relative arrangement of their positions and sizes as complete units. Different vertical positions having the same horizontal position then correspond to all rearrangements of the bees that leave the swarms as they are. This is very schematic, but it is sufficient to explain the scheme.

If the wave function of the universe is static, quantum cosmology reduces to the question of how its values are distributed in Platonia. For the moment, I shall simply give you my guess; arguments for it come later. My guess is a special distribution closely similar to the cloud-chamber one described by Bell. In most of Platonia the wave function has extremely small values – the blue mist has negligible intensity. However, in a few special regions, distributed over a large area, the blue mist’s intensity is, relatively, hugely higher. These regions correspond to some arrangement of the swarms, determined by the horizontal position, and to the detailed positions within them, determined by the vertical positions. It is in the probabilities for these detailed positions that the blue mist is extraordinarily selective. The probabilities for the horizontal positions are relatively uniform over quite large regions. By themselves, they represent a dull state of affairs. The situation is transformed by the configurations that specify the fine details within the swarms. At the very rare configurations where the blue mist shines brightly, the fine details look like records of a history of the swarms as complete units. They suggest that the swarms have moved in a classical history from some past up to a present instant, in the position they now occupy.

This is illustrated in Figure 52, in which the points X and Y in Platonia have large-scale positions B and D. The fine details at X and Y seem to represent records of how the swarms have moved from earlier configurations A and C along curves AB and CD in the large-scale (horizontal) configuration space. They seem to be records of these large-scale histories. The blue mist has a high intensity not only at X and Y but also, for example, at P and Q, at which points the fine details suggest they represent records up to the intermediate stages E and F in the histories AB and CD.

By no means all details need represent history. Footprints in the sand on a wide beach record the movements of people who have walked on it, but over much of the beach there need be no apparent records. Think again of the number of atoms in a pea. A tiny fraction of them can easily record the pea’s history up to its current present. The huge numbers we confront in physics explain why we may have wrong ideas of what history actually is. We may have jumped to a conclusion too quickly.

In the Newtonian picture, in which history is a curve in configuration space, it is extremely hard to understand how records arise. Even if a single curve is realized, any point on it could have any number of histories passing through it. How can one instantaneous configuration of particles suggest the motions that they have? However, if we keep an open mind about the laws that determine things, a fraction of a pea’s atoms may well seem to record a history of its large-scale features. This does not mean that all its atoms had a unique history. Without change in the pea’s large-scale structure, the same large-scale history could be coded in innumerable different ways by only a tiny fraction of its atoms. In the imagery of Figure 52, there will be a whole cloud of points X in the configuration space that correspond to the same large-scale configuration and to the same history up to it. The different points in the cloud simply code the same history in different ways. What is more, for each point along the large-scale history AB there will be a corresponding cloud of points that record the same history up to that point in different ways. There will be a ‘tube’ of such points in the configuration space. No continuous ‘thread’ joins up these points in the tube into Newtonian histories. The points are more like sand grains that fill a glass tube. Each grain tells its story independently of its neighbours. In any section of the tube, the grains all tell essentially the same story but in different ways, though some may tell it with small variations.

Figure 52 The division of Platonia. The horizontal dimensions represent the large-scale configuration space, and the single vertical dimension represents the small-scale space. The ‘horizontal curves’ (AEB and CFD) represent histories of the large-scale features. Each point like A represents, say, the overall position and size of a swarm of bees. In contrast, each of the points Q, P, X, V on the vertical lines represents the huge number of small-scale details.

I think this is the way to think about history in quantum stasis. Could we but see the picture – all Platonia with its misty crannies – we should see it as it is: the lawful definite world for which Einstein, like so many physicists, longed. But it is a timeless book full of different stories that tell of time. Quantum mechanics can create the appearance of multiple histories. However, will it in quantum cosmology? Its conditions are not quite Mott and Heisenberg’s conditions.