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

(1)(p. 247) For physicists I should mention that there is an important alternative to regarding the Wheeler-DeWitt equation as analogous to the stationary Schrödinger equation. It also bears a resemblance to the relativistic Klein-Gordon equation, the role of time in that equation being played, essentially, by the volume of the universe in the case of the Wheeler-DeWitt equation.

(2)(p. 247) Kuchařs objections to my timeless interpretation of the Wheeler-DeWitt equation can be found in the discussion sessions at the end of Barbour and Pfister (1995). Comprehensive reviews of the problems of time in quantum gravity can be found in Kuchaf (1992) and Isham (1993).

(3)(p. 247) In discussions with me in 1994 at an international conference on quantum gravity held at Durham, Bryce DeWitt expressed two main reservations about his ‘damned equation’. The first was that it required a division of space-time into space and time, which he felt was running counter to the great tradition of relativity initiated by Einstein and Minkowski. I have already explained why I feel that this may not necessarily be an objection; indeed, it may not be possible to give objective content to general relativity unless such a split is made. DeWitt’s second objection was that the ‘damned equation’ had not as yet yielded any concrete results and was (is) plagued with mathematical difficulties. This is certainly true, and I have omitted all discussion of these difficulties, which are certainly great. However, I think it is worth noting that as physicists’ understanding of the equations that describe nature becomes deeper, the equations themselves become more sophisticated and harder to solve. It is much harder to find solutions of Einstein’s equations than Newton’s. This tendency—deeper understanding of principles bringing with it greater intractability of equations—will almost certainly mean that progress in quantum gravity is very slow. In fact, for over a decade, a group centred on the relativist Abhay Ashtekar, including my friend Lee Smolin and another friend Carlo Rovelli, has been working intensively on a particular approach to canonical quantum gravity (the broad framework in which DeWitt derived his equation) and have certainly resolved some of the difficulties. An account of this work can be found in Lee’s The Life of the Cosmos and Three Roads to Quantum Gravity . Kuchař too has made many important contributions.

If the ideas described in the note on p. 350 work out as Niall Ó Murchadha and I believe they could, the difficult issues raised in the final part of Chapter 16 and in the above notes will be to a very large degree resolved. The conceptual uncertainties about the correct way to proceed that have plagued the theory for four decades could all be removed. Both for general relativity and the alternative theory that might replace it, the wave function of the universe will certainly be static and give probabilities for configurations as explained in the main text. The main difference is that only the intrinsic structure will count, so that all configurations that have the same structure and differ only in the local scales will have the same probability. They will merely be different representations of the same instants of time. However, for general relativity there will be a curious residual scale that represents a volume of the universe. It will be meaningful to say that the universe has a volume but not how the volume is distributed between the intrinsic structures contained within in.

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.