I explained in connection with Figure 40 how the density of the blue mist can be used to create a collection of configurations in a bag, a heap even, from which the most probable atomic configurations can be drawn at random. Configurations – which are structures – are created as more or less definite potentialities to the extent that the stationary Schrödinger equation tells us to put more or less into the heap. Like the individual structures within it, the heap is static. It is carefully laid up in a Platonic palace, which, since probabilities play such a mysterious role in quantum mechanics, is a kind of ‘antechamber of Being’.
Now I can start to make good my deeper claims about Schrödinger and creation. We have to forget all previous physics and approach things with an open mind. First, we look at what the Machian time-independent Schrödinger equation is and what it does. It is completely self-contained. For a system of three bodies it just works on triangles and masses, and nothing else. In a timeless fashion, it associates a probability with each triangle. This is tantamount to giving them a ranking. It is particularly suggestive that this ranking is determined by the triangles themselves – nothing else is involved. The probabilities for the triangles emerge from a comprehensive testing and comparison programme. The equation ‘looks’ at all possible wave functions that could exist on Platonia and throws out all those that do not ‘resonate’ properly. Those that are left have to be finely tuned, otherwise they will satisfy neither the equation nor the condition of being well behaved. And it is not just the wave function that resonates. We can say that the triangles that get the greatest probability are the ones that ‘resonate best with their peers’, since the triangles alone determine how the probability is distributed. This is what the rationality of best matching in classical dynamics translates into in quantum cosmology. There is a perfect, circle-closing, rational explanation for all the relative probabilities.
I do believe that what we have here are putative rules of creation, or perhaps we should say of being. Considered purely as an intellectual exercise, this quantum-mechanical determination of probabilities for relative configurations is no odder than the classical-dynamical determination of curves in configuration space. The aim of science is to find rational and economic explanations of observed phenomena, not to prejudge the issue. Each hypothetical scheme should be judged on its merits. There should be a clear statement of the phenomena that are to be explained, the conceptual entities that are to be employed and the mechanism that is to yield the explanation.
The first aim is to create a realist (non-solipsistic) cosmology in which there are sentient beings whose primary awareness is of structured instants of time as defined earlier in the book. These instants are like subjective snapshots, and may be called atoms of perceptual existence. Each snapshot holds together in an indissoluble unity everything that we would want to call the actual facts of which we are aware in an instant of time. These include not only the things we see, feel and hear, but also our awareness of them, our memories and our interpretation of everything. The fact that many different things are known at once is regarded (by me at least) as the most remarkable – and defining – property of instants of time. I do not believe that science (or religion) will ever explain why we experience instants, but perhaps it can explain the structure we find within them.
The scheme is realist because the structure of an external, objectively existing real thing is being proposed as the explanation of the structure experienced within a perceptual instant. What we experience in subjective instants reflects, through psychophysical parallelism, physical structure in external things: configurations of the universe. Their actual nature is a matter for ongoing research. The notion has been illustrated by configurations of mass points in Euclidean space, by island-type distributions of fields of Faraday-Maxwell type in Euclidean space, and by closed Riemannian 3-geometries (which may also have fields defined on them). It is at the last level that I believe satisfactory explanations can in principle be obtained for many of the known facts of physics and cosmology. However, some further development, very possibly associated with the notions of superstrings and supersymmetry, may well be needed to explain the actual cocktail of forces and particles that pervades the universe.
What is important about relative configurations is that they are intrinsically defined – they are self-contained things – and that the rule that defines one thing simultaneously defines many. Moreover, they can all be arranged systematically in a relative configuration space: Platonia, as I have called it.
Classical physics before general relativity ‘explained’ the world by assuming it to be a four-dimensional history of such relative configurations located in a rigid external framework of absolute space and time. Such a world is supposed to have evolved from certain initial conditions to the state we now observe by means of the laws of classical dynamics, in which the framework of space and time play a significant role. These laws provide all the explanation of which classical physics is in principle capable. In Part 2 I showed how the external framework can be dispensed with. It does not need to be invoked to formulate the laws of dynamics, nor even to visualize how things are located in space and time. Schrödinger’s Kantian appeal to space and time as the ineluctable forms of thought was unnecessary. We can form a clear conception of structured things that stand alone. We have seen how this is also true of general relativity, in which space-time is ‘constructed’ by fitting together 3-spaces in a very refined and sophisticated way.
So, then, what does the Wheeler-DeWitt equation tell us can happen in a rational universe? The answer is ironic. Nothing! The quantum universe just is. It is static. What a denouement. This is a message that needs to be shouted from the rooftops. But how can this seemingly bleak message reverberate around a static universe? How can we bring dead leaves to life? The poet Shelley called on the wild west wind to carry his thoughts over the universe. What can play the role of the wind in static quantum Platonia?
CHAPTER 18
Static Dynamics and Time Capsules
DYNAMICS WITHOUT DYNAMICS
DeWitt already clearly saw the problem posed at the end of the last chapter – the crass contradiction between a static quantum universe and our direct experience of time and motion – and hinted at its solution in 1967. Quantum correlations must do the job. Somehow they must bring the world alive. I shall not go into the details of DeWitt’s arguments, since he saw them only as a first step. However, the key idea of all that follows is contained in his paper. It is that the static probability density obtained by solving the stationary Schrödinger equation for one fixed energy can exhibit the correlations expected in a world that does evolve – classically or quantum mechanically – in time. We can have the appearance of dynamics without any actual dynamics.
It may surprise you, but it was about fifteen years before physicists, and then only a few, started to take this idea seriously. The truth is that most scientists tend to work on concrete problems within well-established programmes: few can afford the luxury of trying to create a new way of looking at the universe. A particular problem in everything to do with quantum gravity is that direct experimental testing is at present quite impossible because the scales at which observable effects are expected are so small.
Something like a regular research programme to recover the appearance of time from a timeless world probably began with an influential paper by Don Page (a frequent collaborator of Stephen Hawking) and William Wootters in 1983. This was followed by several papers that concentrated on an obvious problem. In ordinary laboratory physics, the fundamental equation used to describe quantum phenomena is the time-dependent Schrödinger equation. It undoubtedly holds to an extraordinarily good accuracy for all ordinary physics: we could not even begin to understand, for example, the radiation of atoms without this equation. But if the universe as a whole is described by a stationary Schrödinger equation and time does not exist at all, how does a Schrödinger equation with time arise? This question seems to have been first addressed by the Russians V. Lapchinskii and V. Rubakov, but a paper in 1985 by the American Tom Banks did more to catch the imagination of physicists. This was followed in 1986 by a paper treating the same problem by Stephen Hawking and his student Jonathan Halliwell. Further papers on the subject appeared in the following years. The whole associated research programme has become known as the semiclassical approach, for a reason I shall explain later. The basic idea is easy to grasp.