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In more technical terms, for people in the know, each point of conformal superspace has a given conformal geometry and is represented by the equivalence class of metrics related by position-dependent scale transformations.

The potentially most interesting implication of this work is that it could resolve the severe problem of the criss-cross fabric of space-time illustrated by Figure 31. At the level of conformal superspace, the universe passes through a unique sequence of states. For latest developments, please consult my website (www.julianbarbour.com) and the final entries in these notes and the notes on p.358.

CHAPTER 12: THE DISCOVERY OF QUANTUM MECHANICS

(p. 191) On the connection between particles and fields, let me mention here that I assume the appropriate ‘Platonic’ representation at the level of quantum field theory to be in terms of the states of fields, not particles.

CHAPTER 13: THE LESSER MYSTERIES

(p. 202) Wheeler and Zurek (1983) have published an excellent collection of original papers on the interpretational problems of quantum mechanics.

CHAPTER 14: THE GREATER MYSTERIES

The Many-Worlds Interpretation (p. 221) Everett’s original Ph.D. thesis, his published paper and the papers of DeWitt (and some other people) relating to the many-worlds idea can be found in the book by DeWitt and Graham (1973).

CHAPTER 16: ‘THAT DAMNED EQUATION’

History and Quantum Cosmology (p. 240) More details on the Leibnizian idea that the actual universe is more varied than any other conceivable universe are given in Smolin (1991), Barbour and Smolin (1992), and Barbour (1994b). The quotation from T. S. Eliot is in Eliot (1964). My book is Barbour (1989).

‘That Damned Equation’ (p. 247) Technical note: In connection with Chapter 11, it is interesting that the form of the Wheeler-DeWitt equation is independent of the signature of space-time.

(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.

CHAPTER 17: THE PHILOSOPHY OF TIMELESSNESS

(p. 255) On the subject of the aims and methods of science, I strongly recommend David Deutsch’s The Fabric of Reality.

CHAPTER 18: STATIC DYNAMICS AND TIME CAPSULES

Dynamics Without Dynamics (p. 258) In this section I refer to investigations by various authors. Their studies will be found in the bibliography. Physicists really interested in the semiclassical approach may also like to consult the review article by Vilenkin (1989), the paper by Brout (1987), the final part of Zeh (1992, 1999) and the introductory article by Kiefer (1997). The fullest account of my own ideas is Barbour (1994a).

CHAPTER 19: LATENT HISTORIES AND WAVE POCKETS

Schrödinger’s Heroic Failure (p. 278) In the first draft of this book I included a long section on the very interesting interpretation of quantum mechanics advanced originally by de Broglie, and revived by Bohm, whose 1952 paper I strongly recommend to physicists together with Peter Holland’s book (Holland 1993). With regret I omitted it, as I felt that it made this book too long, especially since I believe that the interpretation does not really solve the problem. However, I particularly value the way in which it shows that all the results of quantum mechanics can be obtained in a framework in which positions are taken as basic. This made the theory attractive to John Bell, as we shall see in the next chapters.

CHAPTER 20: THE CREATION OF RECORDS

The Creation of Records: First Mechanism (1) (p. 284) Bell’s paper can be found in his collected publications Speakable and Unspeakable in Quantum Mechanics.

(2) (p. 284) Mott’s paper is reproduced in Wheeler and Zurek (1983). Heisenberg’s treatment is in his Physical Principles of Quantum Theory. I am very grateful to Jim Hartle, who first drew my attention to Mott’s paper. At that time he was considering seriously an interpretation of quantum cosmology that is quite close to my own present position. He has since backed away somewhat, and now advocates an interpretation of quantum mechanics in which history is the fundamental concept. I should also like to express my thanks here to Dieter Zeh. Zeh, who was in this business long before me, also made me realize the importance of Mott’s work, and, crucially, alerted me to Bell’s paper. There are not many physicists who take the challenge of timelessness utterly seriously, but Dieter Zeh and his student Claus Kiefer, from both of whom I have gained and learned much, are two of them.