Time appears to move in a single direction - in which order is gradually replaced by chaos, says Mark Buchanan. But if this is so, how did the universe achieve its initial state?

What is time? "If nobody asks me, then I know," Saint Augustine wrote in the 4th century, "but if I were to desire to explain it to one that should ask me, plainly I know not." Some 16 centuries later, the question remains as elusive as ever. Why does time seem to flow like a river, and what is the source of this river? The American physicist John Wheeler once suggested that "time is what keeps everything from happening at once," a curiously seductive formula, though perhaps no less puzzling than the original question.

In his Critique of Pure Reason , the German philosopher Immanuel Kant argued that you can never perceive or imagine anything existing outside space or in the absence of time. These are the "subjective conditions of sensibility", he wrote. Much as a prism resolves light into its separate colours, laying them out in order, so does the mind, according to Kant, separate reality along the axis of time. But is time really only an illusion, or a result of perception? Didn't it exist long before there were any living things and so before there were any perceptions? Today, modern physics traces time's character back to the origins of the universe and questions its place in the fundamental laws of physics.

Isaac Newton's equations of motion involve time in a somewhat sterile way. As the earth orbits perpetually about the sun, gravitation dictates a calculable change in the earth's motion in each small interval of time. But this sort of time is merely a bookkeeper's trick, an artifice of accounting. For Newton, both space and time were absolutes: space, a thoroughly empty void through which objects can pass, and time, a kind of ticker-tape running inexorably in the background. Albert Einstein then revealed that time could be stretched and distorted and that it could be affected by matter and energy.

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But even if the river of time flows faster in some places than others and slows down when passing obstacles, this still does not explain what time is or why it has a direction. And experience suggests that time does have a direction. Washing machines wear out with use, as do automobiles and shoes, and they never return to their former pristine perfection. Mountain peaks crumble into the valley, but never reassemble themselves, and perfume from an opened bottle escapes to fill the room, but never does the reverse. These facts suggest a single direction for time, the direction in which things wear out, spread and erode away, and in which order generally dissolves into disorder.

This tendency also points to a theoretical conundrum. The physics of perfume bottles, mountains and other large-scale things ought to arise out of the workings of their atoms and molecules. But in contrast to the world around us, the atomic realm seems to make no distinction between past and future. Make a movie of a few atoms doing their thing, run it in reverse and you would see nothing strange - the backward movement would again fulfil the laws of physics. But a movie of scattered rocks miraculously gathering again into a rugged peak would fly in the face of reality as we know it.

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So how can the directionless time of the atomic realm give rise to the arrow of time at the larger scale? This is the central question, and its answer has two parts - the first relatively "easy" and more than a century old; the second rather more difficult and a matter for continuing debate.

Why does perfume escape from a bottle, but never, on its own, re-enter? In the late 19th century, the Austrian physicist Ludwig Boltzmann reasoned as follows. Suppose you calculate how many ways you can arrange a large number of perfume molecules so that they are spread out more or less uniformly through the room. Next, calculate how many ways you can arrange the same number of molecules while leaving them packed in the bottle. The former number, Boltzmann proved, is overwhelmingly huge when compared with the latter - bigger by a factor of 1 followed by more zeros than would fill every book in the British Library.

Now, the perfume molecules are slamming into one another and generally flitting about randomly from one detailed arrangement to the next. And it follows, Boltzmann argued, that the perfume, unless somehow prevented, will tend to go from being packed neatly in the bottle to being scattered about outside of it. It is all down to the staggering mismatch in the number of ways the two situations can be realised.

No matter what you consider, there are always far more ways for its parts to be arranged in a disorderly way than in an orderly way. Disorder has a huge numbers advantage over order and as a result, things in our universe have a natural tendency to drift towards a condition of low-grade chaos. This is the Second Law of Thermodynamics: in the absence of any separate, organising force, things tend to drift in the direction of greater disorder, or greater "entropy".

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Boltzmann's way of thinking offers the first striking insight into the nature of time - for it suggests that our subjective feeling of time is intimately wrapped up with the tendency things have to get muddled up and disorganised. "No perception in physics," the great German physicist Erwin Schrodinger once said, "has ever seemed more important to me than that of Boltzmann." The flow from order towards disorder seems to be a one-way stream, and this is why we sense a consistent direction in time, placing the unbroken wine glass or the brand new shoes in the past relative to their shattered or worn out descendants.

But Boltzmann's great perception only brings into focus the nub of the problem. A universal tendency for order to devolve towards disorder could explain why time seems to have a direction. But the explanation works only if we can explain how the universe came to be ordered in the first place. It could have started in a mess, dispersed like the perfume that has already spread through the room. Then there would be no gradual drift towards further disorder and no direction to time. Explaining the direction of time means accounting for the great organisation initially present in the universe.

This is where many scientists are now focusing. In the analogy with perfume, the stuff of our own universe was in the bottle some 10-15 billion years ago, soon after the big bang. At that time, the distribution of energy and matter in the universe was extraordinarily smooth. In the early 1990s, physicists using the Cosmic Microwave Background Explorer telescope discovered just how smooth by studying the faint glow of microwave radiation that fills the universe and offers a snapshot of what it was like just 300,000 years after the big bang. They found that the distribution of matter then was uniform to 1 part in 100,000.

These observations set strong constraints on theories of the early universe. Of the ways the stuff of the early universe could have been arranged, only a minuscule fraction would have given the universe the smoothness that astronomers' telescopes say it had. So the world was in a remarkably special condition - penned up and well-prepared to let time loose. But how did it get that way?

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One of the most popular explanations, first proposed by physicist Alan Guth of the Massachusetts Institute of Technology, posits a special "inflationary phase" of the early universe, a short-lived period in which the universe expanded with incredible speed and during which almost all the ripples in the distribution of stuff would have been quickly ironed out. The idea of inflation makes the special smoothness not so special. It has gained support from measurements of the cosmic microwave background made by a telescope flown over Antarctica in 1998. This telescope revealed ripples in the distribution of matter in the early universe of just the sort predicted by the inflationary idea.

Not everyone accepts the idea, however, or believes that it offers a full explanation. It could predict a bizarre future, such as a universe that eventually collapses on itself to produce a "big crunch", during which time may reverse itself and flow backward as things become more ordered rather than less, violating the familiar Second Law of Thermodynamics. As physicist Sir Roger Penrose has noted, black holes, which result from the gravitational collapse of large stars, offer a small-scale version of such big crunch events, and yet work in a way that is fully in keeping with thermodynamics.

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So our intuitive wondering about the nature of time has landed us at the doorstep of the deepest issues in contemporary cosmology. In the 5th century BC, the Greek philosopher Parmenides went so far as to put all matters of time down to illusion, the true reality being eternal and unchanging. Some physicists and philosophers today might agree. Illusory or not, time's deepest secret has yet to be exposed.

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