The End of Time: The Next Revolution in Physics

CHAPTER 3

A Timeless World

FIRST OUTLINE

Now I want to start on the attempt to show you that, at least as a logical possibility, the appearance of time can arise from utter timelessness. I shall do this by comparing two imaginary exercises. I begin by presenting you with two bags, labelled Current Theory and Timeless Theory. When you open them up, you find that each bag is filled with cardboard triangles, all jumbled up. Now, triangles come in all shapes and sizes. The first thing you notice is that the first bag contains far fewer triangles than the second. Closer examination reveals that the two collections are very different. Let me begin by describing the contents of Current Theory.

First, you notice that it contains triangles of all different sizes. There is a smallest triangle, very tiny; then another very like it, but a little larger and with a slightly different shape; and so on. In fact, you soon realize that you can lay out all the triangles in a sequence. The order in which they should go is clear because each successive triangle differs only slightly from its predecessor. Their increasing size makes the ordering especially easy. Of course, a real bag can contain only finitely many triangles, but I shall suppose that there are infinitely many and that the sequence is endless, the triangles getting ever larger.

Such a sequence of triangles is like the sequence of experienced instants that I suggested ‘photographing’. It is also like the succession of Newtonian instants from the moment God decided to create the universe, or the succession of states of the universe expanding out of the Big Bang, represented by the smallest triangle. In fact, the contents of Current Theory correspond to the simplest Newtonian universe that can begin to model the complexity of the actual universe: three mass points moving in absolute space and time, as in Figure 1. Initially very close to each other, they move apart so rapidly that gravity cannot pull them back, and they fly off to infinity.

According to Newton, the three mass points are, at all instants, at certain positions in absolute space and form certain triangles. The triangles tell us how the points are placed relative to one another, but not where they are in absolute space. It is such triangles, represented in cardboard, that I imagine have been put into the Current Theory bag. Since we cannot experience absolute space and time directly, I have tried to match the model more closely to our actual experience. The sequence of triangles corresponds to one possible history. There could be many such histories that match the dual scheme of laws and initial conditions. But we find only one in the Current Theory bag.

Next, we examine the Timeless Theory bag. There are two big differences. First, it contains vastly more triangles (it could, in fact, contain all conceivable triangles). More significantly, there are so many of them that it is quite impossible to arrange them in a continuous sequence. Second, the triangles are present in multiple copies. That is, we might, after a very extensive search, find ten identical copies of one particular triangle, two of another, and ten million of yet another. That is really the complete story. It is all that most people would notice.

I think you will agree that the Current Theory bag does match experience quite closely. The triangles stand for each of the instants you experience, and they follow one another continuously, just as the instants do. By giving them to you in a bag and getting you to lay them out in a sequence, I am giving you a ‘God’s eye’ view of history. All its instants are, as it were, spread out in eternity as if you surveyed them from a mountain-top. In fact, this way of thinking about time has long been a commonplace among Christian theologians and some philosophers, and has prompted them to claim that time does not exist but that its instants all exist together and at once in eternity. My claim is much stronger. I am saying that reality, if we could see all of it, is not at all like the contents of the Current Theory bag with its single sequence of states. It is like the contents of the Timeless Theory bag, in which in principle all conceivable states can be present. Nothing in it resembles our experience of history as a unique sequence of states: that experience is usually explained by assuming that there is a unique sequence of states. I deny that there is such a sequence, and propose a different explanation for the experience that prompts us to believe in it. The only thing the bags have in common with our direct experience of time is the parallel between individual triangles as models of individual instants of time.

Actually, the bags share another property – their contents satisfy a law. Given the sequence of triangles of the first bag, clever mathematicians could deduce that they correspond to the triangles formed by three gravitationally interacting bodies. They could even reconstruct the bodies’ positions in absolute space, and the amount of time that elapses between any two of the triangles in the sequence. With the second bag, mathematicians would discover that the numbers in which the different triangles occur are not random – chosen by chance – but satisfy a law. The numbers vary from triangle to triangle in an ordered fashion. But at first glance at least, this law seems to have no connection with the law that creates the unique sequence of triangles in the first bag. Also, there is nothing like the dual scheme of law and initial condition that creates the sequence of the first bag. In a sense that I shall not yet try to explain, there is just a law, with nothing like an initial condition that has to be added to it.

How is the appearance of time ever going to emerge from the contents of the Timeless Theory bag as just described? Bare triangles lying in a jumbled heap certainly cannot make that miracle happen. Triangles have a structure that is much too simple. This is why I said that rich structure ordered in a special way is an essential element if a notion of time is to emerge. If, when we open the Timeless Theory bag, we find it contains, not triangles, but vastly richer structures, some of which are time capsules in the sense I have defined, my task does not seem quite so hopeless. By definition, time capsules suggest time. But finding just a few time capsules in a vast heap of otherwise nondescript structures will not get me very far.

This is where the assumption that all the structures found in the bag come in multiple copies, and that the numbers of these copies, which can vary very widely, are determined by a definite timeless rule, becomes crucial. Imagine that all the structures for which the numbers of identical copies in the bag are large are time capsules, while there are few copies of structures that are not time capsules. Since the overwhelming majority of possible structures that can exist are certainly not time capsules, any rule that does fill the bag with time capsules will be remarkably selective, creative one might say. If, in addition, you can find evidence that the universe is governed by a timeless law whose effect is to discriminate between structures and which actually selects time capsules with surprising accuracy, then you might begin to take such ideas more seriously. You might begin to see a way in which the Timeless Theory could still explain our experience of time, and could perhaps be superior to the Current Theory.

However, you will probably dismiss such a possibility as the wildest fantasy. Why should Nature go to such contrived lengths simply to create an impression of time and fool poor mortals? To counter this natural reaction, let me give a little more detail about those hints of the non-existence of time that I mentioned in Chapter 1. This may at least persuade you that some dramatic change could be in the offing.

THE CRISIS OF TIME

Physics is regarded as the most fundamental science. It is an attempt to create a picture of reality as we should see it if we could, somehow, step out of ourselves. For this reason it is rather abstract. In addition, it often deals with conditions far removed from everyday human experience – deep inside the atom, where quantum theory holds sway, and in the farflung reaches of space, where Einstein’s general relativity reigns. The ideas I want to tell you about have come from attempts during the last forty years to unite these two realms (Box 2). They have produced a crisis. The very working of the universe is at stake: it does not seem to be possible, in any natural and convincing way, to give a common description of them in which anything like time occurs.

Frustratingly little progress has been made. However, in 1967 a possible picture did emerge from a paper by the American Bryce DeWitt. He found an equation that, if his reasoning is sound, describes the whole universe – both atoms and galaxies – in a unified manner. Because John Wheeler, the American physicist who coined the term ‘black hole’, played a major part in its discovery, this equation is called the Wheeler-DeWitt equation. It is controversial in at least three respects. First, many experts believe that the very derivation of the equation is flawed – that it was obtained by an invalid procedure. Second, the equation is not yet even properly defined, as there are still many technical difficulties to be overcome. In fact, it is more properly regarded as a conjecture: a tentative proposal for an equation that is not yet proved. And third, the experts argue interminably over what meaning it might have and whether it can ever be promoted to the status of a bona fide equation. Ironically, DeWitt himself thinks that it is probably not the right way to go about things, and he generally refers to it as ‘that damned equation’. Many physicists feel that a different route, through so-called superstring theory, which it is hoped will establish a deep unity between all the forces of nature, is the correct way forward. That many of the best physicists have concentrated on superstring theory is probably the main reason why the ‘crisis of time’ brought to light by the Wheeler-DeWitt equation has not attracted more attention. However, there is no doubt that the equation reflects and unifies deep properties of both quantum theory and general relativity. Quite a sizeable minority of experts take the equation seriously. In particular, much of the work done by Stephen Hawking in the last twenty years or so has been based on it, though he has his own special approach to the problem of time that it raises.

For now, all I want to say about the Wheeler-DeWitt equation is that if one takes it seriously and looks for its simplest interpretation, the picture of the universe that emerges is like the contents of the Timeless Theory bag. For a long time, physicists shied away in distrust from its apparently timeless nature, but during the last fifteen years or so a small but growing number of physicists, myself included, have begun to entertain the idea that time truly does not exist. This also applies to motion: the suggestion is that it too is pure illusion. If we could see the universe as it is, we should see that it is static. Nothing moves, nothing changes. These are large claims, and the bulk of my book will discuss the arguments from physics (presented as simply as I can) that lead me and others to such conclusions. At the end, I shall outline, through the notion of time capsules, a theory of how a static universe can nevertheless appear to teem with motion and change.

Now I want to give you a better feel for what a timeless universe could be like. What we need first is a proper way to think about Nows.

THE ULTIMATE ARENA

One issue that runs through this book is this: what is the ultimate arena of the universe? Is it formed by space and time (space-time), or something else? This is the issue raised by Dirac’s sentence I quoted in the Preface: ‘This result has led me to doubt how fundamental the four-dimensional requirement in physics is.’ I believe that the ultimate arena is not space-time. I can already begin to give you an idea of what might come in its place.

I illustrated the Newtonian scheme by a model universe of just three particles. Its arena is absolute space and time. The Newtonian way of thinking concentrates on the individual particles: what counts are their positions in space and time. However, Newton’s space and time are invisible. Could we do without them? If so, what can we put in their place? An obvious possibility is just to consider the triangles formed by the three particles, each triangle representing one possible relative arrangement of the particles. These are the models of Nows I asked you to contemplate earlier. We can model the totality of Nows for this universe by the totality of triangles. It will be very helpful to start thinking about this totality of triangles, which is actually an infinite collection, as if it were a country, or a landscape.

If you go to any point in a real landscape, you get a view. Except for special and artificial landscapes, the view is different from each point. If you wanted to meet someone, you could give them a snapshot taken from your preferred meeting point. Your friend could then identify it. Thus, points in a real country can be identified by pictures. In a somewhat similar way, I should like you to imagine Triangle Land. Each point in Triangle Land stands for a triangle, which is a real thing you can see or imagine. However, whereas you view a landscape by standing at a point and looking around you, Triangle Land is more like a surface that seems featureless until you touch a point on it. When you do this, a picture lights up on a screen in front of you. Each point you touch gives a different picture. In Triangle Land, which is actually three-dimensional, the pictures you see are triangles. A convenient way of representing Triangle Land is portrayed in Figures 3 and 4.

I have gone to some trouble to describe Triangle Land because it can be used to model the totality of possible Nows. Like real countries, and unlike absolute space, which extends to infinity in all directions, it has frontiers. There are the sheets, ribs and apex of Figure 4. They are there by logical necessity. If Nows were as simple as triangles, the pyramid in Figure 4 could be seen as a model of eternity, for one notion of eternity is surely that it is simply all the Nows that can be, laid out before us so that we can survey them all.

Figure 3 The seven triangles represent several possible arrangements of a model universe of three particles A, B, C. Each triangle is a possible Now. Each Now is associated with a point (black diamond) in the ‘room’ formed by the three grid axes AB, BC, CA, which meet at the corner of the ‘room’ farthest from you. The black diamond that represents a given triangle ABC is situated where the distance to the ‘floor’ is the length of the side AB (measured along the vertical axis), and the distances to the two ‘walls’ are equal to the other two sides, BC and CA. The dash-dotted lines show the grid coordinates. In this way, each model Now is associated with a unique point in the ‘room’. As explained in the text, if you ‘touched’ one of the black diamonds, the corresponding triangle would light up. However, not every point in the ‘room’ corresponds to a possible triangle – see Figure 4.

A three-particle model universe is, of course, unrealistic, but it conveys the idea. In a universe of four particles, the Nows are tetrahedrons. Whatever the number of particles, they form some structure, a configuration. Plastic balls joined by struts to form a rigid structure are often used to model molecules, including macromolecules such as DNA, which are ‘megamolecules’. You can move such a structure around without changing its shape. For any chosen number of balls, many different structures can be formed. That is how I should like you to think about the instants of time. Each Now is a structure.

Figure 4 This shows the same ‘room’ and axes as in Figure 3, but without the walls shaded. Something more important is illustrated here. In any triangle, no one side can be longer than the sum of the other two. Therefore, points in the ‘room’ in Figure 3 for which one coordinate is larger than the sum of the other two do not correspond to possible triangles. All triangles must have coordinates inside the ‘sheets’ spanned between the three ‘ribs’ that run (towards you) at 45° between the three pairs of axes AB, BC (up to the left), AB, CA (up to the right) and BC, CA (along the ‘floor’, almost towards you). Points outside the sheets do not correspond to possible triangles. However, points on the sheets, the ribs and the apex of the pyramid formed by them correspond to special triangles. If vertex A in the thin triangle at the bottom right of Figure 3 is moved until it lies on BC, the triangle becomes a line, which is still just a triangle, because BC is now equal to (but not greater than) the sum of CA and AB. Such a triangle is represented by a point on one of the ‘sheets’ in Figure 4. If point A is then moved, say, towards 8, the point representing the corresponding triangle in Figure 4 moves along the ‘sheet’ to the corresponding ‘rib’, which represents the even more special ‘triangles’ for which two points coincide. Finally, the apex, where the three ribs meet in the far corner of the ‘room’, corresponds to the unique and most special case in which all three particles coincide. Thus, Triangle Land has a ‘shape’ which arises from the rules that triangles must satisfy. The unique point at which the three particles coincide I call Alpha.

For each definite collection of structures – triangles, tetrahedrons, molecules, megamolecules – there is a corresponding ‘country’ whose points correspond to them. The points are the possible configurations. Each configuration is a possible thing; it is also a possible Now. Unfortunately it is impossible to form any sort of picture of even Tetrahedron Land: unlike Triangle Land, which has three dimensions, it has six dimensions. For megamolecules, one needs a huge number of dimensions. In Tetrahedron Land you could ‘move about’ in its six dimensions. As in my earlier example, the way to think about its individual points is that if you were to touch any one of them, a picture of the tetrahedron to which it corresponds would ‘light up’. In any Megamolecule Land, with its vast number of dimensions, ‘touching a point’ would cause the corresponding megamolecule to ‘light up’. The more complicated the structures, the greater the number of dimensions of the ‘land’ that represents them. However, the structures that ‘light up’ are themselves always three-dimensional.

You do not need to try to imagine these much larger spaces – Triangle Land will do. I hope you do not find it a dull structure or too hard to grasp. It is, in fact, an example of a very basic notion in physics called a configuration space that is normally regarded as too abstract to attempt to explain in books for non-scientists. But I cannot begin to get across to you my vision of a timeless universe without this concept. If you can get your mind round this concept – and I do encourage you to try – you will certainly understand a lot of my book. The notion of configuration space opens up a wonderfully clear way to picture, all at once, everything that can possibly be.

It will also give us new notions of time and history, stripping away and revealing as redundant the Newtonian superstructure. The observable history of a three-particle universe, when the invisible absolute space and time are abstracted away, is just a continuous sequence of triangles. Suppose we are given such a history. We can then mark, or plot, the points in Triangle Land that correspond to the triangles. We shall obtain a curve that winds around within the pyramid in Figure 4. In this new picture, history is not something that happens in time but a path through a landscape. A path is just a continuous track of points in a land. In this book I use the word path very often in the generalized sense of a continuous series of configurations taken by some system (consisting, usually, of material points). Understood in this sense, paths are possible histories. There is no time in this picture.

Paths highlight the dilemma brought to light by Boltzmann’s work. On any path, you can call the point where you stand Now. But you can walk along a path in either direction. There is nothing in the notion of a path that can somehow make it a one-way street. You can also see that the notion of a moving present may be redundant. You might try to represent it by a spot of light moving along the path, making each successive point on the path into the present Now, and therefore more real than the ‘past’, through which the spot has already passed, and the ‘future’, which the spot has not yet reached. But if, as I have suggested, all our conscious experiences have their origin in real structure within the Nows, we can do without the fiction of the moving present. The sense we have that time has advanced to the present Now is simply our awareness of being in that Now. Different Nows give rise to different experiences, and hence to the impression that the time in them is different.

I need a name for the land of Nows. Plato, who lived about a century after Heraclitus and Parmenides, taught that the only real things are forms or ideas: perfect paradigms, existing in a timeless realm. In our mortal existence we catch only fleeting glimpses of these ideal forms. Now each point – each thing – in these ‘countries’ I have asked you to imagine could be regarded as a Platonic form. Triangles certainly are. I shall call the corresponding ‘country’ Platonia. The name reflects its mathematical perfection and timeless landscape. Nothing changes in Platonia. Its points are all the instants of time, all the Nows; they are simply there, given once and for all.

Platonia is vast. Size alone is insufficient to convey its vastness. Triangle Land already has three dimensions, and stretches out to infinity from its apex and frontiers. That reflects the already huge number of ways in which three objects can be arranged in space. As the number of objects is increased, the number of ways in which they can be arranged increases incredibly fast. The numbers one encounters in astronomy are as nothing compared with the number of possible arrangements of large numbers of objects. The instants of time are numberless. And each is different.

There is a saying about time, apparently first expressed in a piece of graffiti and much loved by John Wheeler, that seems apt here: ‘Time is nature’s way of preventing everything from happening all at once.’ In a timeless world, verbs of becoming like ‘happen’ have no place. But if Nows are both concrete and distinct, it is a logical contradiction to suppose that they could ‘happen at once’, i.e. be superimposed on one another. I believe that the aphorism expresses a profound truth.

Developing the ‘Platonic’ theme, I conjecture that the actual universe in which we find ourselves corresponds to some Platonia. We have not yet fully grasped the structure of its points, its Nows. Perhaps we never shall, but I assume that in any instant what we experience, including the appearance of motion, is a transmuted representation of a part of one such Now. This is not far removed from Plato’s original idea that we mortals are like beings confined from birth to a cave, and that all we ever comprehend of the outside world and the real beings in it are the shadows they cast on the wall of our cave as they pass its entrance. I also think that Plato was right when he said that Being (one of his forms, one of my instants of time) is real, but that Becoming is an illusion. However, I go further than Plato in attributing the illusion of Becoming to something that is real – a special time-capsule structure of Nows. The illusion of Becoming has its basis in real structure in special Being.

Platonia is the arena that I think must replace space and time. Why this should be so, how it can be done, and what physics in Platonia is like is the meat of the book. But it is already possible to see how differently creation and a supposed beginning of time appear in Platonia. Most people are baffled that time could begin. How many times do we hear the question, ‘But what happened before the Big Bang?’ The question reveals the depth to which the notion of an eternally flowing time is ingrained in the psyche. This is why I call the instants of time ‘things’, so as to break the spell, and why I have chosen the name Platonia for our home. It is also why I use paths as the image of history. In itself, there are no paths in Platonia, just as there were no paths on Earth before animals made them. The points of Platonia – the Nows – are worlds unto themselves. No thread of time joins them up. We must think of Newtonian-type dynamics as something that ‘paints a path’ onto the timeless landscape of Platonia.

Once the instinctive notion of time is expunged, it is easy to see that history, as a path in Platonia, can certainly start or end. The path to Land’s End does terminate there: only the sea lies beyond. Triangle Land has a point like Land’s End: it is the apex of the pyramid, which in Figure 4 I called Alpha. Beyond it is nothing, not even sea. Looking for time before the Big Bang is like looking for Cornwall in the Irish Sea. If we think that time exists and increases or decreases along a path in Triangle Land that terminates at that apex, then we can see that time will certainly begin or end at that point. I think this is how we should think about the Big Bang. It is not in the past, it is at a kind of Land’s End.

All Platonias seem by necessity to possess a distinguished point like the apex of Triangle Land. This is why I call it Alpha. It is suggestive that Platonia has an Alpha but no Omega: there is no limit to the size or complexity of things that can exist. Triangle Land opens out from Alpha to infinity, as do all Platonias. To underline this fact, Figure 5 is my own attempt to give a somewhat more artistic and simultaneously realistic representation of the actual Platonia of our universe, which of necessity is vastly more richly structured than Triangle Land.

Now we must begin to consider how the notion of Platonia will change the way we think about such seemingly simple things as motion. How can it emerge from a scheme without a vestige of time? Is motion really a pure illusion? If we were in London yesterday and New York today, we must have moved. Motion must exist. Let me persuade you that it does not.

IS MOTION REAL?

We had a cat called Lucy, who was a phenomenal hunter. She could catch swifts in flight, leaping two metres into the air. She was seen in the act twice, and must have caught other victims since several times we found just the outermost wing feathers of swifts by the back door. Faced with facts like this, isn’t it ridiculous to claim there is no motion?

The argument seems decisive because we instinctively feel that Lucy has (or, rather had, since sadly she was killed by a car) some unchanging identity. But is the cat that leaps the cat that lands? Except for the changes in her body shape, we do not notice any difference. However, if we could look closely we might begin to have doubts. The number of atoms in even the tiniest thing we can see is huge, and they are in a constant state of flux. Because large numbers play a vital role in my arguments, I shall give two illustrations. Have you ever tried to form a picture of the number of atoms in a pea?

Figure 5 Triangle Land is like an inverted pyramid, with frontiers formed by special triangles as explained in Figure 4. Platonias corresponding to configurations of more than three particles have not only frontiers but also analogous internal topographic features. This illustration, based on the parachute of a salsify seed (shown life-size on left) from my wife’s garden, is an attempt to give some idea of the rich structure of the frontiers of Platonia. No attempt is made to represent the even richer internal structure. Platonia’s Alpha is where the ribs converge. Because Platonia has no Omega, the salsify ribs should extend out from Alpha for ever. (The wind carries the actual seeds rather efficiently into our neighbours’ gardens, where the progeny flourish, but they are not always welcome, although salsify is an excellent vegetable.)

Imagine a row of dots a millimetre apart and a metre long. That will be one thousand dots (10³). (Actually, it will be 1001, but let us forget the last 1.) One thousand such rows next to one another, also a millimetre apart, gives a square metre of dots, one million (10⁶) in total. The number of dots in one or two squares like that is about the number of pounds or dollars ordinary mortals like me can hope to earn in a lifetime. Now stack one thousand such squares into a cube a metre high. That is already a billion (10⁹). So it is surprisingly easy to visualize a billion. Five such cubes are about the world’s human population. Yet we are nowhere remotely near the number of atoms in a pea.

We shall keep trying. We make another cube of these cubes. One thousand of them stretched out a kilometre long takes us up to a trillion (10¹²). A square kilometre of them will be 10¹⁵ (about the number of cells in the human body), and if we pile them a kilometre high we get to 10¹⁸. We still have a long way to go. Make another row of one thousand of these kilometre cubes, and we get to 10²¹. Finally, make that into a square, one thousand kilometres by one thousand kilometres and a kilometre high – it would comfortably cover the entire British Isles to that height. At last we are there: the number of dots we now have (10²⁴) is around the number of atoms in a pea. To get the number in a child’s body, we should have to go up to a cube a thousand kilometres high. It hardly bears thinking about.

Equally remarkable is the order and organized activity in our bodies. Consider this extract from Richard Dawkins’s The Selfish Gene:

The haemoglobin of our blood is a typical protein molecule. It is built up from chains of smaller molecules, amino acids, each containing a few dozen atoms arranged in a precise pattern. In the haemoglobin molecule there are 574 amino acid molecules. These are arranged in four chains, which twist around each other to form a globular three-dimensional structure of bewildering complexity. A model of a haemoglobin molecule looks rather like a dense thornbush. But unlike a real thornbush it is not a haphazard approximate pattern but a definite invariant structure, identically repeated, with not a twig nor a twist out of place, over six thousand million million million times in an average human body. The precise thornbush shape of a protein molecule such as haemoglobin is stable in the sense that two chains consisting of the same sequences of amino acids will tend, like two springs, to come to rest in exactly the same three-dimensional coiled pattern. Haemoglobin thornbushes are springing into their ‘preferred’ shape in your body at a rate of about four hundred million million per second and others are being destroyed at the same rate.

If, as I think they must be, things are properly considered in Platonia, Lucy never did leap to catch the swifts. The fact is, there never was one cat Lucy – there were (or rather are, since Lucy is in Platonia for eternity, as we all are) billions upon billions upon billions of Lucys. This is already true for the Lucys in one leap and descent. Microscopically, her 10²⁶ atoms were rearranged to such an extent that only the stability of her gross features enables us to call her one cat. What is more, compared with her haemoglobin molecules the features by which we identified her – the sharp eyes, the sleek coat, the wicked claws – were gross. Because we do not and cannot look closely at these Lucys, we think they are one. And all these Lucys are themselves embedded in the vast individual Nows of the universe. Uncountable Nows in Platonia contain something we should call Lucy, all in perfect Platonic stillness. It is because we abstract and ‘detach’ one Lucy from her Nows that we think a cat leapt. Cats don’t leap in Platonia. They just are.

You might argue that even if cats do not have a permanent identity, their atoms do. But this presupposes that atoms are like billiard balls with distinguishing marks and permanent identities. They aren’t. Two atoms of the same kind are indistinguishable. One cannot ‘put labels on them’ and recognize them individually later. Moreover, at the deeper, subatomic level the atoms themselves are in a perpetual state of flux. We think things persist in time because structures persist, and we mistake the structure for substance. But looking for enduring substance is like looking for time. It slips through your fingers. One cannot step into the same river twice.

Zeno of Elea, who belonged to the same philosophical school as Parmenides, formulated a famous paradox designed to show that motion is impossible. After an arrow shot at a target has got halfway there, it still has half the distance to go. When it has gone half that distance, it still has half of that way to go. This goes on for ever. The arrow can never reach the target, so motion is impossible. In normal physics, with a notion of time, Zeno’s paradox is readily resolved. However, in my timeless view the paradox is resurrected, but the arrow never reaches the target for a more basic reason: the arrow in the bow is not the arrow in the target.

There are two parts to my claim that time does not exist. I start from the philosophical conviction that the only true things are complete possible configurations of the universe, unchanging Nows. Unchanging things do not travel in time from Now to Now. Material things, we included, are simply parts of Nows. This philosophical standpoint must be matched by a physical theory that seems natural within it. The evidence that such a physical theory exists and seems to describe the universe forms the other part of my claim. This section has merely made the philosophy, the notion of being, clear. The physics, the guts of the story, is still to come.

THE BIG PICTURE

Before Newton was born, René Descartes raised a nightmarish prospect. How do I know, he asked, whether anything exists? Is some malignant demon conjuring up my thoughts and experiences? Perhaps there isn’t any world. How can we be sure of anything? Descartes famously argued that we can at least be certain of our own existence. Cogito ergo sum: I think, therefore I am. In fact, this did not get him very far, and his main argument for a real world was that God would not deceive us on such a fundamental matter.

Modern science has a better answer to the solipsists – those who, like Descartes in that extreme moment of doubt, deny existence outside their own thoughts. The starting point is that we do observe a great variety of phenomena. We can then ask whether we can postulate a world and laws that lead to the phenomena. If this is so, it does not explain how or why the world is there, but it does provide grounds for taking its existence more seriously.

You may think that time capsules and a brain preserved in aspic aware of seeing motion are getting dangerously close to solipsism and the machinations of a demon. Without anticipating the rest of the book, an outline may still be helpful. There are only two rules of the game: there must be an external world subject to laws and a correspondence between it and experiences.

Apart from the fact that Newton placed the material objects of the universe in an arena, my things are his things. They are Nows, the relative configurations of the universe. Newton’s Nows form a string, brought into being by an act of creation at one end, called the past. It is usually assumed that our experiences in some instant reflect the structure in a short segment of the string at a point along it. It is a segment, rather than one Now, because we see things not only in positions but in motion. However, a single Now contains only positional information. It seems that we need at least two Nows to have information about changes of position.

Newtonian history, as modified by Big Bang cosmology, translates into a path in Platonia. It begins at a certain point with a creation event, after which the laws of nature determine the path. Many paths satisfy the same laws, but the laws by themselves do not tell us why one path is chosen by the creation event in preference to others.

The alternative picture, suggested by quantum mechanics and proposed in this book, is quite different. There are no paths with unique starting points conceived as creation events. Indeed, there are no paths at all. Instead, the different points of Platonia, each of which represents a different possible configuration of the universe, are present – as potentialities at least – in different quantities. This matches what we found in the Timeless Theory bag: many different triangles present in different quantities. It will be helpful to represent this in a more graphic way. Imagine that Platonia is covered by a mist. Its intensity does not vary in time – it is static – but it does vary from position to position. Its intensity at each given point is a measure of how many configurations (as in the previous example, with triangles in the Timeless Bag) corresponding to that point are present. All these configurations, present in different quantities, you should imagine for the moment as being collected together in a ‘heap’ or ‘bag’.

So, Platonia is covered with mist. Its intensity cannot change in time (there is no time), but it does vary from point to point. In some places it is much more intense than in others. A timeless law, complete in itself, determines where the mist collects. The law is a kind of competition for the mist between the Nows. Those that ‘resonate’ well with each other get more mist. The outcome is a distribution of mist intensity. This, as I have just explained, is simply another description of the Timeless Theory bag – for mist intensity read numbers of triangle copies. But the Nows of this Platonia are much more complex than triangles.

This opens up possibilities. Triangles tell no stories, they are too simple. But if the Nows are defined by, say, the arrangements of three large bodies and of many thousands of small bodies, things are different. For example, the three large bodies could form the tenth triangle from the right in Figure 1. The remaining small bodies could be arranged in such a way that they literally create the pattern of the first nine triangles from the right of the sequence. This may seem contrived, but it is possible. It is a Now in a greatly enlarged Platonia. Shown such a Now, what could we make of it? One interpretation is that the small bodies record what the large bodies have done: the Now is a time capsule, a picture of a Newtonian history. As soon as a sufficient number of bodies are present, the possibilities for creating time capsules are immense.

I believe the sole reason we believe in time is because we only ever experience the universe through the medium of a time capsule. My assumptions are:

(1) All experience we have in some instant derives from the structure in one Now.

(2) For Nows capable of self-awareness (by containing brains, etc.) the probability of being experienced is proportional to their mist intensity.

(3) The Nows at which the mist has a high intensity are time capsules (they will also possess other specific properties).

Thus, the one law of the universe that determines the mist intensity over Platonia is timeless. The Nows and the distribution of the mist are both static. The appearance of time arises solely because the mist is concentrated on time capsules, and a Now that is a time capsule is therefore much more likely to be experienced than a Now that is not. (Please remember that this is only an outline: the detailed arguments are still to come.)

Of the three assumptions, the second is the most problematic. The first and third may seem strange and implausible, but they can be made definite. If correct, their significance and meaning are clear-cut. Both could be shown to be false, but this is good, since a theory that cannot be disproved is a bad theory. The best theories make firm predictions that can be tested. The main difficulty with the second assumption is in saying what it means. We encounter, in a modified form, the difficulty that Descartes raised. It is acute.

In a Newtonian scheme, the connection between theory and experience is unambiguous. There is a path through Platonia, and all the Nows on it are realized: sentient beings within any Nows on the path do experience those Nows. In the alternative scheme, the distribution of the mist over Platonia – its intensity at each Now – is as definite as the line of the Newtonian path. The difficulty, which is deeply rooted in quantum mechanics, is how to interpret the intensity of the mist. When we get to grips with quantum mechanics, I shall explain my reasons for assuming that the mist intensity at a Now measures its probability of being experienced. Perhaps some cosmic lottery is the best way to explain this.

Each Now has a mist intensity. Suppose that all the Nows participate in a lottery, receiving numbers of tickets proportional to their mist intensities. Nows where the mist is intense get tickets galore, others very few. By assumption (1), conscious experience is always in one Now. If a Now has a special structure, it is capable of self-awareness. But is it actually self-aware? Structure in itself, no matter how intricate and ordered, cannot explain how it can be self-aware. Consciousness is the ultimate mystery.

Perhaps it is a mystery that makes some sense of the mist that covers Platonia. If there is a cosmic lottery, clearly the Nows with the most tickets will have the best chance. If a ticket belonging to a Now capable of self-awareness is drawn, this can, so to speak, ‘bring to life’ the Now. It is aware. The consciousness potentially present in Nows structured the right way is actual in those that are drawn. Two questions about this cosmic lottery may well be asked: when are the tickets drawn, and how many are drawn?

The first question is easily answered: it has no meaning. Think of the brain preserved in aspic, or the unfortunate brain-damaged patient who believes that Harold Macmillan is Prime Minister and Dwight Eisenhower is President. The structure capable of making a Now self-aware is eternal and timeless. Structure is all that counts. Self-awareness does not happen at a certain time and last for some fraction of a second. Yesterday seems to come before today because today contains records (memories) of yesterday. Nothing in the known facts is changed by imagining them hung on a ‘line of time’ – or even reversing their positions on that line. The instant is not in time, time is in the instant. We do not have to worry when the draw is made, only whether our number comes up.

The question of how many tickets are drawn is a tough one. If only one is drawn, your present Now, which does exist, must be the one and only instant realized and experienced. All your memories are then illusions in the sense that you never experienced them. That seems very hard to believe. What is more, memories are legion. If you believe you did actually experience them all, then lots of Nows have been drawn. From this it is a small step to saying that all Nows in Platonia are drawn. In quantum mechanics, this is called the many-worlds hypothesis. But then the theory seems to become vacuous: everything that can be is, no predictions appear to be made. The root of the problem is the assumption, neat and clean in itself, that each experienced instant is always tied to a single Now and that the distribution of the mist over Platonia is determined by a law indifferent to the workings of the cosmic lottery. Whether or not particular Nows are drawn has no effect on the mist intensity. The rules of the scheme make it quite impossible to say how many, if any, of your memories are real. All we know is that the present Now is real. You can see how Descartes’s dilemma is revived in such a scheme. I suspect that it is a problem we just have to live with.

The theory is still testable because only Nows with high mist intensity (and therefore high probability) are likely to be experienced, and such Nows have characteristic properties: above all, they are time capsules. We can therefore test our own experiences and see if they verify the predictions of the theory. This is something that in principle can be settled by mathematics and observations. For if physicists can determine or guess the structure of Platonia and formulate the law that determines how the mist is distributed over it, then it is simply a matter of calculation to find out where in Platonia the mist is most intense. If the mist is indeed concentrated on structures that are time capsules, the theory will make a very strong prediction – any Now that is experienced will contain structures that seem to be records of a past of that Now. It will also contain other characteristic structures.

The huge number of things that can coexist simultaneously in one Now is significant here. It means that many independent tests can be made on a single time capsule to see whether the predictions are confirmed. The laws of nature are usually tested by repeating experiments in time. If the same initial state gives the same outcome, the law is confirmed. However, for an object as richly structured as the Earth (which in any instant belongs to one of the Nows in Platonia), repeating experiments in time can be replaced by repeating them in space. As it happens, even confirming a theory by repeating experiments in time as normally understood boils down to comparing records in one Now. The precondition of all science is the existence of time capsules. All the Nows we experience are time capsules. The question is whether we can explain why this is so from first principles: can the strong impression of time emerge from timelessness? It is a logical possibility, but the real test must await mathematical advances. Unfortunately, they are not likely to be easy.

Strange as a timeless theory may seem, it has the potential to be very powerful. Boltzmann’s work highlighted two difficulties inherent in any theory of time – initial conditions must be imposed arbitrarily; and dull, unstructured situations are far more probable than the interesting structured things we find all around us. Interestingly structured Nows are an extreme rarity among all the Nows that can be. If the mist does pick out time capsules in Platonia, it must be very selective. Since all possible structures are present in Platonia, the vast majority of Nows do not contain any structures at all that could be called records. Even then, the apparent records will be mutually consistent in only a tiny fraction of what is already a tiny fraction. Only our habitual exposure to the time capsules we experience blinds us to the magnitude of the phenomenon that needs to be explained. Stars in real space give us only an inkling of how thinly time capsules are spread. Any scheme that does select them will be very powerful. But more than that, it will be more fully rational than classical physics, with its need to invoke a very special initial condition, can ever be. Once the law that governs the distribution of the mist over Platonia has been specified, nothing more remains to be done. The mist gathers where it does for only two reasons: the structure of the law and the structure of Platonia.

So where is the mist likely to gather? The mathematics needed to answer this question will certainly be difficult, but there are some hints (which I shall elaborate in the final chapters). They suggest that mist is likely to be distributed along thin, gossamer-like filaments that bifurcate and form a tree-like structure (Figure 6).

A tendency to bifurcation is deeply rooted in quantum mechanics. In principle, it could happen in both directions along a filament. However, the Nows we experience all seem to have arisen from a unique past. There seems to be no branching in that direction. Within quantum mechanics, as presently formulated in space and time, this fact is not impossible, but it is as puzzling as the low entropy that so exercised Boltzmann. It does seem improbable. I suspect that everything will look different if we learn to think about quantum mechanics in Platonia. For one thing, the arena has a very different shape. This is why I was keen to show you at this early stage the diagrams of Triangle Land (Figures 3 and 4) and my representation of Platonia (Figure 5). It opens out in one direction from nothing. I suspect that the branching filaments of mist in Figure 6 arise because they reflect this overall, flower-like structure of Platonia. If that is so, the great asymmetries of our existence – past and future, birth and death – arise from a deep asymmetry in being itself. The land of possible things has one absolute end, where it abuts onto mere nothing, but it is unbounded the other way, for there is no limit to the richness of being.

Who knows what experiences are possible in the oases of richly structured Nows strung out along the trade routes that cross the deserts of Platonia? The plurality of experience is remarkable and suggestive. In any instant, we are aware of many things at once. Through memories we are, as it were, present simultaneously in many different Nows in Platonia. Richness of structure permits this. One grand structure contains substructures that are ‘pictures’ – simplified representations that capture the essential features – of other structures. Our memories are pictures of other Nows within this Now, rather like snapshots in an album. Each Now is separate and a world unto itself, but the richly structured Nows ‘know’ about one another because they literally contain one another in certain essential respects. As consciousness surveys many things at once in one Now, it is simultaneously present, at least in part, in other Nows. This awareness of many things in one could well exist in a much more pronounced form in other places in Platonia.

Figure 6 The conjectured filamentary distribution of mist in Platonia. The instant you experience now is marked NOW. To its left lie Nows of which you have memories in NOW. There is no bifurcation in this direction, matching our conviction that we have a unique past. In the other direction there is a branching into different alternative ‘futures’ of NOW. In all of them, you think you have advanced into the future by the same amount from NOW. These different filaments are ‘parallel worlds’ that seem to have a common past, to which NOW belongs. Note that the filaments have a finite width, unlike a Newtonian string of successive instants. All around NOW, along the filament and to either side of it, are other Nows with slightly different versions of yourself. All such Nows are ‘other worlds’ in which there exist somewhat different but still recognizable versions of yourself. In other filaments are worlds you would not recognize at all.

The picture of ourselves dividing into parallel Nows may be unsettling, but the phenomenon itself is familiar. We are used to being in different Nows and being slightly different in all of them – that is simply the effect of time as it is usually conceived. The account of Lucy’s leaps emphasized that the differences in ourselves between Nows are far greater than we realize within consciousness. Huge numbers of microscopically different Nows could give identical conscious experience. As we shall see, quantum mechanics forces us to consider Nows everywhere, not just those on one path. It unsettles by division, seeming to threaten dissolution and personal integrity. But it simultaneously binds us into the far mightier whole of everything that can be, doing so much more decisively than any Newtonian scheme can do. For the Nows that are likely to be experienced are the ones that are most sensitive to the whole of Platonia.

I think this is sufficient introduction. I could go on to talk about free will, the future, our place in the universe, religion, and so on. If the theory is correct, it must change the way we think about these things. However, without some real understanding of the arguments for a timeless universe, I feel further discussion would lack a solid basis. I therefore postpone these issues to later in the book, especially the epilogue. My aim so far has been to outline the scheme and to show that it is truly timeless and at least logically possible.