Julian Barbour

shinichi Post author07/07/2013 at 5:25 am

The End of Time

The Next Revolution in Physics

by Julian Barbour

Chapter 1

http://www.nytimes.com/books/first/b/barbour-time.html

The Main Puzzles

THE NEXT REVOLUTION IN PHYSICS

Nothing is more mysterious and elusive than time. It seems to be the most powerful force in the universe, carrying us inexorably from birth to death. But what exactly is it? St Augustine, who died in AD 430, summed up the problem thus: `If nobody asks me, I know what time is, but if I am asked then I am at a loss what to say.’ All agree that time is associated with change, growth and decay, but is it more than this? Questions abound. Does time move forward, bringing into being an ever-changing present? Does the past still exist? Where is the past? Is the future already predetermined, sitting here waiting for us though we know not what it is? All these questions will be addressed in this book, but the biggest remains the one St Augustine could not answer: what is time?

Curiously, physicists have tended not to ask this question, preferring to leave it to philosophers. The reason is probably the colossal and dominating influence of Isaac Newton and Albert Einstein. They shaped the way physicists think about space, time and motion. Each created a representation of the world of unsurpassed clarity. But having seen their way to a structure of things, they did not bother unduly about its foundations. This creates potential for confusion. Without question, their theories contain wonderful truths, but they both take time as given. It is a building block on a par with space, a primary substance. In fact, Einstein fused it with three-dimensional space to make four-dimensional space-time. This was one of the great revolutions of physics (Box 1).

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BOX 1 The Great Revolutions of Physics

1543: The Copernican Revolution. In On the Revolutions of the Celestial Spheres, Nicolaus Copernicus proposed that the Earth moves around the centre of the universe. The modern meaning of revolution derives from his title. He established the form of the solar system. Curiously, the Sun plays little part in his scheme; he merely placed it near the centre of the universe. About sixty years later Johannes Kepler showed that the Sun is the true centre of the solar system, and with Galileo Galilei he prepared the way for the next revolution.

1687: The Newtonian Revolution. In The Mathematical Principles of Natural Philosophy, Newton formulated his three famous laws of motion and the theory of universal gravitation. He showed that all bodies — terrestrial and celestial — obey the same laws, and thus set up the first scheme capable of describing the entire universe as a unified whole. Newton created the science of mechanics, now often called dynamics, which ushered in the modern scientific age. He claimed that all motions take place in an infinite, immovable, absolute space and that time too is absolute and `flows uniformly without relation to anything external’.

1905: The Special Theory of Relativity. In a relatively short paper on electromagnetism, Einstein showed that simultaneity cannot be defined absolutely at spatially separated points, and that space and time are inextricably linked together. What appears as space and what appears as time depends on the motion of the observer. He made startling predictions about the behaviour of measuring rods and clocks, and found his famous equation E = mc². In 1908 Hermann Minkowski formalized the notion of space-time as a rigid, indissoluble, four-dimensional arena of world events.

1915: The General Theory of Relativity. The special theory of relativity describes a world without gravitation. After an eight-year gestation, Einstein finally formulated his general theory of relativity in which the rigid arena of Minkowski’s space-time is made flexible, responding to the presence of matter in it. Gravity is given a brilliantly original interpretation as an effect of the curving of space-time. The theory showed that time can have a beginning (the Big Bang) and that the universe can expand or contract. Although to a remarkable degree it was a creation of pure thought, many predictions of this theory have now been very well confirmed. It describes the large-scale properties of matter and the universe as a whole.

1925/6: Quantum Mechanics. This gets its name because it shows that some mechanical quantities are found in nature only in multiples of discrete units called quanta. This is a distinctive difference from the theories of Newton and Einstein, which are now called classical (as opposed to quantum) theories. The first quantum effects were discovered and described on an ad hoc basis by Max Planck (1900), Einstein (1905) and Niels Bohr (1913), while a consistent quantum theory was found in two different but equivalent forms: matrix mechanics, by Werner Heisenberg (1925), and wave mechanics, by Erwin Schrödinger (1926). Paul Dirac also made outstanding contributions. Quantum mechanics describes the properties of light, especially lasers, and the microscopic world of atoms and molecules. It is the bedrock of all modern electronic technology, but its results are bafflingly counter-intuitive and raise profound issues about the nature of reality. It is also puzzling that theories of completely different structures are used to describe the macroscopic universe (classical general relativity) and microscopic atoms (quantum mechanics).
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Revolutions are what make physics such a fascinating science. Every now and then a totally new perspective is opened up. But it is not that we close the shutters on one window, open them on another, and find ourselves looking out in wonder on a brand-new landscape. The old insights are retained within the new picture. A better metaphor of physics is mountaineering: the higher we climb, the more comprehensive the view. Each new vantage point yields a better understanding of the interconnection of things. What is more, gradual accumulation of understanding is punctuated by sudden and startling enlargements of the horizon, as when we reach the brow of a hill and see things never conceived of in the ascent. Once we have found our bearings in the new landscape, our path to the most recently attained summit is laid bare and takes its honourable place in the new world.

Today, physicists confidently, indeed impatiently, await the next revolution. But what will it be? In 1979, when, like Newton and Dirac before him, Stephen Hawking became the Lucasian Professor at Cambridge, he announced in his inaugural address the imminent end of physics. Within twenty years physicists would possess a theory of everything, created by a double unification: of all the forces of nature, and of Einstein’s general theory of relativity with quantum mechanics. Physicists would then know all the inner secrets of existence, and it would merely remain to work out the consequences.

Neither unification has yet happened, though one or both certainly could. (Hawking has recently said that his prediction still stands but that `the twenty years starts now’.) For myself, I doubt that would spell the end of physics. But unification of general relativity and quantum mechanics may well spell the end of time. By this, I mean that it will cease to have a role in the foundations of physics. We shall come to see that time does not exist. Though still only a prospect on the horizon, this, I think, could well be the next revolution. What a denouement if it is!

I believe that the basic elements of this potential revolution — the reasons for it and its likely outcome — can already be discerned. In fact, as we shall shortly see, clear hints that time may not exist, and that quantum gravity — the unification of general relativity and quantum mechanics — will yield a static picture of the quantum universe, started to emerge about thirty years ago, but made remarkably little impact. This is one of my reasons for writing this book: these things should be better known. They are only just beginning to be mentioned in books for the general reader, and even most working physicists know little or nothing about them.

No doubt many people will dismiss the suggestion that time may not exist as nonsense. I am not denying the powerful phenomenon we call time. But is it what it seems to be? After all, the Earth seems to be flat. I believe the true phenomenon is so different that, presented to you as I think it is without any mention of the word `time’, it would not occur to you to call it that.

If time is removed from the foundations of physics, we shall not all suddenly feel that the flow of time has ceased. On the contrary, new timeless principles will explain why we do feel that time flows. The pattern of the first great revolution will be repeated. Copernicus, Galileo and Kepler taught us that the Earth moves and rotates while the heavens stand still, but this did not change by one iota our direct perception that the heavens do move and that the Earth does not budge. Our grasp of the interconnection of things was, however, eventually changed out of recognition in ways that were impossible to foresee. Now I think we must, in an ironic twist to the Copernican revolution, go further, to a deeper reality in which nothing at all, neither heavens nor Earth, moves. Stillness reigns.

People often ask me what are the implications of the non-existence of time. What will it mean for everyday life? I think we cannot say. Copernicus had no inkling of what Newton (let alone Einstein) would find, though it all flowed from his revolution. But we can be certain that our ideas about time, causality and origins will be transformed. At the personal level, thinking about these things has persuaded me that we should cherish the present. That certainly exists, and is perhaps even more wonderful than we realize. Carpe diem — seize the day. I expand on this in the Epilogue.

THE ULTIMATE THINGS

This book revolves around three questions: What is time? What is change? What is the plan of the universe? The only way to answer them is to examine the structure of our most successful theories. We must fathom the architecture of nature. What part, if any, is played by time in these theories? Can we identify the ultimate arena of the world?

These questions were forced upon physicists by the work I mentioned in the Preface. It is one of the two big (and almost certainly intimately connected) mysteries of modern physics (Box 2). Both are aspects of an as yet unbridged chasm between classical and quantum physics.

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BOX 2 The Two Big Mysteries

As explained in Box 1, physicists currently describe the world by means of two very different theories. Large things are described by classical physics, small things by quantum physics. There are two problems with this picture.

First, general relativity, Einstein’s theory of gravity, seems to be incompatible with the principles of quantum mechanics in a way that Newtonian dynamics and the theory of electromagnetism, developed by Michael Faraday and James Clerk Maxwell in the nineteenth century, are not. For these theories, it proved possible to transform them, by a process known as quantization, from classical into quantum theories. Attempts to apply the same process to general relativity and create quantum gravity failed. It was this technical work, by Dirac and others, which brought to the fore all the problems about time with which this book is concerned.

The second mystery is the relationship between quantum and classical physics. It seems that quantum physics is more fundamental and ought to apply to large objects, even the universe. There ought to be a quantum theory of the universe: quantum cosmology. But quantum physics does not yet exist in such a form. And its present form is very mysterious. Part of it seems to describe the actual behaviour of atoms, molecules and radiation, but another part consists of rather strange rules that act at the interface between the microscopic and macroscopic worlds. Indeed, the very existence of a seemingly unique universe is a great puzzle within the framework of quantum mechanics. This is very unsatisfactory, since physicists have a deep faith in the unity of nature. Because general relativity is simultaneously a theory of gravity and the large-scale structure of the universe, the creation of quantum cosmology will certainly require the solution of the only slightly narrower problem of quantum gravity.
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One of the themes of my book is that this chasm has arisen because physicists have deep-rooted but false ideas about the nature of space, time and things. Preconceptions obscure the true nature of the world. Physicists are using too many concepts. They assume that there are many things, and that these things move in a great invisible framework of space and time.

A radical alternative put forward by Newton’s rival Leibniz provides my central idea. The world is to be understood, not in the dualistic terms of atoms (things of one kind) that move in the framework and container of space and time (another quite different kind of thing), but in terms of more fundamental entities that fuse space and matter into the single notion of a possible arrangement, or configuration, of the entire universe. Such configurations, which can be fabulously richly structured, are the ultimate things. There are infinitely many of them; they are all different instances of a common principle of construction; and they are all, in my view, the different instants of time. In fact, many people who have written about time have conceived of instants of time in a somewhat similar way, and have called them `nows’. Since I make the concept more precise and put it at the heart of my theory of time, I shall call them Nows. The world is made of Nows.

Space and time in their previous role as the stage of the world are redundant. There is no container. The world does not contain things, it is things. These things are Nows that, so to speak, hover in nothing. Newtonian physics, Einstein’s relativity and quantum mechanics will all be seen to do different things with the Nows. They arrange them in different ways. What is more, the rules that govern the universe as a whole leave imprints on what we find around us. These local imprints, which physicists take as the fundamental laws of nature, reveal few hints of their origin in a deeper scheme of things. The attempt to understand the universe as a whole by `stringing together’ these local imprints without a grasp of their origin must give a false picture. It will be the flat Earth writ large. My aim is to show how the local imprints can arise from a deeper reality, how a theory of time emerges from timelessness. The task is not to study time, but to show how nature creates the impression of time.

It is an ambitious task. How can a static universe appear so dynamic? How is it possible to watch the flashing colours of the kingfisher in flight and say there is no motion? If you read to the end, you will find that I do propose an answer. I make no claim that it is definitely right — choices must be made, and many physicists would not make mine, If all were clear, I should not have promised a but the theory of time. In order not to interrupt the flow of the text, I make few references to the problems in my timeless description of the world. Instead, I have collected together all those of which I am aware in the Notes. Although, as will be evident throughout the book, I do believe rather strongly in the theory I propose, there is a sense in which even clear disproof of my theory would be exciting for me. The problems of time are very deep. Clear proof that I am wrong would certainly mark a significant advance in our understanding of time. In a way, I cannot lose! Whatever the outcome, I shall be more than happy if this book gives you a novel way of thinking about time, exposes you to some of the mysteries of the universe, and encourages even one reader to embark, as I did 35 years ago, on a study of time.

For the study of time is not just that — it is the study of everything.

GETTING TO GRIPS WITH ELUSIVE TIME

The hardest thing of all is to find a black cat in a dark room, especially if there is no cat.
Confucius

We must begin by trying to agree what time is. The problems start already, as St Augustine found. Nearly everybody would agree that time is experienced as something linear. It seems to move forward relentlessly, through instants strung out continuously on a line. We ride on an everchanging Now like passengers on a train. Each point on the line is a new instant. But is time moving forward — and if so through what — or are we moving forward through time? It is all very puzzling, and philosophers have got into interminable arguments. I shall not attempt to sort them out, since I do not think it would get us anywhere. The trouble with time is its invisibility. We shall never agree unless we can talk about something we can see and grasp.

I think it is more fruitful to try to agree on what an instant of time is like. I suggest it is like a `three-dimensional snapshot’. In any instant, we see objects in definite positions. Snapshots confirm our impression; artists were painting pictures that look like snapshots long before cameras were invented. This does seem to be a natural way to think about the experience of an instant. We also have evidence from the other senses. I feel an itch at the same time as seeing a moving object in a certain position. All the things I see, hear, smell and taste are knit together in a whole. `Knitting together’ seems to me the defining property of an instant. It gives it a unity.

The three-dimensional snapshots I have in mind could be constructed if many different people took ordinary two-dimensional snapshots of a scene at the same instant. Comparison of the information in them makes it possible to build up a three-dimensional picture of the world in that instant. That is what I mean by a Now. It is very remarkable that such completely different two-dimensional pictures can be reconciled in a three-dimensional representation. The possibility of this ordering is what leads us to say that things exist in three-dimensional space. It leads to an even deeper `knitting together’ over and above the directly experienced sense of being aware of many different things at once (it is this that enables us to know instantly that we are seeing, say, six distinct objects without counting them individually). I regard space as a `glue’, or a set of rules, that binds things together. It is a plurality within a deep unity, and it makes a Now.

You may object that no experience is instantaneous, just as snapshots require finite exposures. True, but we can still liken instants to snapshots. It is the best idealization I know. It allows us to begin to get our hands on time, which is otherwise for ever slipping through our fingers. As instants, rather than an invisible river, time becomes concrete. We can pore over photographs, looking for evidence in them like military intelligence analysts studying satellite pictures. We can imagine `photographing’ our successive experiences, obtaining innumerable snapshots. Using them, we can identify the most important properties of experienced time.

THE PROPERTIES OF EXPERIENCED TIME

Suppose that the snapshots are taken when we are witnessing lots of things happening, say people streaming past us in a street, and that the snapshots (either two-dimensional, as directly experienced, or `three-dimensional’, as explained above), once taken, are jumbled up in a heap. A different person, given the heap, could relatively easily, by examining the details in the snapshots, arrange them in the order they were experienced. A movie can be reassembled from its individual frames. My notion of time depends crucially on the details that the `snapshots’ carry. It requires the richly structured world we do experience.

This imaginary exercise brings out the most important property of experienced time: its instants can all be laid out in a row. They come in a linear sequence. This is a very strong impression. It is created not by invisible time, but by concrete things.

It is harder to pin down other properties. I have already mentioned the difficulty of saying precisely what the powerful impression of moving forward in time consists of. We also have the intuition of length of time, or duration. Indeed, seconds, minutes, hours dominate our age, though you may not know how these precise notions have arisen. That is an important issue. Finally, there is the remarkably strong sense that time has a direction. A line traced in the sand does not by itself define a direction. If time is a line, it is a special one.

The evidence for time’s direction is in the `snapshots’. Many contain memories of other snapshots. We can do a test on time. We can stop at one of our experienced instants laid out in a line, and see that it contains a memory. We locate the remembered instant somewhere in the line. That defines a direction — from it to the memory of it. We can do this with other pairs of instants. They always define the same direction. Many other phenomena define a direction. Coffee cools down unless we put it in the microwave; it never heats up. Cups shatter when we drop them; shards never reassemble themselves and leap back up onto the table as a whole cup. All these phenomena, like memories, define a direction in time, and they all point the same way. Time has an arrow.

Thus, experienced time is linear, it can be measured and it has an arrow. These are not properties of an invisible river: they belong to concrete instants. Everything we know about time is garnered from them. Time is inferred from things.

NEWTON’S CONCEPTS

In 1687, Newton created precise notions of space, time and motion. Despite major revisions, much of his scheme remains intact. It is still close to the way many people, including scientists, think about time.

Newton’s time is absolute. It flows with perfect uniformity for ever and nothing in the world affects its flow. Space, too, is absolute. Newton conceived of space as a limitless container. It stretches from infinity to infinity like a translucent block of glass, through which, nevertheless, objects can move unhindered. Space is a huge arena; time is a clock in the grandstand. Both are more fundamental than things. Newton could imagine an empty world but not a world without space and time. Many philosophers have agreed with him. So does the proverbial man in the pub, convinced that space goes on for ever and that `there must have been time before the Big Bang’.

At any instant, all the things in the Newtonian world are at definite positions. His absolute space performs two distinct roles. As in the discussion above, it binds, or holds, things together, in one instant. But it also places them in a container. Imagine taking two-dimensional snapshots of a table in a room. Paint out the background room, and you could still reconstruct the form of the three-dimensional table, but you would not know where to place it. Newton insisted that the things in the world in any instant have a definite place, and he posited absolute space as a kind of room to provide that place. His fixed container persists through time. We could take real snapshots of the things in the world (Figure 1). Ideally, these snapshots should be three-dimensional, like space, and show all things relative to each other and their positions in absolute space, just as snapshots of a soccer match show the players, ball and referee on the pitch with its markings. The grandstand clock records the time.

According to Newton, all bodies move through absolute space in accordance with definite laws of motion which govern the speed and direction of the bodies in that space as measured by absolute time. The laws are such that if the motions of the bodies are known at some instant, the laws determine all the future movements. All the world’s history can be determined from two snapshots taken in quick succession. (If you know where something is at two closely spaced instants, you can tell its speed and direction. Two such snapshots thus encode the future.)

Newton’s picture is close to everyday experience. We do not see absolute space and time, but we do see something quite like them — the rigid Earth, which defines positions, and the Sun, whose motion is a kind of clock. Newton’s revolution was the establishment of strict laws that hold in such a framework.

LAWS AND INITIAL CONDITIONS

These laws have a curious property. They determine motions only if certain initial conditions are combined with them. Newton believed that God `set up’ (created) the universe at some time in the past by placing objects in absolute space with definite motions; after that, the laws of motion took over. The statement that Newton’s is a clockwork universe is a bit misleading. Clocks have one predetermined motion: the pendulum of the grandfather clock simply goes backwards and forwards. The Newtonian universe is much more remarkable, being capable of many motions. However, once an initial condition has been chosen, everything follows.

Thus, there are two disparate elements in the scientific account of the universe: eternal laws, and a freely specifiable initial condition. Einstein’s relativity and major astronomical discoveries have merely added to this dual scheme the exciting novelty of a universe exploding into being about fifteen billion years ago. The initial condition was set at the Big Bang.

Some people question this dual scheme. Is it an immutable feature? Might we not find laws that stand alone, without initial conditions? These questions are particularly relevant because Newton’s laws (and also Einstein’s theories of relativity, which replaced them) have a property that seems quite at variance with the way we feel the universe works — that the past determines the future. We do not think that causality works from the future to the past. Scientists always consider initial conditions. But Newton’s and Einstein’s laws work equally well in both directions. The truth is that the string of triangles in Figure 1 is determined by Newton’s laws acting in both directions by any two neighboring triangles anywhere along the string. You can persuade yourself of this by looking at the figure again. It is impossible to say in which direction time flows. The caption speaks of `strobe lighting’ illuminating the triangles at equal time intervals, but does not say which is illuminated first. Scientists could examine the triangles until the crack of doom but could never find which came first. This is related to one of the biggest puzzles in science.

WHY IS THE UNIVERSE SO SPECIAL?

The universe we see around us today is special: it is very highly ordered. For example, light streams away in a very regular flow from billions upon billions of stars throughout the universe. These stars are themselves collected together in galaxies, of which there are just a few basic types. Here on Earth we find very complex molecules and very complicated life forms that could not possibly exist were it not for the steady stream of sunlight that constantly bathes our planet. However, the vast majority of conceivable initial conditions there could have been at the Big Bang would have led to universes much less interesting — indeed, positively dull — compared with ours. Only an exceptional initial condition could have led to the present order. That is the puzzle. Modern science is in the remarkable position of possessing beautiful and very well tested laws without really being able to explain the universe. In the dual scheme of laws and initial conditions, the great burden of explaining why the universe is as it is falls to the initial conditions. Science can as yet give no explanation of why those conditions were as they must have been to explain the presently observed universe. The universe looks like a fluke.

There are two remarkable things about the order in the universe: the amount of it and the way it degrades. One of the greatest discoveries of science, made about a hundred and fifty years ago, was the second law of thermodynamics. Studies of the efficiency with which steam engines turn heat into mechanically useful motion led to the concept of entropy. As originally discovered, this is a measure of how much useful work can be got out of hot gas, say. It is here that the arrow of time, which we know from direct experience, enters physics. Almost all processes observed in the universe have a directionality. In an isolated system, temperature differences are always equalized. This means, for example, that you cannot extract energy from a cooler gas to make a hotter gas even hotter and chuff along in your steam engine even faster. More strictly, if you did, you would degrade more energy than you gain and finish up worse off.

I have already mentioned the unidirectional process of a cup breaking. Another is mixing cream with coffee. It is virtually impossible to reverse these processes. This is beautifully illustrated by running a film backwards: you see things that are impossible in the real world. This unidirectionality, or arrow, is precisely reflected in the fact that the entropy of any isolated system left to itself always increases (or perhaps stays constant).

It was recognized in the late nineteenth century that this unidirectionality of observed processes was in sharp conflict with the fact that Newton’s laws should work equally well in either time direction. Why do natural processes always run one way, while the laws of physics say they could run equally well either way? For four decades, from 1866 until his suicide on 5 September 1906 in the picturesque Adriatic resort of Duino, the Austrian physicist Ludwig Boltzmann attempted to resolve this conflict. He introduced a theoretical definition of entropy as the probability of a state. He firmly believed in atoms — the existence of which remained controversial until the early years of the twentieth century — conceived of as tiny particles rushing around at great speed in accordance with Newtonian laws. Heat was assumed to be a measure of the speed of atoms: the faster the atoms, the hotter the substance. By the second half of the nineteenth century, physicists had a good idea of the immense number of atoms (assuming that they existed) there must be even in a grain of sand, and Boltzmann, among others, saw that statistical arguments must be used to describe how atoms behave.

He asked how probable a state should be. Imagine a grid of 100 holes into which you drop 1000 marbles at random. It is hugely improbable that they will all finish up in one hole. I am not going to give numbers, but it is simple to work out the probability that all will land in one hole or, say, in four adjacent holes. In fact, one can list every possible distribution of the marbles in the grid, and then see in how many of these distributions all the marbles fall in one hole, in four adjacent holes, eight adjacent holes, and so on. If each distribution is assumed to be equally probable, the number of ways a particular outcome can happen becomes the relative probability of that outcome, or state. Boltzmann had the inspired idea that, applied to atoms, this probability (which must also take into account the velocities of the atoms) is a measure of the entropy that had been found through study of the thermodynamics of steam engines.

There is no need to worry about the technical details. The important thing is that states with low entropy are inherently improbable. Boltzmann’s idea was brilliantly successful, and much of modern chemistry, for example, would be unthinkable without it. However, his attempt to explain the more fundamental issues associated with the unidirectionality of physical processes was only partly successful.

He wanted to show that, matching the behaviour of macroscopic entropy, his microscopic entropy would necessarily increase solely by virtue of Newton’s laws. This seems plausible. If a large number of atoms are in some unlikely state, say all in a small region, so that they have a low entropy, it seems clear that they will pass to a more probable state with higher entropy. However, it was soon noted that there are exactly as many dynamically possible motions of the atoms that go from states of low probability to states of high probability as vice versa. This is a straight consequence of the fact that Newton’s laws have the same form for the two directions of time. Newton’s laws alone cannot explain the arrow of time.

Only two ways have ever been found to explain the arrow: either the universe was created in a highly unlikely special state, and its initial order has been `degrading’ ever since, or it has existed for ever, and at some time in the recent past it entered by chance an exceedingly improbable state of very low entropy, from which it is now emerging. The second possibility is entirely compatible with the laws of physics. For example, if a collection of atoms (which obey Newton’s laws) is confined in a box and completely isolated, it will, over a sufficiently long period of time, visit (or rather come arbitrarily near) all the states that it can in principle ever reach, even those that are highly ordered and statistically very unlikely. However, the intervals of time between returns to states of very low entropy are stupendously long (vastly longer than the presently assumed age of the universe), and neither explanation is attractive.

The fact is that mechanical laws of motion allow an almost incomprehensibly large number of different possible situations. Interesting structure and order arise only in the tiniest fraction of them. Scientists feel they should not invoke miracles to explain the order we see, but that leaves only statistical arguments, which give bleak answers (only dull situations can be expected), or the so-called anthropic principle that if the world were not in a highly structured but extremely unlikely state, we should not exist and be here to observe it.

One of my reasons for writing this book is that timeless physics opens up new ways of thinking about structure and entropy. It may be easier to explain the arrow of time if there is no time!

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shinichi Post author07/07/2013 at 5:25 am

The End of Time

The Next Revolution in Physics

by Julian Barbour

Chapter 1

http://www.nytimes.com/books/first/b/barbour-time.html

The Main Puzzles

THE NEXT REVOLUTION IN PHYSICS

Nothing is more mysterious and elusive than time. It seems to be the most powerful force in the universe, carrying us inexorably from birth to death. But what exactly is it? St Augustine, who died in AD 430, summed up the problem thus: `If nobody asks me, I know what time is, but if I am asked then I am at a loss what to say.’ All agree that time is associated with change, growth and decay, but is it more than this? Questions abound. Does time move forward, bringing into being an ever-changing present? Does the past still exist? Where is the past? Is the future already predetermined, sitting here waiting for us though we know not what it is? All these questions will be addressed in this book, but the biggest remains the one St Augustine could not answer: what is time?

Curiously, physicists have tended not to ask this question, preferring to leave it to philosophers. The reason is probably the colossal and dominating influence of Isaac Newton and Albert Einstein. They shaped the way physicists think about space, time and motion. Each created a representation of the world of unsurpassed clarity. But having seen their way to a structure of things, they did not bother unduly about its foundations. This creates potential for confusion. Without question, their theories contain wonderful truths, but they both take time as given. It is a building block on a par with space, a primary substance. In fact, Einstein fused it with three-dimensional space to make four-dimensional space-time. This was one of the great revolutions of physics (Box 1).

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BOX 1 The Great Revolutions of Physics

1543: The Copernican Revolution. In On the Revolutions of the Celestial Spheres, Nicolaus Copernicus proposed that the Earth moves around the centre of the universe. The modern meaning of revolution derives from his title. He established the form of the solar system. Curiously, the Sun plays little part in his scheme; he merely placed it near the centre of the universe. About sixty years later Johannes Kepler showed that the Sun is the true centre of the solar system, and with Galileo Galilei he prepared the way for the next revolution.

1687: The Newtonian Revolution. In The Mathematical Principles of Natural Philosophy, Newton formulated his three famous laws of motion and the theory of universal gravitation. He showed that all bodies — terrestrial and celestial — obey the same laws, and thus set up the first scheme capable of describing the entire universe as a unified whole. Newton created the science of mechanics, now often called dynamics, which ushered in the modern scientific age. He claimed that all motions take place in an infinite, immovable, absolute space and that time too is absolute and `flows uniformly without relation to anything external’.

1905: The Special Theory of Relativity. In a relatively short paper on electromagnetism, Einstein showed that simultaneity cannot be defined absolutely at spatially separated points, and that space and time are inextricably linked together. What appears as space and what appears as time depends on the motion of the observer. He made startling predictions about the behaviour of measuring rods and clocks, and found his famous equation E = mc². In 1908 Hermann Minkowski formalized the notion of space-time as a rigid, indissoluble, four-dimensional arena of world events.

1915: The General Theory of Relativity. The special theory of relativity describes a world without gravitation. After an eight-year gestation, Einstein finally formulated his general theory of relativity in which the rigid arena of Minkowski’s space-time is made flexible, responding to the presence of matter in it. Gravity is given a brilliantly original interpretation as an effect of the curving of space-time. The theory showed that time can have a beginning (the Big Bang) and that the universe can expand or contract. Although to a remarkable degree it was a creation of pure thought, many predictions of this theory have now been very well confirmed. It describes the large-scale properties of matter and the universe as a whole.

1925/6: Quantum Mechanics. This gets its name because it shows that some mechanical quantities are found in nature only in multiples of discrete units called quanta. This is a distinctive difference from the theories of Newton and Einstein, which are now called classical (as opposed to quantum) theories. The first quantum effects were discovered and described on an ad hoc basis by Max Planck (1900), Einstein (1905) and Niels Bohr (1913), while a consistent quantum theory was found in two different but equivalent forms: matrix mechanics, by Werner Heisenberg (1925), and wave mechanics, by Erwin Schrödinger (1926). Paul Dirac also made outstanding contributions. Quantum mechanics describes the properties of light, especially lasers, and the microscopic world of atoms and molecules. It is the bedrock of all modern electronic technology, but its results are bafflingly counter-intuitive and raise profound issues about the nature of reality. It is also puzzling that theories of completely different structures are used to describe the macroscopic universe (classical general relativity) and microscopic atoms (quantum mechanics).
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Revolutions are what make physics such a fascinating science. Every now and then a totally new perspective is opened up. But it is not that we close the shutters on one window, open them on another, and find ourselves looking out in wonder on a brand-new landscape. The old insights are retained within the new picture. A better metaphor of physics is mountaineering: the higher we climb, the more comprehensive the view. Each new vantage point yields a better understanding of the interconnection of things. What is more, gradual accumulation of understanding is punctuated by sudden and startling enlargements of the horizon, as when we reach the brow of a hill and see things never conceived of in the ascent. Once we have found our bearings in the new landscape, our path to the most recently attained summit is laid bare and takes its honourable place in the new world.

Today, physicists confidently, indeed impatiently, await the next revolution. But what will it be? In 1979, when, like Newton and Dirac before him, Stephen Hawking became the Lucasian Professor at Cambridge, he announced in his inaugural address the imminent end of physics. Within twenty years physicists would possess a theory of everything, created by a double unification: of all the forces of nature, and of Einstein’s general theory of relativity with quantum mechanics. Physicists would then know all the inner secrets of existence, and it would merely remain to work out the consequences.

Neither unification has yet happened, though one or both certainly could. (Hawking has recently said that his prediction still stands but that `the twenty years starts now’.) For myself, I doubt that would spell the end of physics. But unification of general relativity and quantum mechanics may well spell the end of time. By this, I mean that it will cease to have a role in the foundations of physics. We shall come to see that time does not exist. Though still only a prospect on the horizon, this, I think, could well be the next revolution. What a denouement if it is!

I believe that the basic elements of this potential revolution — the reasons for it and its likely outcome — can already be discerned. In fact, as we shall shortly see, clear hints that time may not exist, and that quantum gravity — the unification of general relativity and quantum mechanics — will yield a static picture of the quantum universe, started to emerge about thirty years ago, but made remarkably little impact. This is one of my reasons for writing this book: these things should be better known. They are only just beginning to be mentioned in books for the general reader, and even most working physicists know little or nothing about them.

No doubt many people will dismiss the suggestion that time may not exist as nonsense. I am not denying the powerful phenomenon we call time. But is it what it seems to be? After all, the Earth seems to be flat. I believe the true phenomenon is so different that, presented to you as I think it is without any mention of the word `time’, it would not occur to you to call it that.

If time is removed from the foundations of physics, we shall not all suddenly feel that the flow of time has ceased. On the contrary, new timeless principles will explain why we do feel that time flows. The pattern of the first great revolution will be repeated. Copernicus, Galileo and Kepler taught us that the Earth moves and rotates while the heavens stand still, but this did not change by one iota our direct perception that the heavens do move and that the Earth does not budge. Our grasp of the interconnection of things was, however, eventually changed out of recognition in ways that were impossible to foresee. Now I think we must, in an ironic twist to the Copernican revolution, go further, to a deeper reality in which nothing at all, neither heavens nor Earth, moves. Stillness reigns.

People often ask me what are the implications of the non-existence of time. What will it mean for everyday life? I think we cannot say. Copernicus had no inkling of what Newton (let alone Einstein) would find, though it all flowed from his revolution. But we can be certain that our ideas about time, causality and origins will be transformed. At the personal level, thinking about these things has persuaded me that we should cherish the present. That certainly exists, and is perhaps even more wonderful than we realize. Carpe diem — seize the day. I expand on this in the Epilogue.

THE ULTIMATE THINGS

This book revolves around three questions: What is time? What is change? What is the plan of the universe? The only way to answer them is to examine the structure of our most successful theories. We must fathom the architecture of nature. What part, if any, is played by time in these theories? Can we identify the ultimate arena of the world?

These questions were forced upon physicists by the work I mentioned in the Preface. It is one of the two big (and almost certainly intimately connected) mysteries of modern physics (Box 2). Both are aspects of an as yet unbridged chasm between classical and quantum physics.

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BOX 2 The Two Big Mysteries

As explained in Box 1, physicists currently describe the world by means of two very different theories. Large things are described by classical physics, small things by quantum physics. There are two problems with this picture.

First, general relativity, Einstein’s theory of gravity, seems to be incompatible with the principles of quantum mechanics in a way that Newtonian dynamics and the theory of electromagnetism, developed by Michael Faraday and James Clerk Maxwell in the nineteenth century, are not. For these theories, it proved possible to transform them, by a process known as quantization, from classical into quantum theories. Attempts to apply the same process to general relativity and create quantum gravity failed. It was this technical work, by Dirac and others, which brought to the fore all the problems about time with which this book is concerned.

The second mystery is the relationship between quantum and classical physics. It seems that quantum physics is more fundamental and ought to apply to large objects, even the universe. There ought to be a quantum theory of the universe: quantum cosmology. But quantum physics does not yet exist in such a form. And its present form is very mysterious. Part of it seems to describe the actual behaviour of atoms, molecules and radiation, but another part consists of rather strange rules that act at the interface between the microscopic and macroscopic worlds. Indeed, the very existence of a seemingly unique universe is a great puzzle within the framework of quantum mechanics. This is very unsatisfactory, since physicists have a deep faith in the unity of nature. Because general relativity is simultaneously a theory of gravity and the large-scale structure of the universe, the creation of quantum cosmology will certainly require the solution of the only slightly narrower problem of quantum gravity.
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One of the themes of my book is that this chasm has arisen because physicists have deep-rooted but false ideas about the nature of space, time and things. Preconceptions obscure the true nature of the world. Physicists are using too many concepts. They assume that there are many things, and that these things move in a great invisible framework of space and time.

A radical alternative put forward by Newton’s rival Leibniz provides my central idea. The world is to be understood, not in the dualistic terms of atoms (things of one kind) that move in the framework and container of space and time (another quite different kind of thing), but in terms of more fundamental entities that fuse space and matter into the single notion of a possible arrangement, or configuration, of the entire universe. Such configurations, which can be fabulously richly structured, are the ultimate things. There are infinitely many of them; they are all different instances of a common principle of construction; and they are all, in my view, the different instants of time. In fact, many people who have written about time have conceived of instants of time in a somewhat similar way, and have called them `nows’. Since I make the concept more precise and put it at the heart of my theory of time, I shall call them Nows. The world is made of Nows.

Space and time in their previous role as the stage of the world are redundant. There is no container. The world does not contain things, it is things. These things are Nows that, so to speak, hover in nothing. Newtonian physics, Einstein’s relativity and quantum mechanics will all be seen to do different things with the Nows. They arrange them in different ways. What is more, the rules that govern the universe as a whole leave imprints on what we find around us. These local imprints, which physicists take as the fundamental laws of nature, reveal few hints of their origin in a deeper scheme of things. The attempt to understand the universe as a whole by `stringing together’ these local imprints without a grasp of their origin must give a false picture. It will be the flat Earth writ large. My aim is to show how the local imprints can arise from a deeper reality, how a theory of time emerges from timelessness. The task is not to study time, but to show how nature creates the impression of time.

It is an ambitious task. How can a static universe appear so dynamic? How is it possible to watch the flashing colours of the kingfisher in flight and say there is no motion? If you read to the end, you will find that I do propose an answer. I make no claim that it is definitely right — choices must be made, and many physicists would not make mine, If all were clear, I should not have promised a but the theory of time. In order not to interrupt the flow of the text, I make few references to the problems in my timeless description of the world. Instead, I have collected together all those of which I am aware in the Notes. Although, as will be evident throughout the book, I do believe rather strongly in the theory I propose, there is a sense in which even clear disproof of my theory would be exciting for me. The problems of time are very deep. Clear proof that I am wrong would certainly mark a significant advance in our understanding of time. In a way, I cannot lose! Whatever the outcome, I shall be more than happy if this book gives you a novel way of thinking about time, exposes you to some of the mysteries of the universe, and encourages even one reader to embark, as I did 35 years ago, on a study of time.

For the study of time is not just that — it is the study of everything.

GETTING TO GRIPS WITH ELUSIVE TIME

The hardest thing of all is to find a black cat in a dark room, especially if there is no cat.
Confucius

We must begin by trying to agree what time is. The problems start already, as St Augustine found. Nearly everybody would agree that time is experienced as something linear. It seems to move forward relentlessly, through instants strung out continuously on a line. We ride on an everchanging Now like passengers on a train. Each point on the line is a new instant. But is time moving forward — and if so through what — or are we moving forward through time? It is all very puzzling, and philosophers have got into interminable arguments. I shall not attempt to sort them out, since I do not think it would get us anywhere. The trouble with time is its invisibility. We shall never agree unless we can talk about something we can see and grasp.

I think it is more fruitful to try to agree on what an instant of time is like. I suggest it is like a `three-dimensional snapshot’. In any instant, we see objects in definite positions. Snapshots confirm our impression; artists were painting pictures that look like snapshots long before cameras were invented. This does seem to be a natural way to think about the experience of an instant. We also have evidence from the other senses. I feel an itch at the same time as seeing a moving object in a certain position. All the things I see, hear, smell and taste are knit together in a whole. `Knitting together’ seems to me the defining property of an instant. It gives it a unity.

The three-dimensional snapshots I have in mind could be constructed if many different people took ordinary two-dimensional snapshots of a scene at the same instant. Comparison of the information in them makes it possible to build up a three-dimensional picture of the world in that instant. That is what I mean by a Now. It is very remarkable that such completely different two-dimensional pictures can be reconciled in a three-dimensional representation. The possibility of this ordering is what leads us to say that things exist in three-dimensional space. It leads to an even deeper `knitting together’ over and above the directly experienced sense of being aware of many different things at once (it is this that enables us to know instantly that we are seeing, say, six distinct objects without counting them individually). I regard space as a `glue’, or a set of rules, that binds things together. It is a plurality within a deep unity, and it makes a Now.

You may object that no experience is instantaneous, just as snapshots require finite exposures. True, but we can still liken instants to snapshots. It is the best idealization I know. It allows us to begin to get our hands on time, which is otherwise for ever slipping through our fingers. As instants, rather than an invisible river, time becomes concrete. We can pore over photographs, looking for evidence in them like military intelligence analysts studying satellite pictures. We can imagine `photographing’ our successive experiences, obtaining innumerable snapshots. Using them, we can identify the most important properties of experienced time.

THE PROPERTIES OF EXPERIENCED TIME

Suppose that the snapshots are taken when we are witnessing lots of things happening, say people streaming past us in a street, and that the snapshots (either two-dimensional, as directly experienced, or `three-dimensional’, as explained above), once taken, are jumbled up in a heap. A different person, given the heap, could relatively easily, by examining the details in the snapshots, arrange them in the order they were experienced. A movie can be reassembled from its individual frames. My notion of time depends crucially on the details that the `snapshots’ carry. It requires the richly structured world we do experience.

This imaginary exercise brings out the most important property of experienced time: its instants can all be laid out in a row. They come in a linear sequence. This is a very strong impression. It is created not by invisible time, but by concrete things.

It is harder to pin down other properties. I have already mentioned the difficulty of saying precisely what the powerful impression of moving forward in time consists of. We also have the intuition of length of time, or duration. Indeed, seconds, minutes, hours dominate our age, though you may not know how these precise notions have arisen. That is an important issue. Finally, there is the remarkably strong sense that time has a direction. A line traced in the sand does not by itself define a direction. If time is a line, it is a special one.

The evidence for time’s direction is in the `snapshots’. Many contain memories of other snapshots. We can do a test on time. We can stop at one of our experienced instants laid out in a line, and see that it contains a memory. We locate the remembered instant somewhere in the line. That defines a direction — from it to the memory of it. We can do this with other pairs of instants. They always define the same direction. Many other phenomena define a direction. Coffee cools down unless we put it in the microwave; it never heats up. Cups shatter when we drop them; shards never reassemble themselves and leap back up onto the table as a whole cup. All these phenomena, like memories, define a direction in time, and they all point the same way. Time has an arrow.

Thus, experienced time is linear, it can be measured and it has an arrow. These are not properties of an invisible river: they belong to concrete instants. Everything we know about time is garnered from them. Time is inferred from things.

NEWTON’S CONCEPTS

In 1687, Newton created precise notions of space, time and motion. Despite major revisions, much of his scheme remains intact. It is still close to the way many people, including scientists, think about time.

Newton’s time is absolute. It flows with perfect uniformity for ever and nothing in the world affects its flow. Space, too, is absolute. Newton conceived of space as a limitless container. It stretches from infinity to infinity like a translucent block of glass, through which, nevertheless, objects can move unhindered. Space is a huge arena; time is a clock in the grandstand. Both are more fundamental than things. Newton could imagine an empty world but not a world without space and time. Many philosophers have agreed with him. So does the proverbial man in the pub, convinced that space goes on for ever and that `there must have been time before the Big Bang’.

At any instant, all the things in the Newtonian world are at definite positions. His absolute space performs two distinct roles. As in the discussion above, it binds, or holds, things together, in one instant. But it also places them in a container. Imagine taking two-dimensional snapshots of a table in a room. Paint out the background room, and you could still reconstruct the form of the three-dimensional table, but you would not know where to place it. Newton insisted that the things in the world in any instant have a definite place, and he posited absolute space as a kind of room to provide that place. His fixed container persists through time. We could take real snapshots of the things in the world (Figure 1). Ideally, these snapshots should be three-dimensional, like space, and show all things relative to each other and their positions in absolute space, just as snapshots of a soccer match show the players, ball and referee on the pitch with its markings. The grandstand clock records the time.

According to Newton, all bodies move through absolute space in accordance with definite laws of motion which govern the speed and direction of the bodies in that space as measured by absolute time. The laws are such that if the motions of the bodies are known at some instant, the laws determine all the future movements. All the world’s history can be determined from two snapshots taken in quick succession. (If you know where something is at two closely spaced instants, you can tell its speed and direction. Two such snapshots thus encode the future.)

Newton’s picture is close to everyday experience. We do not see absolute space and time, but we do see something quite like them — the rigid Earth, which defines positions, and the Sun, whose motion is a kind of clock. Newton’s revolution was the establishment of strict laws that hold in such a framework.

LAWS AND INITIAL CONDITIONS

These laws have a curious property. They determine motions only if certain initial conditions are combined with them. Newton believed that God `set up’ (created) the universe at some time in the past by placing objects in absolute space with definite motions; after that, the laws of motion took over. The statement that Newton’s is a clockwork universe is a bit misleading. Clocks have one predetermined motion: the pendulum of the grandfather clock simply goes backwards and forwards. The Newtonian universe is much more remarkable, being capable of many motions. However, once an initial condition has been chosen, everything follows.

Thus, there are two disparate elements in the scientific account of the universe: eternal laws, and a freely specifiable initial condition. Einstein’s relativity and major astronomical discoveries have merely added to this dual scheme the exciting novelty of a universe exploding into being about fifteen billion years ago. The initial condition was set at the Big Bang.

Some people question this dual scheme. Is it an immutable feature? Might we not find laws that stand alone, without initial conditions? These questions are particularly relevant because Newton’s laws (and also Einstein’s theories of relativity, which replaced them) have a property that seems quite at variance with the way we feel the universe works — that the past determines the future. We do not think that causality works from the future to the past. Scientists always consider initial conditions. But Newton’s and Einstein’s laws work equally well in both directions. The truth is that the string of triangles in Figure 1 is determined by Newton’s laws acting in both directions by any two neighboring triangles anywhere along the string. You can persuade yourself of this by looking at the figure again. It is impossible to say in which direction time flows. The caption speaks of `strobe lighting’ illuminating the triangles at equal time intervals, but does not say which is illuminated first. Scientists could examine the triangles until the crack of doom but could never find which came first. This is related to one of the biggest puzzles in science.

WHY IS THE UNIVERSE SO SPECIAL?

The universe we see around us today is special: it is very highly ordered. For example, light streams away in a very regular flow from billions upon billions of stars throughout the universe. These stars are themselves collected together in galaxies, of which there are just a few basic types. Here on Earth we find very complex molecules and very complicated life forms that could not possibly exist were it not for the steady stream of sunlight that constantly bathes our planet. However, the vast majority of conceivable initial conditions there could have been at the Big Bang would have led to universes much less interesting — indeed, positively dull — compared with ours. Only an exceptional initial condition could have led to the present order. That is the puzzle. Modern science is in the remarkable position of possessing beautiful and very well tested laws without really being able to explain the universe. In the dual scheme of laws and initial conditions, the great burden of explaining why the universe is as it is falls to the initial conditions. Science can as yet give no explanation of why those conditions were as they must have been to explain the presently observed universe. The universe looks like a fluke.

There are two remarkable things about the order in the universe: the amount of it and the way it degrades. One of the greatest discoveries of science, made about a hundred and fifty years ago, was the second law of thermodynamics. Studies of the efficiency with which steam engines turn heat into mechanically useful motion led to the concept of entropy. As originally discovered, this is a measure of how much useful work can be got out of hot gas, say. It is here that the arrow of time, which we know from direct experience, enters physics. Almost all processes observed in the universe have a directionality. In an isolated system, temperature differences are always equalized. This means, for example, that you cannot extract energy from a cooler gas to make a hotter gas even hotter and chuff along in your steam engine even faster. More strictly, if you did, you would degrade more energy than you gain and finish up worse off.

I have already mentioned the unidirectional process of a cup breaking. Another is mixing cream with coffee. It is virtually impossible to reverse these processes. This is beautifully illustrated by running a film backwards: you see things that are impossible in the real world. This unidirectionality, or arrow, is precisely reflected in the fact that the entropy of any isolated system left to itself always increases (or perhaps stays constant).

It was recognized in the late nineteenth century that this unidirectionality of observed processes was in sharp conflict with the fact that Newton’s laws should work equally well in either time direction. Why do natural processes always run one way, while the laws of physics say they could run equally well either way? For four decades, from 1866 until his suicide on 5 September 1906 in the picturesque Adriatic resort of Duino, the Austrian physicist Ludwig Boltzmann attempted to resolve this conflict. He introduced a theoretical definition of entropy as the probability of a state. He firmly believed in atoms — the existence of which remained controversial until the early years of the twentieth century — conceived of as tiny particles rushing around at great speed in accordance with Newtonian laws. Heat was assumed to be a measure of the speed of atoms: the faster the atoms, the hotter the substance. By the second half of the nineteenth century, physicists had a good idea of the immense number of atoms (assuming that they existed) there must be even in a grain of sand, and Boltzmann, among others, saw that statistical arguments must be used to describe how atoms behave.

He asked how probable a state should be. Imagine a grid of 100 holes into which you drop 1000 marbles at random. It is hugely improbable that they will all finish up in one hole. I am not going to give numbers, but it is simple to work out the probability that all will land in one hole or, say, in four adjacent holes. In fact, one can list every possible distribution of the marbles in the grid, and then see in how many of these distributions all the marbles fall in one hole, in four adjacent holes, eight adjacent holes, and so on. If each distribution is assumed to be equally probable, the number of ways a particular outcome can happen becomes the relative probability of that outcome, or state. Boltzmann had the inspired idea that, applied to atoms, this probability (which must also take into account the velocities of the atoms) is a measure of the entropy that had been found through study of the thermodynamics of steam engines.

There is no need to worry about the technical details. The important thing is that states with low entropy are inherently improbable. Boltzmann’s idea was brilliantly successful, and much of modern chemistry, for example, would be unthinkable without it. However, his attempt to explain the more fundamental issues associated with the unidirectionality of physical processes was only partly successful.

He wanted to show that, matching the behaviour of macroscopic entropy, his microscopic entropy would necessarily increase solely by virtue of Newton’s laws. This seems plausible. If a large number of atoms are in some unlikely state, say all in a small region, so that they have a low entropy, it seems clear that they will pass to a more probable state with higher entropy. However, it was soon noted that there are exactly as many dynamically possible motions of the atoms that go from states of low probability to states of high probability as vice versa. This is a straight consequence of the fact that Newton’s laws have the same form for the two directions of time. Newton’s laws alone cannot explain the arrow of time.

Only two ways have ever been found to explain the arrow: either the universe was created in a highly unlikely special state, and its initial order has been `degrading’ ever since, or it has existed for ever, and at some time in the recent past it entered by chance an exceedingly improbable state of very low entropy, from which it is now emerging. The second possibility is entirely compatible with the laws of physics. For example, if a collection of atoms (which obey Newton’s laws) is confined in a box and completely isolated, it will, over a sufficiently long period of time, visit (or rather come arbitrarily near) all the states that it can in principle ever reach, even those that are highly ordered and statistically very unlikely. However, the intervals of time between returns to states of very low entropy are stupendously long (vastly longer than the presently assumed age of the universe), and neither explanation is attractive.

The fact is that mechanical laws of motion allow an almost incomprehensibly large number of different possible situations. Interesting structure and order arise only in the tiniest fraction of them. Scientists feel they should not invoke miracles to explain the order we see, but that leaves only statistical arguments, which give bleak answers (only dull situations can be expected), or the so-called anthropic principle that if the world were not in a highly structured but extremely unlikely state, we should not exist and be here to observe it.

One of my reasons for writing this book is that timeless physics opens up new ways of thinking about structure and entropy. It may be easier to explain the arrow of time if there is no time!

(C) 1999 Julian Barbour

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