The End of Time: The Next Revolution in Physics

NOTES

PREFACE

(1) (p. 2) The article about Dirac appeared in the Süddeutsche Zeitung for Friday, 18 October 1963, and was based on an article by Dirac that appeared in Scientific American in May 1963.

(2) (p. 4) On hearing about my plans for this book, Michael Purser brought to my attention the following rebuke from Prince Hal to Falstaff:

Unless hours were cups of sack, and minutes capons, and clocks the tongues of bawds, and dials the signs of leaping-houses, and the blessed sun himself a fair hot wench in flame-colour’d taffeta, I see no reason why thou shouldst be so superfluous to inquire the nature of time.

Henry IV, Part I (1. ii)

(I comment on this in the Epilogue.)

CHAPTER 1: THE MAIN PUZZLES

The Next Revolution in Physics (p. 14) The possible non-existence of time has just begun to be discussed in authoritative books for the general public. Both Paul Davies, in his About Time, and Kip Thorne, in his Black Holes and Time Warps, devote a few pages to the topic. In apocalyptic vein, Thorne likens the fate of space-time near a black hole singularity to

a piece of wood impregnated with water . . . the wood represents space, the water represents time, and the two (wood and water, space and time) are tightly interwoven, unified. The singularity and the laws of quantum gravity that rule it are like a fire into which the water-impregnated wood is thrown. The fire boils the water out of the wood, leaving the wood alone and vulnerable; in the singularity the laws of quantum gravity destroy time . . . (p. 477)

However, Thorne’s magnificent book is devoted to other topics, and nothing prepares the reader for this dramatic and singular end of time. Moreover, the evidence, as I read it, is that timelessness permeates the whole universe, not just the vicinity of singularities. Paul Davies, for his part, repeatedly expresses a deep mystification about time. His book is almost a compendium of conundrums, and he candidly consoles the reader with ‘you may well be even more confused about time after reading this book than you were before. That’s all right; I was more confused myself after writing it’ (p. 10). In fact, I think Paul’s subtitle, Einstein’s Unfinished Revolution, is the key to a lot of the puzzles. As we shall see in Part 3, there are aspects of physical time which Einstein did not address.

Among the popular books that I know, the two that undoubtedly give most prominence to the problem of time in quantum gravity are Lee Smolin’s The Life of the Cosmos, which contains some discussion of my own ideas, and David Deutsch’s The Fabric of Reality. There is considerable overlap between my book and Deutsch’s chapter ‘Time: the first quantum concept’. One technical book, now going into a third edition, that from the start has taken timelessness very seriously is Dieter Zeh’s The Physical Basis of the Direction of Time.

It may be that the reason why a book like this one, devoted exclusively to the idea that time does not exist, has not hitherto been published by a physicist has a sociological explanation. For professionals working in institutes and dependent on the opinions of peers for research funding, such a book might damage their reputation and put further research in jeopardy. After all, at first it does seem outrageous to suggest that time does not exist. It may not be accidental that I, as an independent not reliant on conventional funding, have been prepared to ‘come out’.

In this connection, my experience at a big international conference in Spain in 1991 devoted to the arrow of time was very interesting. The following is quoted from my paper in the conference proceedings (available in paperback as Halliwell et al., 1994):

During the Workshop, I conducted a very informal straw-poll, putting the following question to each of the 42 participants:

Do you believe time is a truly basic concept that must appear in the foundations of any theory of the world, or is it an effective concept that can be derived from more primitive notions in the same way that a notion of temperature can be recovered in statistical mechanics?

The results were as follows: 20 said there was no time at a fundamental level, 12 declared themselves to be undecided or wished to abstain, and 10 believed time did exist at the most basic level. However, among the 12 in the undecided/abstain column, 5 were sympathetic to or inclined to the belief that time should not appear at the most basic level of theory.

Thus, a clear majority doubted the existence of time. When I took my straw-poll, I said that I intended to publish the names with their opinions, which was why two people abstained, to remain anonymous. As it happens the conference generated immense media interest in Spain, not least because of the presence of Stephen Hawking and Nobel Laureate Murray Gell-Mann, and the reporter from El Pais got hold of a copy of my results. One of the participants (neither of the above), finding his own opinion quoted in a big article the day after the conference, was none too pleased and greeted me when we met six months later at a conference in Cincinnati with ‘You and your damned straw-poll!’ I then realized why the editors had meanwhile asked me to withhold the names in my paper, which I happily did.

It was at the later conference that I learned a bon mot of Mark Twain that somehow seems appropriate here: ‘If the end of the world is nigh, it is time to be in Cincinnati. Everything comes to Cincinnati twenty years late.’

The Ultimate Things (p. 15) I mentioned in the Preface the difficulty of writing without using temporal notions. The curious state of modern physics as outlined in Box 2 compounds the problem. Because quantum theories are obtained from classical theories by so-called quantization, and classical concepts are much closer to everyday experience, the language used by most physicists, myself included, often seems to imply that the classical theories are somehow deeper than the quantum theories obtained from them. But that is certainly only a reflection of our way to the truth. What is needed is a clear language in which to describe the quantum truth directly and an explanation, based on it, of why the world appears classical to us. I am proposing the notion of a Now as the basic quantum notion.

Getting to Grips with Elusive Time (p. 17) The idea that instants of time are distinct entities that should not be thought of as joined up in a linear sequence is a powerful intuitive experience for at least one non-scientist. A few days after the Sunday Times published its article ‘Time’s assassin’ about my ideas in October 1998, I received by email a ‘Question for Julian Barbour’ from Gretchen Mills Kubasiak, who had read the article about me. She introduced herself with: I am merely a girl who lives in Chicago, works for a construction company and finds herself thoroughly captivated by your ideas. In fact, I have been unable to think of little else this past week.’ She asked if she could put a question to me. Well, who could resist that request? I said yes, asking if by any chance, with her first name, she had German ancestry, and commented: ‘I guess you know the German expression Gretchenfrage and its origin in Goethe’s Faust, when Gretchen asks Faust about his attitude to religion and if he believed in God. It was especially nice to get your Gretchenfrage.’ Subsequent correspondence persuades me that ‘merely a girl’ might not be the most accurate description of her, since she is a voracious reader and traveller (among much else). Some of her thoughts about time are worth passing on:

Several weeks before I read the London Times article which brought your ideas to my attention, I started having a debate with a friend of mine on traveling. He stated that when a person travels between two places, it is the time spent on the journey which makes the person able to appreciate and comprehend the final destination. Only by making a linear tour of the world and having a passage of time connect the two locations are we able to understand our final destination.

I disagreed. I have always believed that our lives are made up of individual moments that layer and co-exist with other moments, not a linear sequence of events. I did not accept his notion that time spent on a journey is relative to one’s experience at their final destination. The passage of time, that for my friend constituted the journey, did not exist for me. That is not to say that what he viewed as his journey did not consist of moments but I could not accept that they were relative to the moment of the final destination simply because they preceded it.

Despite the fact that I had these beliefs in my head, I found that I lacked the vocabulary to make a satisfactory argument on paper. It is one thing to state your beliefs and quite another to be able to back up your argument. I had developed a few descriptive examples of moments in my life that I believed began to illustrate this idea but I knew of nothing that would support them.

One of my ideas addressed my moments with Buckingham Palace. As a small child I had listened to my mother recite the poem about Christopher Robin’s visit to the changing of the guard and I stood silently alongside him and Alice. As a young girl I watched on television the newly married Prince and Princess of Wales venture forth onto the balcony to greet their public and I stood among the crowds. In both instances I was not ‘there’ and yet I was. When I actually stood in front of the palace as a teenager, the physical journey associated with that moment mattered not. What mattered were these other moments. When I stood in front of the palace, I was living not just that moment but co-existing with the other moments as well.

Then I came across the London Times article outlining your notion of the illusion of time and a spark of recognition within me was lit. Something I had always felt, but had never been able to express, was suddenly being put into words.

If, as you say, all moments are simultaneous and there is no linear sequence of events, does this not imply that the ‘length’ of a journey is completely irrelevant? If we exist in isolated moments, then the notion that time spent on a journey makes the experience cannot be true because time does not exist. If time is merely an illusion, the time spent on a journey is also an illusion.

My memories never fade. Memories from my supposed past shine as clearly as my present. I remember climbing out of my crib after a nap at 1 ½ years old as clearly as I remember getting out of bed this morning. Aren’t memories supposed to become less clear with time? These moments remain in my head as individual events. I rarely think of them in conjunction with moments that preceded or followed them. The memories in my head feel somewhat like a piece of sedimentary rock—as if these moments have all been compressed together and the connector pieces—the time that I thought held them together—has been blown away with the wind. These thoughts all exist simultaneously in my mind yet they reveal themselves to me one by one.

I think most important was my prevailing feeling of a stronger connection between moments perceived as being separated by time than between moments believed to be connected by time. What I am unclear about, however, is what causes this feeling of connection. Can there be a relationship between these moments? Not in the sense of a linear connection, but rather a feeling of empathy between them. To a certain extent, I think there is a subconscious awareness that there are these other moments occurring simultaneously and that there can be an acknowledgement between moments that are connected by subject matter.

If all moments are simultaneous, I am concurrently hearing the Christopher Robin poem being read, watching the Prince and Princess of Wales on the balcony, and standing in front of the Palace myself. My conscious mind feeds them to me in a linear sequence strung out with a bunch of other moments in an illusion of a continuous flow of action. While I am being read to, however, my subconscious is aware that I really am in front of Buckingham Palace and so a sense of really being there is brought to the Christopher Robin reading or to the Royal Wedding viewing.

This awareness that this other moment is occurring out there right now has struck me at many times. Sometimes it’s when I’m reading a book, other times I’m walking down the street listening to music. Always, however, there is the feeling that I am somewhat connected to that other moment and I can almost feel there is the chance of stepping out of this moment and into another. It is the knowledge that there is another possibility to this moment.

To a certain extent, I often feel as if we are moving towards a timeless existence. The increasing usage of the computer by people on an everyday basis is one factor heading us in this direction. At any moment, without any thought to time, we can shop on our computers, chat, read newspapers, research, do our banking, etc. Also, more and more we are creating environments in which timelessness is the objectivity. Nowhere is this more obvious than in the twentieth-century environments of the department store, the amusement park and the casino. The goal is one dream-like moment, where there is no beginning and no end—no time.

Reading these comments again three months after they came, they strike me as often very close to my position. Incidentally, I address the original Gretchen’s questions (Glaubst du an Gott? Wie halt’s du es mit der Religion?) in the Epilogue.

Note for physicists (p. 18): Space plays two roles in Newtonian physics: it binds its contents together to form the plurality within the unity mentioned in this section (the separations between N objects in Euclidean space are constrained by both inequalities and algebraic relations, which give expression to this unity) and if defines positions at non-coincident times. In the type of physics I am advocating, only the first property is used, as will become clear in Part 3.

In relativity theory, the construction of ‘three-dimensional’ snapshots from two-dimensional photographs is greatly (but not insuperably) complicated by the fact that light travels at finite speed, so that objects are no longer where they seem to be. Readers familiar with relativity theory and concerned that my concept of a Now seems very non-relativistic are asked to defer judgment until Part 3. Einstein did not abolish Nows, he simply made them relative.

Laws and Initial Conditions (p. 22) Although Newton’s and Einstein’s laws work equally well in both time directions, there is one known phenomenon in quantum physics that seems to determine a direction of time at a truly fundamental level. It is observed in the decay of particles called kaons. Paul Davies discusses this phenomenon in some detail in his About Time. Most authors are agreed that this phenomenon does not seem capable of explaining the pronounced directionality of temporal processes, which is one of my main concerns in this book, but it is probably very important in other respects and may provide evidence that time really does exist as an autonomous governing factor in the universe. However, the evidence that it defines a direction in time is indirect, being based on something called the TCP theorem. Although this is most important in modern physics, what form if any it will take in the as yet non-existent theory of quantum gravity is not at all clear.

CHAPTER 2: TIME CAPSULES

The Physical World and Consciousness (1) (p. 26) There is a clear and detailed account of Boltzmann’s ideas in Huw Price’s book listed in Further Reading.

(2) (p. 27) It is worth quoting here two passages from Boltzmann himself. In 1895 he published (in perfect English—I wonder if he had assistance) a paper in Nature with the title ‘On certain questions of the theory of gases’. It ends with a truly remarkable and concise statement of what much later became known as the anthropic principle. This expression was coined in 1970 by the English relativist Brandon Carter (who had earlier made important discoveries about the physics of black holes in the period leading up to Hawking’s discovery that they can evaporate). The anthropic principle, which gained widespread attention initially through the book The Anthropic Cosmological Principle by John Barrow and Frank Tipler, expresses the idea that any universe in which intelligent life exists must have special and unexpected (from a purely statistical viewpoint) properties, since otherwise the intelligent life that observes these properties could not exist. Therefore we should not be surprised to find ourselves in a universe that does have special and remarkable properties.

In the following passage, the summits of the H curve to which Boltzmann refers correspond to states with very low entropy and high order. Note that Boltzmann credits his assistant with the idea.

1 will conclude this paper with an idea of my old assistant, Dr. Schuetz.

We assume that the whole universe is, and rests for ever, in thermal equilibrium. The probability that one (only one) part of the universe is in a certain state, is the smaller the further this state is from thermal equilibrium; but this probability is greater, the greater the universe itself. If we assume the universe great enough we can make the probability of one relatively small part being in any given state (however far from the state of thermal equilibrium), as great as we please. We can also make the probability great that, though the whole universe is in thermal equilibrium, our world is in its present state. It may be sayd [sic] that the world is so far from thermal equilibrium that we cannot imagine the improbability of such a state. But can we imagine, on the other side, how small a part of the whole universe this world is? Assuming the universe great enough, the probability that such a small part of it as our world should be in its present state, is no longer small.

If this assumption were correct, our world would return more and more to thermal equilibrium; but because the whole universe is so great, it might be probable that at some future time some other world might deviate as far from thermal equilibrium as our world does at present. Then the aforementioned H curve would form a representation of what takes place in the universe. The summits of the curve would represent the worlds where visible motion and life exist.

Boltzmann returned to this theme a year later, this time writing in German. The following is my translation:

One has a choice between two pictures. One can suppose that the complete universe is currently in a most unlikely state. However, one can also suppose that the eons during which improbable states occur are relatively short compared with all time, and the distance to Sirius is small compared with the scale of the universe. Then in the universe, which otherwise is everywhere in thermal equilibrium, i.e. is dead, one can find, here and there, relatively small regions on the scale of our stellar region (let us call them isolated worlds) that during the relatively short eons are far from equilibrium. What is more, there will be as many of these in which the probability of the state is increasing as decreasing. Thus, for the universe the two directions of time are indistinguishable, just as in space there is no up or down. But just as we, at a certain point on the surface of the Earth, regard the direction to the centre of the Earth as down, a living creature that at a certain time is present in one of these isolated worlds will regard the direction of time towards the more improbable state as different from the opposite direction (calling the former the past, or beginning, and the latter the future, or end). Therefore, in these small regions that become isolated from the universe the ‘beginning’ will always be in an improbable state.

Time Without Time (p. 29) In connection with my suggestion that the brain may be deceiving us when we see motion, it is interesting to note that, as Steven Pinker points out in his How the Mind Works, people with specific types of brain damage see no motion when normal people do see motion. In his words, they ‘can see objects change their positions but cannot see them move—a syndrome that a philosopher once tried to convince me was logically impossible! The stream from a teapot does not flow but looks like an icicle; the cup does not gradually fill with tea but is empty and then suddenly full’.

If the mind can do these things, it may be creating the impression of motion in undamaged brains.

CHAPTER 3: A TIMELESS WORLD

First Outline (p. 36) The philosopher best known for questioning the existence of time and its flow was John McTaggart, who is often quoted for his espousal of the ‘unreality’ of time and the denial of transience. The following argument of his is very characteristic of professional philosophers:

Past, present, and future are incompatible determinations. Every event must be one or the other, but no event can be more than one. If I say that any event is past, that implies that it is neither present nor future, and so with the others. And this exclusiveness is essential to change, and therefore to time. For the only change we can get is from future to present, and from present to past.

The characteristics, therefore, are incompatible. But every event has them all. if [an event] is past, it has been present and future. If it is future, it will be present and past. If it is present, it has been future and will be past. Thus all the three characteristics belong to each event. How is this consistent with their being incompatible? (McTaggart 1927, Vol. 2, p. 20)

Some thoughts here certainly match my own thinking, especially that ‘exclusiveness is essential to change’, but McTaggart’s arguments are purely logical and make no appeal to physics. Abner Shimony (1997)—to whom I am indebted for several discussions—compares McTaggart’s position with mine, but I think he has not quite understood my notion of time capsules, so I do not feel that his arguments force me to accept transience.

A typical example of theological thought about time is this extract from Conversations with God—An Uncommon Dialogue by Neale Donald Walsch (kindly sent me by Ann Gill):

Think of [time] as a spindle, representing the Eternal Moment of Now.

Now picture leafs [sic] of paper on the spindle, one atop the other. These are the elements of time. Each element separate and distinct, yet each existing simultaneously with the other. All the paper on the spindle at once! As much as there will ever be—as much as there ever was . . .

There is only One Moment—this moment—the Eternal Moment of Now (p-29).

Again, there is some overlap with my position. Walsch’s ‘leafs’, his elements of time, are my Nows. But the spindle of time, the Eternal Moment, is not at all part of my picture. My Nows are all constructed according to the same rule. There is no Eternal Moment, only the common rule of construction. I think Walsch is trying to grasp eternal substance where there is none, though I think he is right to say that the ‘leafs’ are all there at once and that this is a consoling thought. But we should not ask for more than we can get. Also, the image of time as a spindle is beautiful but misleading. In my view, the ‘leafs’ of time most definitely cannot be arranged along a single line, as the striking spindle image implies.

The Ultimate Arena (1) (p. 39) In this section I say that all structures that represent possible instants of time are three-dimensional. This is because the space we actually observe has three dimensions. However, in some modern theories (super-string theories) it is assumed that space actually has ten or even more dimensions. All but three of the dimensions are ‘rolled up’ so tightly that we cannot see them. In principle, my instants of time could fit into this picture. They would then have ten (or more) dimensions.

(2) This note is for experts. Platonia is a special type of configuration space known as a stratified manifold. The sheets, ribs and singular point that form the frontiers of Triangle Land are called strata. I believe that the stratified structure of Platonia is highly significant. Mathematicians and physicists really interested in this can consult DeWitt (1970) and Fischer (1970). The strata are generally regarded as something of a nuisance, since at them normal well-behaved mathematics breaks down. They are like grit in the works. But in the world’s oyster they may be the grit from which grows ‘a peal richer than all his tribe’: not Desdemona, but time (Chapter 22). (After Othello had strangled Desdemona and then realized his dreadful mistake, he said before stabbing himself that he was ‘one whose hand, Like the base Indian, threw away a pearl richer than all his tribe’.)

CHAPTER 4: ALTERNATIVE FRAMEWORKS

(1) (p. 61) I have written at considerable length about the early history of astronomy and mechanics and the absolute versus relative debate in my Absolute or Relative Motion? This has recently been reprinted as a paperback with the new title The Discovery of Dynamics (OUP, 2001). I still hope to complete a further volume bringing the story up to the present, and much has already been written, but my plans are in flux because of the developments mentioned at the end of the Preface and at various places in these notes. Readers wanting a full academic (and mathematical) treatment of the topics presented in Parts 2 and 3 of this book are asked to consult the above and the papers (Barbour 1994a, 1999, 2000, 2001), which cite earlier papers. For references to recent developments see p. 358 and my website (www.julianbarbour.com).

(2) (p. 64) In the main body of the text, I mention the importance of the fortunate circumstances of the world in enabling physicists to avoid worrying about foundations. Another very important factor is the clarity of the notion of empty space, developed so early by the Greek mathematicians, which deeply impressed Newton. He felt that he really could see space in his mind’s eye, and regarded it as being rather like some infinite translucent block of glass. He and many other mathematicians pictured its points as being like tiny identical grains of sand that, close-packed, make up the block. But this is all rather ghostly and mysterious. Unlike glass and tiny grains of sand, which are just visible, space and its points are utterly invisible. This is a suspect, unreal world.

We are not bound to hang onto old notions. We can open our eyes to something new. Let me try to persuade you that points of space are not what mathematicians would sometimes have us believe. Imagine yourself in a magnificent mountain range, and that someone asked, ‘Where are you?’ Would you kneel down with a magnifying glass and look for that invisible ‘point’ at which you happen to be in the ‘space’ that the mountain range occupies? You would look in vain. Indeed, you would never do such a silly thing. You would just look around you at the mountains. They tell you where you are. The point you occupy in the world is defined by what the world looks like as seen by you: it is a snapshot of the world as seen by you. Real points of space are not tiny grains of sand, they are actual pictures. To see the point where you are in the world, you must look not inward but outward.

The plaque near the grave of Christopher Wren in St. Paul’s Cathedral says simply: ‘If you seek a monument, look around you.’ The point where you are is a monument too, and you see it by looking around you. It is this sort of change of mindset that I think we need if we are to understand the universe and time.

To conclude this note, a word about what is perhaps the most serious problem in my approach. It is how to deal with infinity. As so far defined, each place in Platonia corresponds to a configuration of a finite number of objects. Such a universe is like an island of finite extent. One could allow the configurations to have infinite extent and contain infinitely many objects. That is not an insuperable problem. The difficulty arises with the operations that one needs to perform. As presented in this book, the operations work only if the points in Platonia, the instants of time, are in some sense finite. There may be ways around this problem—Einstein’s theory can deal beautifully with either finite or infinite universes—but infinity is always rather difficult. There is something ‘beyond the horizon’, and we can never close the circle of cause and effect. In short, we cannot build a model of a completely rational world. Precisely for this reason Einstein’s first and most famous cosmological model was spatially finite, closed up on itself. The constructions of this book are to be seen as a similar attempt to create a rational model of the universe in which the elusive circle does close.

In fact, if the work with Niall O Murchadha mentioned at the end of the Preface, which suggests that absolute distance can be eliminated as a basic concept (see Box 3), can be transformed into a complete theory, the problem of infinity may well be solved in the process. If size has no meaning, the distinction between a spatially finite or infinite universe becomes meaningless.

CHAPTER 5: NEWTON’S EVIDENCE

The Aims of Machian Mechanics (1) (p. 71) In creating the beautiful diagrams that form such an important part of this section, Dierck Liebscher was able to draw on initial data devised by Douglas Heggie (University of Edinburgh), using software written by Piet Hut (Institute for Advanced Study), Steve McMillan (Drexel University) and Jun Makino (University of Tokyo). Dierck has written a very interesting book (alas, as yet published only in German) on the connection between different possible geometries and Einstein’s relativity theory (Liebscher 1999). It contains many striking computer-generated diagrams.

(2) Poincaré’s discussion is contained in his Science and Hypothesis, which, along with the writings of his contemporary, Mach, became a popular-science best-seller. In fact, in this book I am actually revisiting many of the themes discussed by Poincaré and Mach, but with the advantage of hindsight. How are the great issues they raised changed by the discovery of general relativity and quantum mechanics? I have adapted Poincaré’s discussion somewhat to match the requirements of a timeless theory (he considered only the possibility of eliminating absolute space).

(3) Since writing Box 3, which draws attention to the present unsatisfactory use of absolute dislance in physics, I have discovered a way to create dynamical theories in which distance is not absolute. This is achieved by a very natural extension of the best-matching idea described later in the book. The new insights that I mention in the Preface are in part connected with this development. One of the most exciting is that, if such theories do indeed describe the world, gravitation and the other forces of nature are precisely the mechanism by means of which absolute distance is made irrelevant. Since this work is still in progress, I shall make no attempt to describe it in detail, but I shall keep my website (www.julianbarbour.com) up to date with any progress (see also p.358).

CHAPTER 6: THE TWO GREAT CLOCKS IN THE SKY

The Inertial Clock (p. 99) Tait’s work, which I feel is very important, passed almost completely unnoticed. This is probably because two years later the young German Ludwig Lange introduced an alternative construction for finding inertial frames of reference, coining the expression ‘inertial system’. Lange deserves great credit for bringing to the fore the issue of the determination of such systems from purely relative data, but Tait’s construction is far more illuminating. Lange’s work is discussed in detail in Barbour (1989) and Tait’s in Barbour (forthcoming).

The Second Great Clock (p. 107) A very nice account of the history of the introduction of ephemeris time was given by the American astronomer Gerald Clemence (1957).

CHAPTER 7: PATHS IN PLATONIA

Nature and Exploration (p. 109) For physicists and mathematicians who do not know the book, a wonderful account of the variational principles of mechanics, together with much historical material, is given by Lanczos (1986).

Developing Machian Ideas (p. 115) Translations of the papers by Hofrnann, Reissner and Schrödinger, along with other historical and technical papers on Mach’s principle, can be found in Barbour and Pfister (1995).

Exploring Platonia (p. 115) The special properties of Newtonian motions with vanishing angular momentum were discovered independently of the work of Bertotti and myself by A. Guichardet in the theory of molecular motions and by A. Shapere and E Wilczek in the theory of how micro-organisms swim in viscous fluids! A rich mathematical theory has meanwhile developed, and is excellently reviewed in the article by Littlejohn and Reinsch (1997), which contains references to the original work mentioned above. All mathematical details, as well as references to the earlier work by Bertotti and myself, can be found in Barbour (1994a).

CHAPTER 8: THE BOLT FROM THE BLUE

Historical accidents (p. 123) Poincaré’s paper can be found in his The Value of Science, Chapter 2. Pais’s book is in the Bibliography.

Background to the Crisis (p. 124) The best (moderately technical) historical background to the relativity revolution that I know of is the book by Max Born. It is available in paperback.

The Forgotten Aspects of Time (p. 135) My claims about the topics that somehow escaped Einstein’s attention are spelled out in detail in Barbour (1999, forthcoming). I have tried to make good the gap in the literature on the theory of clocks and duration in Barbour (1994a).

CHAPTER 10: THE DISCOVERY OF GENERAL RELATIVITY

Einstein’s Way to General Relativity (p. 151) Einstein’s papers and correspondence are currently being published (with translations into English) by Princeton University Press. The letter to his wife mentioned in this section can be found in the first volume of correspondence (Stachel et al. 1987).

CHAPTER 11: GENERAL RELATIVITY: THE TIMELESS PICTURE

Platonia for Relativity (p. 167) This is a technical note about the definition of superspace. The equations of general relativity lead to a great variety of different kinds of solution, including ones in which there are so-called closed time-like loops. These are solutions in which a kind of time travel seems to be possible. The question then arises of whether a given solution of general relativity—that is, a space-time that satisfies Einstein’s equations—can be represented as a path in superspace, in technical terms, as a unique succession of Riemannian three-geometries. If this is always so, then superspace does indeed seem a natural and appropriate concept. Unfortunately, it is definitely not so. There are two ways in which we can attempt to get round this difficulty. We could say that classical general relativity is not the fundamental theory of the universe, since it is not a quantum theory. This allows us to argue that superspace is the appropriate quantum concept and that it will allow only certain ‘well-behaved’ solutions of general relativity to emerge as approximate classical histories. For these, superspace will be an appropriate concept. Alternatively, we could extend the definition of super-space to include not only proper Riemannian 3-geometries (in which the geometry in small regions is always Euclidean), but also pscudo-Riemannian 3-geometries (in which the local geometry has a Minkowski type signature), and also geometries in which the signature changes within the space. For the reasons given in the long note starting on p. 348 below, I prefer the second option.

The above note was written before my new insights mentioned at the end of the Preface. I now believe that there is a potentially much more attractive resolution of the difficulty: the true arena of the world is not superspace but conformal superspace, which I describe on p. 350.

Catching Up with Einstein (1) (p. 175) Figure 30 is modelled directly on well-known diagrams in Wheeler (1964) and Misner et al. (1973).

(2) Technical note: Einstein’s field equations relate a four-dimensional tensor formed from geometrical quantities to the four-dimensional energy-momentum tensor, which is formed from the variables that describe the matter. Machian geometrodynamics shows how these four-dimensional tensors are built up from three-dimensional quantities. The two principles by which this is done are best matching, and Minkowski’s rule that the space and time directions must be treated in exactly the same way (see the following note). As far as I know, the mathematics of how this is done when matter is present was first spelled out in a recent paper by Domenico Giulini (1999), to whom I am indebted for numerous discussions on this and many other topics covered in this book.

A Summary and the Dilemma (1) (p. 177) This is another technical note. My image of space-time as a tapestry of interwoven lovers rests on the following property of Einstein’s field equations. If, in any given space-time that is a solution of the field equations, we lay out an arbitrary four-dimensional grid in any small region of the space-time, we can then, in principle, attempt to take the data on one three-dimensional hypersurface and use Einstein’s equations to evolve these data and recover the space-time in the complete region. Normally, we attempt to do this in a time-like direction. However, the form of the equation is exactly the same whichever direction in which we choose to attempt the evolution from initial data. This is an immediate consequence of an aspect of the relativity principle that Minkowski gave a special emphasis: as regards the structure of the equations, whatever holds for space holds for time and vice versa.

What is more, however we choose the ‘direction of attempted evolution’, Einstein’s equations always have a very characteristic structure. There are ten equations in all. One of them does not contain any derivative with respect to the variable in which we are going to attempt the evolution. Three of them contain only first derivatives with respect to that variable. The remaining six equations contain second derivatives with respect to it and have the form of equations that are suitable for evolution in the chosen direction. But we must first solve the other four equations, which are so-called constraints. Unless the initial data satisfy these four equations, evolution is impossible.

There are two ways to look at a space-time that satisfies Einstein’s equations: either as a structure obtained from initial data that have been (somehow) obtained in a form that satisfies the constraints and then built by the more or less conventional evolution equations, or as a structure that satisfies everywhere the constraints however we choose to draw the coordinate lines. In the second way of looking at space-time, conventional evolution does not come into the picture at all. Much suggests that this is the more fundamental way of looking at Einstein’s equations (see, in particular, Kuchaf’s beautiful 1992 paper).The connection with my timeless way of thinking about general relativity is expressed by the fact that the three constraint equations containing only first derivatives of the evolution variable are precisely the expression of the fact that a best-matching condition holds along the corresponding ‘initial’ hypersurface, while the fourth constraint equation, containing no derivatives of the evolution variable, expresses the fact that proper time is determined in geometrodynamics as a local analogue of the astronomers’ ephemeris time. It is this complete freedom to draw coordinate lines as we wish and, at least formally, to attempt evolution in any direction, that makes me feel that the second alternative envisaged in the Platonia for Relativity note is appropriate. I think it is also very significant that Einstein’s equations have the same form whatever the signature of space-time. The signature is not part of the equations, it is a condition normally imposed on the solutions. The demonstration that Einstein’s general relativity is the unique theory that satisfies the criterion (mentioned at the end of this section) of a higher four-dimensional symmetry was given by Hojman et al. (1976).

1 mentioned on p. 346 at the end of the notes on Chapter 4 my recent discovery of a way to create dynamical theories of the universe in which absolute distance is no longer relevant. My Irish colleague Niall Ó Murchadha, of University College Cork, and I are currently working on the application of the new idea to theories like general relativity, in which geometry is dynamical. There is a possibility that this work will not only give new insight into the structure of general relativity, in which a kind of residual absolute distance does play a role, but also lead to a rival alternative theory in which no distance of any kind occurs.

The key step is to extend the principle of best matching from superspace to so-called conformal superspace. In the context of geometrodynamics, this is analogous to the passage from Triangle Land to Shape Space as described in Box 3. However, whereas in Box 3 it is only the overall scale that is removed, and it is still meaningful to talk about the ratios of lengths of sides, the transition to conformal superspace is much more drastic and removes from physics all trace of distance comparison at spatially separated points.

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.

CHAPTER 21: THE MANY-INSTANTS INTERPRETATION

Bell’s ‘Many-Worlds’ Interpretation (p. 299) In his ‘cosmological interpretation’ of quantum mechanics, Bell combined elements derived from both Everett and the de Broglie-Bohm interpretation (see the note to Chapter 19). In fact, Bell’s account of his mixed interpretation is rather terse, and can be misunderstood. I am most grateful to Fay Dowker and Harvey Brown for drawing my attention to an error I made in reporting Bell’s idea in my first draft of this book. In this section I follow their interpretation of Bell, which I am sure is what he did mean.

The Many-Instants Interpretation (p. 302) I hope I have made it clear that probability ‘to be experienced’ or ‘to exist’ is a problematic concept. If consciousness is determined by structure, the consciousness is already in the Nows and must be experienced irrespective of their probabilities. What role remains for probabilities? It is a very difficult issue. Probability is already puzzling in ordinary quantum mechanics, and even in classical physics. Cold water could boil spontaneously, but we never see this happen. Standard probability arguments suggest that what is possible but hugely improbable will not be experienced. Much suggests that probabilities in some form are inescapable in quantum theory simply because it explores mutually exclusive possibilities. Instants of time are natural candidates for the ultimate exclusive possibilities. If certain very specially structured instants do get hugely larger probabilities than others, and are the ones habitually experienced, that must, I feel, count as explanation. But as an indication of the depth of this problem, I add here in Box 16 an edited email exchange I had with Fay Dowker of Imperial College, London. I had especially asked her to read my first draft, since she is a very clear thinker but is sceptical about both many worlds and canonical quantization, the approach to quantum gravity that I favour.

CHAPTER 22: THE EMERGENCE OF TIME AND ITS ARROW

Soccer in the Matterhorn (p. 307) In the second edition of The Physical Basis of the Direction of Tune, Zeh says that the intrinsic dynamical asymmetry of quantum gravity ‘offers the possibility of deriving an arrow of time (perhaps even without imposing any special conditions)’.

Timeless Descriptions of Dynamics (1) (p. 309) For specialists: for each stage of a perturbation expansion, Mott always chooses a kernel in an integral representation corresponding to outgoing waves. However, nothing in the mathematics rules out the (occasional) choice of incoming waves. This would mess up everything.

(2) (p. 309) I should emphasize that Mott, like Bell, never used any expression like ‘time capsule’, and clearly did not think in such terms about alpha-particle tracks. Neither did Mott’s work on alpha-particle tracks seem to have prompted him to any intimations of a many-worlds type interpretation of quantum mechanics. I learned this from Jim Hartle. Over a decade ago, when collaborating with Stephen Hawking in Cambridge, Jim lodged at his college, Gronville and Caius (featured famously in Chariots of Fire), which was also Mott’s college. Over dinner Jim asked Mott whether his paper had not led him to anticipate some form of Everett’s idea, and was told no. Apparently, all the ‘young Turks’ followed the Copenhagen line without hesitation at that time. Shortly before his death about two years ago, when he was still mentally very alert, I contact Mott and asked if I could talk to him about his paper. Alas, he was too ill to keep the appointment, telling his secretary he was very disappointed ‘since the man wanted to talk about work I did nearly sixty years ago’.

A Well-Ordered Cosmos? (p. 321) This final section follows closely the final section of Barbour (1994a).

BOX 16 An Email Dialogue

DOWKER. It seems to me that you provide no scheme for making predictions, and I would further claim that no such scheme can exist which contains the two aspects that are fundamental to your scheme: canonical quantum gravity (CQG) and the Bell version of the many-worlds interpretation (MWI).

BARBOUR. I think you are right, subject to what one means by prediction. I cannot make the kinds of prediction you want, and you correctly identify the reasons. I feel the arguments for CQG and MWI outweigh desire for predictions of the kind you would like.

DOWKER. I freely admit that I am rather attached to the notion of the universe (and I) having had, and being about to have, a continuous history. But my criticism here is not the absence of history in your approach, but, to repeat, that there is no way to make predictions about the results of our observations. In my view this is a deficiency that cannot be overcome. Whatever else science tells us about the world, it must allow us to make predictions about our observations that we can check.

BARBOUR. I am not sure we can impose such a criterion on Nature. The Greeks had the notion of saving appearances (finding a rational explanation for the phenomena we observe) that is already very valuable. You may be asking more of Nature than she is prepared to give.

DOWKER. In backing up this criticism I shall focus on the aspect that I am most familiar with and on which I have most confidence in my own views, which is the aspect of the interpretation of quantum mechanics. I am pleased that your book draws attention to the work of Bell on the many-worlds interpretation, since it has not had the recognition it deserves. In my view his version is the only well-defined many-worlds interpretation (I’ll call it BMWI) that exists in the literature.

BARBOUR. I agree it is well defined, but with reservations about the role of time. The time of an observation, like any other observable, must be extracted from present records. When you start to ask how that is done in practice and how Nature does put time into the records, I think things may become less well defined. I do believe that almost all physicists this century have blindly followed Einstein in declining to try to understand duration at a fundamental level. A lot of the first part of my book is about that. I think my position might be stronger than you realize.

DOWKER. I think that neither your version (which I’ll call JMWI) nor BMWI allows us to make predictions about what we observe (so I disagree with Everett’s statement ‘the theory itself predicts that our experience will be what it in fact is’). Let me take your version. There we have many configurations at time t. The most serious problem is that in a scheme like yours, in which all the possibilities are realized, there is no role for the probabilities. The usual probabilistic Copenhagen predictions for the results of our observations cannot be recovered. An excellent reference which analyses the MWI literature and the various attempts to derive the Born interpretation from MWI is Adrian Kent [1990, International Journal of Modern Physics, A5, 1745]. Adrian concludes that they fail. I’ll just state again the main reason that they fail: when all the elements in a sample space of possibilities are realized, then probability is not involved. Your idea is that it is the sample space itself, i.e. how many copies of each configuration are included in the sample space, which is determined by the (squares of the) coefficients of the terms in the wave function. That is all well and good (if bizarre). But there’s no reason then to call those numbers probabilities, and no way to recover the probabilistic predictions of Copenhagen quantum mechanics. In fact the MWI proponents themselves agree that the failure to reproduce the Copenhagen predictions is a problem and do try to address it, but without success.

BARBOUR. I accept that this is a strong critique. I nevertheless feel that my scheme does in principle have predictive strength. If you could see Platonia and Born’s probability density concentrated incredibly strongly on a tiny proportion of its points that all turn out to be time capsules as I define them and Bell describes them, would you not find that impressive, and something like a rational explanation for our experiences?

DOWKER. As well as the MWI, you base your conjecture of timelessness on the technical result that when a canonical quantization scheme is applied to general relativity, the wave function cannot contain the time. My understanding of the state of affairs in canonical quantum gravity is that, because of this, no one knows how to make the kind of predictions we’d like to make: explanations such as ‘What happens in the final stages of black hole collapse?’, ‘Why is the cosmological constant so very small?’, etc.

BARBOUR. I agree with your first example (and do not think it is too serious—there may be questions that it is just not sensible to ask), but in principle my scheme could predict that virtually all time capsules will appear to have been created in nearly classical universes with a very small cosmological constant. After all, that is what our present records indicate. If all probable configurations seem to contain records that indicate a small cosmological constant, I am okay.

DOWKER. My reaction to the situation is that formulating general relativity in a canonical way has been shown to be the wrong thing to do—we did what we weren’t supposed to—divided up space-time into space and time again. Even if it wasn’t clear from the beginning that it would be incredibly difficult to maintain general covariance of the theory whilst trying to treat space and time differently, I find the lack of any insight into how to recover predictions within the canonical quantum gravity program convinces me that we should look elsewhere for a quantum theory of gravity.

BARBOUR. As he was creating general relativity, Einstein was convinced general covariance had deep physical significance. Two years later, correctly in my opinion, he completely abandoned that position. In my opinion, general covariance is an empty shell (I say something about this at the end of Chapter 10 and in the notes to it). I believe it is not possible to give any meaning to the objective content of general relativity without saying how the three-dimensional slices in space-time are related to each other. That is the very content of the theory. That is why I think the arguments for canonical quantum gravity are very strong indeed. The constraints of the canonical theory are its complete content.

DOWKER. Having made my basic points, let me now just say that I find it incredibly hard to understand how, as a solipsist of the moment, you must view science and the scientific enterprise.

BARBOUR. Answered above I think. Science should explain what we observe. We habitually observe and experience time capsules. Even granting the real difficulties with calling the square of a static amplitude a probability, should it turn out that the Wheeler-DeWitt equation does strongly concentrate the square of the amplitude on time capsules, I think that would be an incredibly strong and suggestive result.

DOWKER. Take the idea that a good scientific theory should be falsifiable.

BARBOUR. I think my idea is falsifiable in the following sense. There may well be configurations of the universe with records of my idea and mathematical proofs that the Wheeler-DeWitt equation most definitely does not concentrate the square of the amplitude on time capsules. If I too am in them, I would have to say my proposal for an explanation of why we think time flows has failed.

DOWKER. That presupposes that there will be a future in which we can try new experiments that test the theory and find that these experiments may be in contradiction to our predictions. The very word ‘prediction’, which I have used so many times in this letter, is laden with time-meaning. A prediction is a statement of expectation of something that will happen. Prediction is the lifeblood of science. How could we do science without it?

BARBOUR. I totally agree about the importance of prediction. But it does not necessarily have to involve time in the way you suggest. From observations of one side of the Moon, astronomers tried to predict what was on the other side. They got it wrong when the other side was seen. I do not think time comes into such predictions at all significantly. Consider, as Jim Hartle once did when he was quite close to my present position, geology. The rocks of the Earth hardly change. Suppose the idea of continental drift had been proposed before America had been discovered. It would have predicted the existence of America and the geology of its east coast (the west of Ireland exactly matches Newfoundland, I believe). Again, time is not essentially involved in this prediction. I think Bell puts my case very well: ‘We have no access to the past. We have only our “memories” and “records”. But these memories and records are in fact present phenomena.’ The italics are Bell’s. Predictions are always verified in the present. That is my apologia.

Notes Added for This Printing.

As mentioned at the end of the Preface and at various places in the Notes, there have been some promising developments of the ideas presented in this book since it was sent to press in spring 1999. They are contained in two joint papers published electronically and available on the web: Julian Barbour and Niall Ó Murchadha, ‘Classical and quantum gravity on conformal superspace’, http//xxx.lanl.gov/abs/gr-qc/9911071 and Julian Barbour, Brendan Z. Foster, and Niall Ó Murchadha, ‘Relativity without relativity’, http//xxx.lanl.gov/abs/gr-qc/0012089 [the xxx is correct].

The potential significance of the first paper has already been explained on p. 349/350. At this stage, I do not wish to make any firm statements about this new work since it is incomplete and has not yet been exposed to scrutiny by other physicists, but I can at least give some idea of what is at stake. The basic issue is the status of the relativity principle. When Einstein and Minkowski created special relativity, they deliberately made no attempt to explain the remarkable structure that their work had brought to light: the existence of spacetime and its associated light cone, both being reflected in the Lorentz invariance of the laws of nature. They adopted Lorentz invariance, which assumes the existence of length, as the basis of physics. In small regions of spacetime, this still remains true in general relativity.

Taken together the two papers cited above suggest that all of the presently known facts of relativity and electromagnetism can be derived in a new and hitherto unsuspected manner from three assumptions: 1) an independent time plays no role in dynamics; 2) best matching (pp. 116/7) is the essential element in the action principle of the universe; 3) any theory satisfying these principles must have nontrivial solutions. It is the third assumption that makes a dramatic difference. Hitherto, in common with other colleagues, I had assumed (see p. 181) many different theories could satisfy the first two conditions, but, as my collaborator Niall Ó Murchadha discovered, this is not the case. The reasons for this and its remarkable potential consequences are spelled out in the second cited paper. It is frustrating not to be able to say more at the present moment, but at a time of uncertainty about the final outcome it is better to say less rather than too much. My website (julianbarbour.com) will carry more detailed information.

I conclude with some additional comments that have mostly already appeared in the UK paperback.

My website now carries an email dialogue between myself and Don Page (whom Hawking, in A Brief History of Time, credits with pointing out, with Raymond Laflamme, ‘his greatest blunder’). I think Don has made some interesting and valuable comments, including both valid criticism of some points but also reassurance on other issues on which I had doubts. Don is another person who takes the timelessness of physics utterly seriously, and, in fact, our views are very close. He has written several papers on the problem of consciousness and quantum mechanics (Sensible Quantum Mechanics). Full details can be found on my website. I should also like to mention here an idea that Dieter Zeh put forward in the meeting at Huelva in Spain at which I conducted my straw poll. This is that the universe must, of necessity, always be observed as expanding. I find this an intriguing idea and, if it is correct, it would fit beautifully with the open-ended, flowerlike structure of Platonia. I think Dieter’s idea, which I hope is correct though I have hedged my bets in this book, influenced me somewhat in the writing of Box 3 and parts of the Epilogue.

I regret that in the final chapter I made no mention of the idea of inflation, which is explained in a gripping and candid book by Alan Guth that I have at least now included in the books recommended for further reading. From reading Guth’s book I also learned that an interesting proposal of a mechanism for the ‘creation of the universe’ was made by Edward Tryon in 1973. I should also have mentioned that in 1982 Alexander Vilenkin proposed an influential alternative proposal to Hawking’s no-boundary idea (1981) and that Jim Hartle played a significant role in its development, which culminated the Hartle-Hawking wave function. My apologies to these authors (none of whom have registered any complaint). Details can be found in Guth’s book.

It has also been pointed out to me by several email correspondents that there is a clear anticipation of some of my ideas about time in Fred Hoyle’s novel October the First Is Too Late, which Paul Davies discusses in his About Time. Sir Fred’s ‘pigeonholes’ are essentially my time capsules. American reviewers and correspondents also noted a similarity with the philosophy of time that underlies Kurt Vonnegut’s Slaughterhouse Five. Having now read the book, I can confirm that this is the case. Of course, as I make clear in the text, John Bell also formulated the idea of time capsules (without giving them any name) quite clearly long before me. Another correspondent, Andrew Clifton, regretted that I had not devoted at least a few words to demolishing the idea that there really is a ‘moving present’. I think he was right. Happily, David Deutsch has done the job very well in his The Fabric of Reality.

I should also like to thank Damien Broderick, who has reviewed my book for The Australian, for drawing my attention to various misprints.

It is also now clear to me that in the body of the text I should have said more about possible ways in which my ideas could be refuted. A theory is no use to science unless it is capable of disproof. In the email exchange with Fay Dowker, I did mention the possibility of mathematical disproof of my conjecture that the Wheeler—DeWitt equation concentrates its solutions on time capsules. However, I think that (in normal parlance) that might take decades. Something that might occur much sooner is a completely convincing definitive form of superstring theory (or some other unified theory) that reintroduces an external time (string theory does currently use background structures). That would kill my idea. My own feeling is that in fact superstring theory will, if and when it is found, turn out to be timeless.

Then there is one other quite different way in which my ideas could be disproved. This is if experimental evidence can be found that shows collapse of the quantum wave function to be a real physical process. In this connection, I should like to mention especially an experiment proposed by Roger Penrose to test this very possibility. He is developing it in collaboration with Anton Zeilinger, the Austrian physicist based in Vienna, who has performed so many incredibly beautiful quantum experiments. Penrose, very understandably, finds the many-worlds interpretation of quantum mechanics extremely hard to accept (see my comments about the death of Diana), and with great persistence is trying to find a way round it. He has certainly identified the greatest single issue in modern physics. If his experiment, which could perhaps be performed within a decade, works out in the way he hopes, it will be a huge development and destroy my approach (because it will show that quantum mechanics does not hold macroscopically). The volume containing my paper (Barbour 2000) also contains Penrose’s most important paper on the subject, and also a related paper by Joy Christian, who was a student of Abner Shimony. Joy, following Abner (see my Epilogue), is trying to establish transience as a real physical thing. I think that if collapse of the wave function could be demonstrated as a real physical phenomenon, that would be true demonstration of something that one might call transience.

JB

January 2001