The End of Time: The Next Revolution in Physics

CHAPTER 17

The Philosophy of Timelessness

You should by now recognize the connection between the picture that emerges from the simplest interpretation of the Wheeler-DeWitt equation and the timeless world I sketched in Part 1. I outlined there, using the notion of the time capsule, how the seemingly dead and static Platonia might correspond to the vibrant living world we experience in every instant. In this final part of the book, I want to explain the arguments from physics that led me to the notion of time capsules, and also to show that the structure of quantum cosmology may well cause the wave function of the universe to ‘seek out’ time capsules. This is the story of how physics brings the Platonic forms to life. I start with some general comments.

I believe in a timeless universe for the childlike reason that time cannot be seen – the emperor has no clothes. I believe that the universe is static and is described by something like the Wheeler-DeWitt equation. I would like you to accept this as a working hypothesis, so we can see where it leads. As I said earlier, I believe that it leads to the rules of creation. Let me now explain why.

According to many accounts, in both mainstream science and religion, the universe either has existed for ever or was created in the distant past. Creation in a primordial fireball is now orthodox science – the Big Bang. But why is it supposed that the universe was created in the past rather than newly created in every instant that is experienced? No two instants are identical. The things we find in one are not exactly the same as the things we find in another. What, then, is the justification for saying that something was created in the past and that its existence has continued into the present?

The most obvious reason is the apparent persistence of objects and living beings. If pressed, though, we acknowledge that they never remain exactly the same. Even rocks weather slowly. However, enough properties remain unchanged for us to say that the same things do continue to exist. Indeed, human existence is inconceivable without a significant degree of stability in the world. No doubt the baby’s recognition of the continually reappearing smiling face of its mother soon implants the notion of persistence. But if we want to think rationally and as philosophers about these matters, we ought to cultivate a degree of detachment. We must practise Cartesian doubt and, just once at least, question all our preconceptions.

I am not persuaded that the people who ought to be best at this – theoretical physicists – do achieve full freedom of thought. Many are passionately committed to an objectively existing external world. They hate anything that smacks of solipsism or creationism. This explains the controversies, virulent at times, about the reality of atoms that took place a century ago, and the equally impassioned debates today about the meaning of quantum mechanics (in many ways a continuation of the debate about atoms). For scientists committed to realism, atoms that remain the same in themselves and merely move in space and time are very welcome. Atoms, space and time are the things that either existed for ever or else came into being with the Big Bang.

However, the fields introduced by Faraday and Maxwell now provide the basis of quantum field theory, which is currently the deepest known form of quantum theory, and such fields are in perpetual flux. And within classical physics Einstein made space and time equally fluid and transient. Today there is only one scientific justification for saying that the universe was created in the past: the hypothesis of lawful dynamical evolution from some past, into the present, and on into an as yet unexperienced future. If an initial state uniquely determines a subsequent state of the same generic kind which differs only in detail, it is reasonable to speak of initial creation and subsequent evolution.

But this view must be challenged. It belongs to a mindset that holds the world either to be classical in its entirety, or to have quantum objects within the old classical framework of space and time. How slow we are to move out of old quarters! All the evidence indicates that anything dynamical must obey the rules of quantum mechanics even if it appears classical to our senses. But Einstein made space dynamical – that is the lesson of geometrodynamics taught us in detail by Dirac; by Arnowitt, Deser and Misner (ADM); and by Baierlein, Sharpe and Wheeler (BSW). When space submits to the quantum, as it surely must, the last vestige of a created but persisting framework is lost. Moreover, the transition from the classical world we see to the quantum world that underlies it is fixed in its broad outlines. All we need do is put together the two things that go into quantization – a classical theory and the rules to quantize it – and see what comes out.

The central insight is this. A classical theory that treats time in a Machian manner can allow the universe only one value of its energy. But then its quantum theory is singular – it can only have one energy eigen-value. Since quantum dynamics of necessity has more than one energy eigenvalue, quantum dynamics of the universe is impossible. There can only be quantum statics. It’s as simple as that!

In Part 1 I mentioned the dichotomy in physics between laws and initial conditions. Most equations in physics do not by themselves give complete information, they only put limits on what is possible. To arrive at some definite prediction, further conditions are necessary. Neither Newton’s nor Einstein’s equations tell us why the universe has its present form. They have to be augmented by information about a past state. We could invoke a deity in the way Einstein was wont, who goes through two steps in creating the universe. First, laws are chosen, then an initial condition is added. Many people have wondered whether this is a permanent condition of physics.

The stationary Schrödinger equation is quite different in this respect. It obviously cannot have initial conditions, since it is a timeless equation. It does not require boundary conditions, either. Let me explain what this means. There are many equations in physics which describe how quantities vary in space without there being any change in time. Such equations can have many different solutions, and to find the one that is applicable in a specific case, mathematicians often stipulate the actual values the solution must have at the boundary of some region. This stipulation is what is called a boundary condition. Boundary conditions have the same kind of importance as initial conditions. However, as explained in Box 13, the stationary Schrödinger equation requires no such conditions. Instead, there is just a general condition on the way the wave function behaves. It must be continuous (not make any jumps), it must have only one value at each point and it must remain finite everywhere. As we saw, the condition of remaining finite – of not rushing off to infinity – is very powerful. It was what unlocked the quantum treasure chest. In fact, the first two conditions are also very powerful and lead to many important results. To distinguish these conditions from normal initial or boundary conditions, let me call them conditions of being well behaved. Mathematicians may regard this as somewhat artificial, since the condition of remaining finite does actually enforce a definite kind of behaviour at boundaries. It is therefore in some sense equivalent to a boundary condition. However, I prefer not to think of it in that way, since it is very general and can be formulated in a completely timeless fashion. It avoids all particular specification, which must always be arbitrary.

Now, my suggestion is this. There are no laws of nature, just one law of the universe. There is no dichotomy in it – there is no distinction between the law and supplementary initial or boundary conditions. Just one, all-embracing static equation. We can call it the universal equation. Its solutions (which may be one or many) must merely be well behaved, in the sense explained in the previous paragraph. It is an equation that creates structure as a first principle, just as the ordinary stationary Schrödinger equation creates atomic and molecular structure. This is because it attaches a ranking – a greater or lesser probability – to each conceivable static configuration of the universe.

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?