Julian Barbour - The End of Time - The Next Revolution in Physics

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.