The End of Time: The Next Revolution in Physics

CHAPTER 22

The Emergence of Time and its Arrow

CAUSALITY IN QUANTUM COSMOLOGY

John Bell’s account of time-capsule selection contains a very large configuration space, time, the wave function and its equation (the time-dependent Schrödinger equation) and a special initial state. This last is most important. If quantum cosmology is static, something else must replace it. We cannot impose an initial condition in the past because there is no past. But we can try something similar. Suppose that the universal configuration space had only three dimensions and not the monstrous number I have so often asked you to consider. We could then specify the wave function on a two-dimensional plane in that three-dimensional space, and use the equation satisfied by the wave function to find it at other points. This is like evolving a state in time except that the evolution is in the third, spatial direction.

If we attempt this in ordinary quantum mechanics with the stationary Schrödinger equation, which in some respects at least is like the Wheeler-DeWitt equation, the wave function starts to misbehave sooner or later. Either it becomes infinite, or it cannot be evolved continuously, or some other disaster happens: it ceases to be ‘well behaved’. The remarkable and exciting discovery that Schrödinger made was that the hydrogen atom does have a very special set of solutions that are well behaved everywhere and for which therefore no disaster happens. These very special states correspond exactly to the negative-energy states of the hydrogen atom. He had explained what had hitherto been one of the deepest mysteries of physics – the spectral lines of atoms and molecules.

My main interest here is the transformation of our notions about causality that a solution of this kind could represent. The traditional view is that what happens now was ‘caused’ by some state in the past. There is always arbitrariness in this picture because the past state is arbitrary. But suppose the world is described instead by a solution of some Wheeler-De Witt equation that is everywhere well behaved in Schrödinger’s sense. I have already pointed out that such solutions are ultra-sensitive to the domain on which they are defined – otherwise they could not remain well behaved everywhere. Such solutions present a kind of pre-established harmony.

The Wheeler-DeWitt equation then constitutes the rules of a game played in eternity. The wave function is the ball, Platonia is the pitch. If a well-behaved solution exists, then only two things can have conspired to create it: the rules of the game and the shape (the topography) of the pitch. In contrast, Bell’s time capsules are created by the rules, time, the topography and a special initial condition. What a prize if we could create time capsules by the rules and the shape of the pitch alone! Arbitrary, vertical causality (through time) would then be replaced by timeless horizontal and rational causation – across Platonia.

SOCCER IN THE MATTERHORN

It is possible. There are plenty of time capsules in Platonia. It is not just time and the special initial conditions that enable the wave function to find time capsules. The rules of the game and, above all, the pitch size and topography are most conducive to it. Indeed, the configuration space is a prerequisite. As Nevill Mott remarked, ‘The difficulty that we have in picturing how it is that a spherical wave can produce a straight track arises from our tendency to picture the wave as existing in ordinary three-dimensional space, whereas we are really dealing with wave functions in the multispace formed by the co-ordinates both of the alpha-particle and of every atom in the Wilson chamber.’ What interests me now is not so much the dimensions as the pitch’s shape. What follows is speculation. Mine. I am not aware that anyone else has made it (though Dieter Zeh considered something rather similar). I have lectured several times on the idea, and in 1994 published quite a long paper on it in the journal Classical and Quantum Gravity. A problem with the idea is that as yet it is purely qualitative. Physicists rightly want to see real calculations (which, alas, are bound to be difficult), not mere speculation, before they endorse an idea. But the more I think about the idea, the more plausible, indeed almost inescapable, it appears to be. It is about the origin of the arrow of time – and time itself.

The arrow of time, manifested in the ubiquity of time capsules, is a colossal asymmetry. It is well-nigh inexplicable in time-symmetric physics, the present rules. Since Boltzmann’s age, it has towered there, an unsealed Everest. It can be described but not yet explained.

This book has been one long, sustained effort to shed redundant concepts. We now are down to two: a static but well-behaved wave function and the configuration space. The latter is Platonia, our pitch. I look at it as a child might – what a lopsided thing it is! However I turn in my mind the notion of ‘thing’, the space of all things constructed according to one rule comes out asymmetric. All the mathematical structures built by physicists to model the world have this inherent asymmetry. One rule creates triangles, but they are all different. No matter how you arrange them, their configuration space falls out oddly. Have another look at Triangle Land (Figures 3 and 4), which is just about the simplest Platonia there can be. And what does it look like? An upturned Matterhorn. Imagine trying to play football on that pitch.

The barest arena in which we can hope to represent appearances is the set of possible things. If we banish things, we banish all the world. So we have kept things and made them the instants of time. As we experience them, they are invariably time capsules. This is the principal contingent fact of existence: the wave function of the universe, playing the great game in timelessness, seeks and finds time capsules. What all-pervasive influence can put such a rooted bias into the game? The explanation seems to scream at us. Platonia is a skewed continent.

My conjecture is this. The Wheeler-DeWitt equation of our universe concentrates any of its well-behaved solutions on time capsules. I suspect the same result would hold for many different equations and configuration spaces. The inherent asymmetry of the configuration space will always ‘funnel’ the wave function onto time capsules.

I could fill up pages with hand-waving arguments for why this should be so, but they would baffle the non-specialist and offend the specialist. I shall attempt only to show that the ‘seeking out’ of time capsules need not depend on time and a special initial condition. Stationary equations may also do the trick. I may also mention that if, as explained in the Notes, the universe can, in accordance with my recent insights, be understood solely in terms of pure structure, so that absolute distance plays no role, it will certainly be possible to make the arguments of the remaining parts of this chapter more precise and convincing.

TIMELESS DESCRIPTIONS OF DYNAMICS

In Part 2, we saw that Newtonian classical histories of the universe can be described in a timeless fashion as ‘shortest’ curves (geodesics) in configuration space. All histories that have the same energy can be described this way. This fact is often helpful, simplifying the solution of problems. In quantum mechanics something similar happens.

Physicists often want to know what will happen if some atomic particle is shot at a target of other particles. One way is to represent it by a ‘cloud’ of wave function – a wave packet – that moves towards the target. As Schrödinger showed, such a packet can be formed from waves corresponding to a relatively small range of momenta and energies, and it moves with a more or less definite velocity. When it reaches the target, it is ‘scattered’ – the wave function flies off in many directions. Physicists use the time-dependent Schrödinger equation to find the probabilities for these various directions. In this picture, the wave packet moves and is in different positions at different times. This is rather like the representation of history in Newtonian physics as an illuminated spot moving along a curve in configuration space.

There is, however, an alternative method. A single static wave covers the whole region – before, at, and after the target – traversed by the wave packet in the first picture. This one wave satisfies the stationary Schrödinger equation and corresponds to a particle with the average momentum and energy of the packet. As far as the target, the static wave is regular and plane, but at the target its pattern gets broken up. The interesting thing is that if we examine the pattern of the disrupted (but still static) wave in the region behind the target, we can deduce from it the probabilities with which the particle will be scattered in different directions in the first picture. I shall not go into details; suffice it to say that the one static wave is a kind of record of all the successive wave-packet positions in the first description. This is closely analogous to the way in classical physics in which the curve in the configuration space is a summary of all positions of the illuminated spot taken to represent the system at different times.

Interestingly, Max Born made his pioneering scattering calculations in the newly created wave mechanics by the second method. At that time Schrödinger had not even published his time-dependent equation. All the great early discoveries in wave mechanics, including Born’s statistical interpretation of the wave function (which he came to by mulling over his scattering calculations), were made before the supposedly more fundamental and ‘correct’ time-dependent equation had been found. I find this suggestive. It strengthens my belief that all the physics of the universe can be described by a timeless wave equation. In fact, Mott also used the stationary equation to obtain the alpha-particle tracks. That timeless equation can locate time capsules.

But ‘can’ is not ‘must’. The fact is that Mott used a special technique, always followed in such calculations, that mimics the wave-packet behaviour. The answer is to some extent simply assumed rather than truly derived and demonstrated. This can be done because the time-dependent and stationary Schrödinger equations have different structures, the latter having an extra freedom not present in the former. At each stage of his calculations, Mott systematically exploited this extra degree by making a definite kind of choice. This choice was not imposed by the mathematics but was made, probably instinctively, to match his temporal intuition. In fact, Mott’s solution is not a proper solution at all but a kind of bookkeeping record of how the real process would unfold in time. In addition, the condition corresponding to low entropy was also assumed rather than derived.

My conjecture seems to rest on a shaky basis. But there is more than one way of looking at this. The arguments for a timeless quantum universe are strong. The timelessness of the Wheeler-DeWitt equation, found by well-tried quantization methods, reflects the deepest structure of Einstein’s theory. Quite independently, we never observe anything other than time capsules – the entire observable universe is marked, at all epochs, by profound temporal asymmetry. If we trust the equation, our observations tell us the outcome of a mathematical calculation performed by the universe itself using that equation. For that is what the contingent universe must be: a solution of the equation. If what we observe – a profusion of time capsules – is a representative fact, then the equation does concentrate ψ on time capsules.

We can take Mott’s solution more seriously. Several points can be made. Situations in which part of a quantum system is in the semiclassical regime, so that Hamilton’s ‘light rays’ are present as latent or even incipient classical histories, are rather common and characteristic. The Heisenberg-Mott work then shows that such latent histories will become entangled with the remaining quantum variables, which must, in some way, reflect and carry information about those histories. What is not clear is whether the histories will exhibit a pronounced sense of direction – an arrow of time. That, above all, is put into the Mott solution by hand.

Also relevant is the mathematically somewhat suspect procedure known as successive approximation used to construct the Mott solution. There is no global arena in which the cloud chamber resides. Its atoms are effectively located in empty Euclidean space, and Mott could keep on adding approximations without worrying about their behaviour far from the cloud chamber. He was not constructing a genuine well-behaved solution, in which one must ensure the behaviour is right everywhere, especially at infinity. Instead, Mott used infinity as a kind of dustbin. This could not be done in a realistic situation, as I would now like to show.

A QUANTUM ORIGIN OF THE UNIVERSE?

When Planck made the first quantum discovery, he noted an interesting fact. The speed of light, Newton’s gravitational constant, and Planck’s constant clearly reflect fundamental properties of the world. From them it is possible to derive the characteristic mass length l_planck and time f_planck with approximate values

On atomic scales the Planck mass is huge, corresponding to about 10¹⁹ hydrogen atoms. In contrast, the Planck length and time are far smaller than anything physicists can currently measure.

Much of current cosmology is concerned with the ‘interface’ of quantum gravity and classical physics. The universe around us is described by general relativity. This classical treatment is said to be valid right back into the distant past, very close to the Big Bang. The quantum phase of cosmology is supposed to become important only at extraordinarily small scales, of the order of the Planck length, 10^–33 centimetres. Lights travel this distance in 10^–43 seconds, and it is argued that quantum gravity ‘comes into its own’ only in this almost incomprehensibly early epoch.

All researchers agree that the nature of reality changes qualitatively in this domain. Different laws must be used. Time ceases to be an appropriate concept: things do not become, they are. In a process often likened to radioactive decay, our classical universe that emerges at the Big Bang is represented as somehow ‘springing’ out of timelessness, or even nothing. A mysterious quantum birth creates the initial conditions that apply at the start of the classical evolution. Our present universe is then the outcome of the conditions created by quantum gravity. The dichotomy between the laws of nature and initial conditions is thus resolved if the quantum creation process can be uniquely determined.

Stephen Hawking has long been working on this problem, and believes it can be solved by his so-called no-boundary proposal, a mechanism which should lead to a unique prediction for the initial conditions. His ‘imaginary-time’ mechanism, described in his A Brief History of Time, seemed to have the potential to do this. However, it has been widely criticized, and there are technical problems. The most serious seems to be that even if the mechanism can be made to work it will not produce unique initial conditions. Where Hawking has led, many have followed, and numerous creation schemes have been proposed.

My difficulty with this approach is the division introduced between the quantum and classical domains. One could almost get the impression that the laws of nature actually change, and I am sure that no theoretical physicist believes that. The approach is adopted because the physical conditions are hugely different in the two domains. In physics it is very common to use quite different schemes if the conditions studied are different. No engineer would use quantum mechanics to describe water flow in pipes, for example. But the much more appropriate hydrodynamic equations are consequences of the deeper quantum equations, and are valid in the appropriate domain.

Cosmology may be different. Most physicists have a deeply rooted notion of causality: explanations for the present must be sought in the past (vertical causality, as I have called it). This instinctive approach will be flawed if the very concept of the past is suspect. If quantum cosmology really is timeless, our notion of causality may have to be changed radically. We cannot look to a past to explain what we find around us. The here and now arises not from a past, but from the totality of things (horizontal causality).

Figure 53 A schematic representation of Platonia. All points in each horizontal section represent configurations of the universe with the same volume but different curvatures and matter distributions in them. According to the ideas of quantum creation, as yet unknown laws of quantum gravity hold near Alpha, and in some rather mysterious way give rise to conditions under which our universe – and with it, time – ‘spring out of Alpha’. The thread shown ascending from Alpha represents the history of our universe that results from the enigmatic quantum creation.

Figure 53, a schematic representation of Platonia, may help. This is the skewed continent, as the cone shape makes clear. The quantum-creation approaches imply that the enigmatic and as yet unknown laws of quantum gravity create at the vertex – Alpha – a ‘spark in eternity’. The spark, in its turn, creates close to Alpha the initial conditions of our actual universe. Time is born at the ‘spark’. Our classical universe is the thread ascending through Platonia to our present location.

Figure 54 shows what is often called the chronology of the universe (the vertical axis is time, and the ‘quantum creation’ at Alpha occurs at the bottom left). Here each horizontal section is one point on the thread through Platonia in Figure 53: it is space at the corresponding time. The characteristic structures in space at the various cosmic epochs are shown: quarks in a soup near Alpha, primordial hydrogen and helium after the first three minutes, incipient galaxies a few thousand years later, and so on, right through to life on Earth at the present. Such is the thread ‘born in the quantum spark’. The Everettian quantum cosmologists believe that the one quantum spark creates many such threads, one of them ours. But is there a ‘spark’ at Alpha? The laws of quantum gravity hold not just near Alpha, but throughout Platonia – they are the conjectured universal and ultimate laws. We have to ask what kind of solutions they can have, and how the solutions are created. How do threads, one or many, emerge?

Figure 54 Chronology of the universe. Redrawn from A Short History of the Universe by Joseph Silk (W. H. Freeman/Scientific American Library, 1994). The vertical axis represents time. Alpha, the ‘quantum creation’, occurs at the bottom left.

Our entire experience tells us that the well-behaved solutions of the stationary Schrödinger equation that describe the characteristic structures of atoms, molecules and solids are determined by the complete structure of the configuration spaces on which they are defined. They exhibit global sensitivity – their behaviour has to be right everywhere. Since the governing equation does not contain the time, this delicate ‘testing out of all possible behaviours’ takes place in timelessness. If the Wheeler-DeWitt equation is like the stationary Schrödinger equation, then Alpha, where time is allegedly born, plays an important role, but it is not the locus at which some all-decisive die is cast. Of course it is singular – Platonia abuts on nothing at Alpha – but there are innumerable other special points scattered all over Platonia. None are quite like Alpha but, together with the overall shape of Platonia, they all have their role to play. Quantum mechanics is nothing if not democratic. Solutions of the Wheeler-DeWitt equation must be produced by a kind of dialogue between every point in Platonia.

The picture suggested by such arguments is this. Platonia as a whole determines how the static wave function ‘beds down’ on its landscape. There will be regions of semiclassical behaviour with respect to a large set of macroscopic quantities in which latent classical histories are defined. Just as the latent alpha-particle tracks get correlated through the wave function with the chamber electrons, ‘nudging’ the wave function onto time capsules, the same thing can happen in Platonia.

VISION OF A TIMELESS UNIVERSE

Let me now give you my vision of quantum cosmology, contrasting it with the chronology of the universe (Figure 54), that temporal representation of the ‘thread’ in Figure 53. Every instant of time you can conceive of is somewhere in Platonia. But the instants of time can themselves be richly structured beyond imagination. All things we see around us now in the universe are just parts of instants of time. All over Platonia there exist instants of time in which Wagner is composing Tristan and Isolde, astronauts are repairing the Hubble Space Telescope, birds are building nests and I am baking bread. The wave function of the universe finds its way to very few of them. The structure of the wave function and the form of the laws of nature – in which the tendency of gravity to clump matter is surely vital – forces the blue mist to seek out the most special instants, strung out along delicate threads. I think it is wrong of cosmologists to call Figure 54 a chronology of the universe. It is the map of a footpath in Platonia. The blue mist shines at instants containing time capsules, all of which, in their different ways, tell stories of a journey from Alpha along a fine thread of ‘history’ – a path winding through Platonia. Time is in such instants since they reflect the story of the path and, since the structure of Platonia in its totality forces the universal wave function to ‘light up’ the paths, there is a sense in which these instants reflect everything that is.

However, whereas alpha particles create, through their tracks, a literal image of history, the time capsules of the real universe embody their stories in a much subtler manner. This is inevitable given the grandeur of the story – cosmology in its entirety. Consider, for example, the Sun. Quantum mechanically, it will need to be represented in a configuration space of, say, 10⁶⁰ dimensions, but vast stretches of it will be virtually devoid of wave function. The mere fact that the Sun is roughly spherical and can be well modelled by the laws of stellar structure sweeps most of the configuration space clean of wave function. The particular abundances of the chemical elements within the Sun have the same effect, drastically limiting the region of the solar configuration space in which the blue mist is concentrated.

One configuration at which the blue mist does shine brightly will be a characteristic distribution of all the particles in the Sun. To an experienced astrophysicist, this distribution tells an immensely rich story stretching back to the first three minutes (in the standard picture) when the primordial hydrogen and helium abundances were established. The whole story of the cosmos that we call our own is written in the distribution of the Sun’s particles: the formation of galaxies and the earliest generations of stars; the supernova explosion that triggered the formation of the Sun and the solar system, and left the radioactivity that still powers so much tectonic and volcanic activity on the Earth; and the Sun’s steady burning of its nuclear fuel.

The decisive element in this picture is the seed – or rather, seeds – from which these stories can all grow by the penetration of the wave function into the nooks and crannies in Platonia where the configurations are coherent stories. The wave function can be present there only if it is entangled with the latent histories of a semiclassical wave function established at least somewhere in Platonia. These are the Hamiltonian ‘light rays’ from which everything must ‘grow’. Where are they likely to run, and what will their properties be? This is where the shape of Platonia must become decisive. The points in Platonia near Alpha containing Wagner and kingfishers are simply not visited by the blue mist, since Platonia as a whole lays out the latent histories in patterns that do not get entangled with such points.

Modern classical cosmology gives some hints as to where the latent histories might run. The simplest Big Bang cosmological solutions of Einstein’s equations, first discovered by the Russian mathematician Alexander Friedmann in the early 1920s, have the maximum degree of symmetry and therefore ascend the central line in Figure 53. This is the history distinguished in cosmology by the universe’s contents, despite the relativity of simultaneity. The universe explodes out of the singular state of zero volume, expands to a maximum volume and then recon-tracts to zero volume, gravity having halted and then reversed the initial, very rapid expansion. As shown schematically in Figure 55 (see p. 321), the universe ends in a Big Crunch. In other cosmological models, which normally require the universe to be spatially infinite, the expansion is so violent that the expansion is never halted.

In reality the universe is not completely symmetric, and the path out from Alpha is not exactly retraced, as shown in Figure 55, in which the rays emanating from Alpha are a measure of the relative ‘irregularity’ of the spatial configurations of the universe. Up the vertical ray, the universe is perfectly smooth, but on the rays that fan out at progressively larger angles the relative irregularity increases. The diagram shows one classical history which, at one end, starts in an almost perfectly smooth state but then becomes more and more irregular, due to the formation of galaxies, stars, black holes, planets and even human beings. This history reaches maximum expansion, turns round and recontracts, becoming more irregular all the time. It returns to the state of very small volume at a different point of Platonia, since although the volumes are small in both cases there are many additional variables that describe the structure of the state. Thus Alpha, the ‘end of Platonia’, is not a true point but actually a huge space of different possibilities, all with vanishingly small volumes.

Regarded purely as a path through Platonia, we cannot say that one end of this history is its beginning and the other is its end. I have lapsed into conventional talk. Such a priori notions do not belong in a timeless theory. Nevertheless, the two ends of the path are very different in nature, and it is tempting to say that, if our own existence is associated with such a path, its smooth end is what we would call the past and the irregular end the future. This would be very much in the tradition, initiated by Boltzmann, of suggesting that our sense of the forward flow of time, its arrow, is grounded solely in the increase in disorder that virtually all classical trajectories must exhibit if they pass through an exceptionally ordered region. Normally there are trajectories that both enter and leave such regions, and the entropic explanation of the arrow of time suggests that time will seem to flow forward in both directions out of these regions. In the present example, the exceptional region is on the frontier of Platonia, so the path truly ends there. This is beginning to look quite promising as the basis for a total explanation of time, but several conditions must be met. Before we address them, it is worth saying a little about gravity and thermodynamics.

The central conclusion of standard thermodynamics with an external time is that, if the low entropy of the world and its habitual increase are to be explained, the universe must presently be evolving out of a statistically most unlikely state. In systems in which gravity does not act, the unlikely state is generally one that is structured, while the likely state is characterized by a bland uniformity. Gas confined in a finite volume tends quickly to a very uniform state in which it occupies all the available space and all temperature differences are levelled out. This is the equilibrium state. It is vastly more probable than any ordered state because there are so many more ways in which it can be realized microscopically. The situation is much more complicated when gravity comes into play, since there is no well-defined equilibrium state for a gravitating system. Gravity is attractive, so a uniform state is unstable and will tend to break into self-gravitating clumps. This is the exact opposite of a gas.

Currently there is no fully satisfactory thermodynamics of cosmology, mainly because of the way in which gravity acts. But it does seem certain that black holes, which almost certainly exist, have a well-defined entropy associated with them. This was the final and most dramatic outcome of the intensely exciting ‘golden decade’ in the study of black holes that ended with the discovery of black-hole evaporation by Stephen Hawking in 1974. This fascinating story has been told with great verve by Kip Thorne in his Black Holes and Time Warps. The entropy associated with black holes is staggeringly large. Since there is little evidence that black holes existed at very early times but a lot that many have since been formed and more will be formed, the universe seems to have begun in an extraordinarily unlikely state.

No one has done more than Roger Penrose to highlight this fact. His The Emperor’s New Mind has an entertaining illustration of the creating divinity seeking with a pin to find the tiny improbable point of the initial condition of the universe from which its utterly unlikely history must have sprung. Penrose seeks to explain this in a theory in which both time and actual quantum-mechanical collapse are real, and the laws of nature are inherently asymmetric in time. My approach is quite different because I think that the whole problem of time and its arrow can – paradoxically – be formulated more precisely and transparently in a context in which time does not exist at all. I also believe that, far from being highly unlikely, the kind of history and cosmos we experience are characteristic and likely in a timeless scenario.

It all depends on how a static wave function ‘beds down’ on the starkly asymmetric continent of Platonia. The issue of the correct arena is all-important. The collective intuition of most physicists, wedded to time and honed on translucent structures like absolute space, is forced to see the observed universe as highly improbable. But in Platonia it may appear inevitable. Wave functions have a way of finding special structures: for example, they can create complex molecules like proteins and DNA.

Let it be granted, not unreasonably I think, that the wave function of the universe will be semiclassical with respect to at least some variables in some part of Platonia. Where is it likely to be, and how will the corresponding Hamiltonian ‘light rays’ run? Do they emerge from Alpha? Here, one of the most famous results of classical general relativity may be relevant. Penrose and Hawking showed that its solutions have a remarkable propensity to evolve into a singular state. All that is necessary is for sufficient matter to be concentrated within a certain finite region. After that, as Penrose showed, collapse to a black hole is inevitable. Hawking showed that there is a sense in which the Big Bang itself can be regarded as the time-reverse of the Penrose collapse to a black hole. (Collapse here has nothing to do with quantum-mechanical collapse of the wave function.) Solutions that terminate at one or both ends in singular states are characteristic of general relativity.

What happens in a quantum theory cannot be totally unrelated to the corresponding classical theory. It therefore seems likely that in quantum gravity there will be a semiclassical region near the central ray in Figure 55. The Hamiltonian ‘light rays’ in it may well, reflecting the structure of Platonia, appear to emanate from Alpha, and rise up in a kind of jet which then spreads out and falls back, as in a fountain, returning to small volumes but in a much more irregular state. Alternatively, they may go on for ever, receding ever farther from Alpha. I have described these trajectories as if they were traced in time, but they are only paths.

Moreover, the paths are still only ‘seeds’. The finding of the full rich structures which tell us so insistently that time exists and flows must result from entanglement with the host of the remaining quantum variables that constitute the expanses of Platonia. When discussing alpha-particle tracks, I emphasized that Mott employed a special device to concentrate the wave function on time capsules. Considered purely in terms of the stationary Schrödinger equation, this was artificial. This is what created the static alpha-particle tracks and such a strong sense of time and history out of the ‘seed’ of a spherical wave pattern.

If my proposal is along the right lines, there must be some natural and plausible mechanism within static quantum cosmology which performs this task. Platonia at large must force it to happen. As I have already said, I see the cause in the rooted asymmetry of contingent things. Platonia is necessarily skew. It is easy to imagine that the cone of Figure 55 ‘funnels entanglement outwards’, much as a trumpeter blows air from a bugle. I deliberately chose this last simile. The bugle does create a nice image of what I have in mind, but it also creates hot air. There are no hard mathematical proofs to support my idea, but I hope you are now persuaded that at least the arguments for a timeless universe are strong. If it nevertheless appears intensely temporal, there must somewhere be a massive reason for the fact. I think it is the asymmetry of being. Being can be more or less. Sitting in the midst of things, we feel ourselves carried forward on the mighty arrow of time. But it is an arrow that does not move. It is simply an arrow that points from the simple to the complex, from less to more, most fundamentally of all from nothing to something. If we could look over our shoulder in Platonia, we should see where this trek began: at the edge of nothing.

Figure 55 Explosion out of the Big Bang and recontraction to the Big Crunch according to present standard cosmology.

A WELL-ORDERED COSMOS?

Let me end the main part of the book with a few comments on structure, and what strikes a theoretical physicist as improbable. If we think that dynamical histories in space and time are the fundamental things in nature, then all statistical reflections on the world lead to great difficulties. Most histories are unutterably boring over all but a minuscule fraction of their length. We can never understand the miracle of the structured world. Things are completely changed if quantum cosmology is really about some well-behaved distribution of a static wave function over Platonia. The configurations at which ψ collects strongly must be special – in some sense they must resonate with all the other configurations that are competing for wave function. Quantum cosmology becomes a kind of beauty contest in eternity. The winners – those that get a high probability density – must be exceptional, like the DNA molecule. This is just the opposite of what classical physics leads us to expect. There, the winners are boring.

When I wrote my book on the history of dynamics, I was exposed to the beautiful poetic notion of the well-ordered cosmos. Intermittent reading of Leibniz had already made me deeply interested in structure, and this was greatly strengthened by my collaboration with Lee Smolin on the Leibnizian idea that the actual universe is more varied than any other conceivable universe. That still remains a mere idea (though Paul Davies was sufficiently intrigued to include a brief account of the idea in his The Mind of God), but I became persuaded that a scientific theory of the universe in which structure is created as a first principle is possible. We may need to get back to the wonder of childhood to comprehend what the world really is. Yeats once wrote of Bishop Berkeley that he ‘has brought back to us the world that only exists because it shines and sounds. A child, smothering its laughter because the elders are standing around, has opened once more the great box of toys.’

The single most striking thing about the universe we see around us is its rich structure, which is so difficult to understand on a priori statistical grounds. Until the modern scientific age, all thinkers saw the first task of science as being the direct description and explanation of this structure. This natural impulse is reflected in the Pythagorean notion of the well-ordered cosmos. It was still very strong in both Kepler and Galileo. However, when Newton demonstrated the supreme importance of accelerations in dynamics, the perspective of science changed, for the world at the present instant became the mere consequence of its initial conditions. Instead of asking directly how structure is fashioned, science turned to asking how it is refashioned.

It seems to me that the abolition of time in quantum gravity must bring us back to a more Pythagorean perspective, though with a quantum slant, for now we must simply ask what structures are probable. It seems to me that the first decisive step in this direction was the discovery by Schrödinger of his time-independent wave equation, with its all-important condition that its solutions must be well behaved, and Born’s probability interpretation of quantum mechanics. For we know that these two basic elements of quantum mechanics work together to bring forth exquisite structures in great profusion, doing so moreover without any boundary or initial conditions and with total disregard for what might seem statistically likely. That is the story of atomic, molecular and solid-state physics. I think it may even be the story of the universe.