Why does time only go forwards? Scientists suspect that in some cases it doesn't. On a scale so small that atoms look like galaxies, time may be flipping forwards and backwards like a coin tumbling through the air
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WE HAVE never seen it in reality, but enough home videos and cine- films have been shown in reverse to give us a clear vision of how things would look if time ran backwards. The image of a broken egg splattered on a kitchen floor, shell shattered like Humpty Dumpty, spontaneously leaping up and reforming into a smooth, geometric ovoid, is familiar enough. People would rise from perfectly made beds at night and climb into rumpled ones in the morning. Wrinkles on faces would gradually smooth out as we walked backwards through life.

On a larger scale, we can imagine the whole cosmos running backwards. Stars would erupt out of black holes, planets would disappear in swirling clouds of primordial dust and all the mass of the universe would collapse into a single point, the Big Crunch, mirror image of the Big Bang. This is exactly what many scientists believe will actually happen a few billion years from now. They are perplexed by the problem of whether time will in fact run backwards in the second half of the universe's life, when it is collapsing back towards a single dense point of matter. How does their research affect our understanding of time and the arrow it points, unerringly, into what we think is the future?

Unlike Dr Who, the television time lord who wanders haphazardly from future to past in his malfunctioning Tardis, we remain firmly rooted in the present as it slips steadily into the future at a rate of one second per second, one year per year. But why should this be so? Isn't time just a convenient psychological convention, a mass delusion that we force upon the world to help us make sense of it? Perhaps the human brain, magnificent though it is, could not handle being aware of past, present and future all at once.

The answers to all these questions are still hotly debated. Time, to paraphrase St Augustine of Hippo, the fourth-century theologian who was one of the early thinkers to consider the subject seriously, is something everyone understands until they try to explain it. While scientists frequently use time to explain almost every aspect of the universe around us, few of them truly understand it.

Physicists come closest, though they are divided into several camps on the subject. One argues that there is but a single particle in the universe, ricocheting from future to past and back again, weaving the cosmos as it goes. Another says time's direction is due to the bizarre laws governing sub-atomic particles being felt in the everyday universe. Still another argues that the uni-directional flow stems from a flaw in the symmetry, the perfect equality, that existed at the moment when time began. One short-lived theory even called for chronons, individual atoms of time. Mainstream theorists, led by Cambridge don Stephen Hawking, believe it all comes down to thermodynamics and a concept almost as elusive as time itself - entropy.

Given the significance of time to everything in the world where change can be observed, it is surprising that theorising on the subject was minimal until the last century. Debates have raged over whether time is linear or cyclical, with events repeating themselves exactly after a set period of time. Intellectual wars have been fought over whether the future is fixed or open to influence by human will. None came close to asking the fundamental questions that the High Priests of Chronos are now trying to answer.

The first scientific theory that tried to define time was Sir Isaac Newton's Principia, which saw it as an absolute, unchanging constant. No matter who measured the interval between two events, they would get the same answer. This was not a consequence of his three laws of motion, or the universe they described, but rather his belief that an absolute God had to have an absolute space and time. It was not until Albert Einstein showed that time is relative that Newton's assertion was overthrown.

Einsteinian relativity created a new model for the universe in which time and space were linked. Time became the fourth dimension, like length and breadth and height. Einstein also had an absolute, however - the speed of light. Spaceships travelling close to that velocity would find time moving more slowly than those that were not moving at all. His claim seems to defy common logic, but experiments with atomic clocks carried in fast jet aircraft have proven his arguments to be true.

His theories had another consequence, however. By linking space and time in one continuum, they threw up the question of why time should be different from the other dimensions at all. One can travel up as well as down, left as well as right. If the speed of time varies, then why should its direction be fixed?

Despite the influence of relativity theory, Newton's laws remain sound in one respect - their ability to describe things equally well, no matter what direction time is supposed to go in. One metaphor for Newton's laws describes the universe as cosmic billiard balls, with everything from dust motes to galaxies caroming around under the influence of gravity. Film them, reverse the celluloid, and their movements in space would still look plausible.

Most of the laws of physics, including quantum mechanics, that have been discovered since are also "time invariant", or "time symmetric." Radio waves, for example, should in theory travel both forward and backward in time. But so far experimenters have been unable to tune in to Radio 4 broadcasts from the 25th century. The puzzling thing is that there are exceptions to this rule. One of them, entropy, is at the heart of the main theory that tries to explain why time only moves forward.

Entropy can be summed up as a mathematical variant of Sod's Law - Things Invariably Get Worse. Worse in this sense means more chaotic and less ordered. In an ordered ("low-entropy") world, there are well defined, complex structures; in a chaotic ("high-entropy") one, there is a fuzzy and entirely boring litter of matter and energy. The unusual thing about entropy, unlike other physical processes, is that it cannot be reversed. Chance alone can turn a whole, well-ordered egg into a chaotic mess on the kitchen floor, but the reverse process, if not entirely impossible, would require so many coincidences as to be vanishingly unlikely.

The part of the definition concerned with mathematical proof comes from Ludwig Boltzmann, a 19th-century Viennese statistician who took Newton's laws of motion and derived from them the Second Law of Thermodynamics, which had already been observed and named by experimenters earlier in the century.

The idea was received by Boltzmann's contemporaries with derision. One went to the trouble of showing mathematically that chance reversals were possible, though unlikely. Others argued that what was then seen as the Darwinian ascent from pond-scum to human beings was proof that order could arise from chaos. Boltzmann, dispirited, shot himself. Only later was it realised that forming order out of chaos involves creating an even larger amount of chaos as a by-product. It is this law alone that stands in the way of closet inventors wishing to patent perpetual motion machines.

Boltzmann has received posthumous recognition for his work on entropy, and it is now an accepted part of the physics canon. As scientists in the 20th century contemplated time, Boltzmann's entropy theory seemed increasingly to be what defined the way it was pointing. Time is just another way of saying that the universe invariably moves from order to chaos.

Over the last century, however, other theories have also been proven - or have at least become widely accepted by scientists. Some have created problems for the entropic theorists. One such is the Big Bang theory of the creation and expansion of the universe. Marry that with entropy and you reach the conclusion that the universe was highly ordered at its start. But what might happen later, after chaos eventually triumphs?

One suggestion is that gravity will suck all the matter in the universe together again in a Big Crunch. But if the first half of the life of the universe involves increasing entropy, the second half must involve reducing it - and if entropy is what defines the direction of time, that implies that time would have to run backwards in this scenario. Cambridge physicist Stephen Hawking used to believe just that, postulating the type of bizarre world described at the start of this article. But in 1986 he made a remarkable U-turn. Hawking and James Hartle, director of the Institute for Theoretical Physics at the University of California at Santa Barbara, still saw entropy having a central role, but they have defined two other "arrows" of time as well. The first is psychological time, in which we remember the past but not the future. The second is cosmological time, which matches the direction in which the universe is expanding.

Hawking and Hartle addressed various key problems surrounding the start of time at the Big Bang. Their work is still somewhat speculative and far from proven, but physicists like its elegance and (relative) simplicity. For the non-scientist, it contains concepts, such as imaginary time, which can seem daunting.

Most people can find the distance between two points on a plane, using a graph with x and y axes and Pythagoras's Theorem. Doing the same thing in three-dimensional space, by adding a z axis, is not much harder. But when a fourth dimension, time, is added, the equations sometimes call for the square root of a negative number to be calculated.

Normally this can't be done, but mathematicians get around the problem by introducing an "imaginary" number called i , defined as the root of -1. The main consequence of this algebraic sleight of hand is that, at the incredibly short distances involved during the Big Bang, imaginary time has some of the qualities of space. It becomes, in a sense, an ordinary dimension in which things are able to move in any direction. In this context, the question "What happened before the Big Bang?" becomes meaningless.

The same thing may be happening throughout the Universe on an extremely small scale. The change in natural laws between the world we see around us and the sub-atomic world of quantum mechanics is not the only one based on size. Below 10-33cm - a trillion, trillion times smaller than an atom - the laws change again - and this time we're not sure what the new ones are. There are two competing theories which attempt to explain them - "quantum gravity" and "superstrings". Both allow for time to become "imaginary" in the mathematical sense. On a scale so small that atoms look like galaxies, time may be flipping back and forth like a coin tumbling through the air.

The Hawking-Hartle theory is not the last word on the direction of time. There are other theories, some that may eventually be merged with Hawking- Hartle, that may one day be seen as the route to a better understanding of the fourth dimension. One possibility is that the direction of time arises from the asymmetry of the universe. The Big Bang should have created equal amounts of both matter and anti-matter - particles with opposite electrical charge and spin to normal matter. The two types of particle should almost instantly have collided with each other in a frenzy of mutual annihilation. The cosmic background radiation, a faint electromagnetic hum that fills the universe, is thought to be the echo of that destruction. But the balance was not quite exact. Matter outweighed anti-matter by a tiny fraction, and expanded into all the galaxies, stars and planets that we find in the cosmos.

The intimate relationship between matter and anti-matter was first worked out by the American theorist Richard Feynman, known as much for his wit as his scientific brilliance. He argued that an anti-matter particle - for example, an anti-electron, or positron - was indistinguishable from an electron moving backwards in time. From this came the somewhat flippant suggestion that the entire universe was made of one fundamental particle, smaller than the quarks that make up electrons, protons and neutrons, ricocheting backwards and forwards in time to weave our universe.

A more plausible theory hinges on the fact that matter and anti-matter are mirror images of each other. Their charge is reversed, and so is their spin or parity, and the direction they move in time. The imbalance of matter over anti-matter during the Big Bang represented a break in this symmetry, which could only happen if time had a distinct direction. This suggests that there might be another universe, identical to ours - except that electrons have a positive charge, spin in the opposite direction and move backwards in time. Any intelligent beings in it would see this as an entirely natural state of affairs, and might imagine it is our universe that is reversed.

There is also a quantum explanation. At the sub-atomic level where quantum laws hold sway, particles can behave like waves and only resolve into particles when someone looks at them. If they could influence the macro- universe which we directly experience, the future could be defined as those quantum waves which have not been resolved into particles; the past would be those which have been resolved, like distant images being brought into focus by a pair of binoculars.

Unfortunately, though several experiments have been proposed, no empirical evidence for such quantum laws applying to the day-to-day world exists. Such thinking produces more complexities: for instance, who was the observer was who resolved the distant past into reality before humans came along?

At this point the debate about time takes an unexpected turn. While most of the processes observed in nature are "time symmetric" - that is, they look exactly the same going in either direction in time - not all are. One exception involves kaons and pions, two categories of sub-atomic particle. According to the laws of quantum mechanics, it should take just as long to turn a kaon into a pion as it takes to turn a pion into a kaon. Instead it takes much longer. If you could film the process and then replay it in reverse, it would not look like what really happens. The discovery led to a new category of sub-atomic particles with a characteristic aptly dubbed "strangeness". These appear to have an arrow of time built into them.

It's certainly true that few things in the universe are quite as strange as time. Exploring the field is almost as difficult a task as the King's Men had trying to put Humpty Dumpty together again. Perhaps one day, a theory of time will be so well understood that it will be taught in sixth- form classrooms and broadcast as part of the Rutherford Lectures. Unfortunately, though, we are not likely to hear those broadcasts until after they are made. !