Time's Arrow New Scientist 1 Nov 97 Paul Davies
GATHER ye rosebuds while ye may, Old Time is still a'flying." So wrote Robert Herrick, the 17th even century poet. And who one could doubt that time does indeed fly or at least flow? In daily life, the past, present and future have distinctly different qualities. The past is gone, remembered perhaps, but unalterable. The future has yet to come into being, and is still open. Only the present moment is truly real. All this seems like common sense. Yet many scientists and philosophers are adamant that we have got it all wrong. They insist that time does not flow at all. The Cambridge philosopher John McTaggart set the scene for this debate at the turn of the century, when he put forward two seemingly contradictory images of time. One view treats time simply as a coordinate to label events, just as latitude and longitude label places. The other view refers to flowing time, where events happen and the future comes into being. Which is right?
Philosopher Donald Williams of Harvard University tried to answer this in a famous essay published in 1951 entitled "The Myth of Passage", in which he argued that only the static, coordinate time is real. It is a point of view supported by many other philosophers. Jack Smart, a retired philosopher now living in Canberra, concedes that we certainly feel time passing. But he believes that this feeling arises out of "a metaphysical con fusion". After all, he asks, how fast does time pass? Well, one second per second, of course. But for us to go beyond tautology and talk meaning fully of the motion or passage of some thing, we need a time to gauge it against, as when we say an arrow t moves at ten metres per second. When that something is time itself, what do we use as a measure? an This may seem like simply playing ten with words, but there are also sound mec physical reasons to doubt the flow of of time. The trouble started with Einstein's Give theory of relativity, which demolished the idea that time is universal with a common present moment for everybody. Einstein showed that two spatially separated events judged to occur simultaneously by one observer can occur at different moments for another. For instance, suppose you want to know what the Pathfinder space probe is doing on Mars now. According to rela tivity theory, it depends on how you are moving when you ask the question. If you are sitting at home, you will get one answer, if you are flying in an aircraft you will get another. If you could move close to the speed of light relative to Earth, the difference could amount to many minutes.
This strange phenomenon, called the relativity of simultaneity, has been thoroughly verified by experiment. It ts, dramatically changes the way we must think about time. If there are many Martian "nows" for each Earth now (and vice versa) it is clearly meaningless to claim that only one moment of time now-is real. Einstein himself expressed it succinctly when he said that "past, present and future are only in illusions, however persistent". Physicists prefer to envisage time as all there at once, a timescape stretched out in its entirety, like a landscape. It is a concept often referred to as "block time". But if our perception of the flow of time is just some sort of mental quirk, rather than a property of the physical Universe, what causes it? Explanations vary. Some attribute it to the structure of our language, others seek explanations in the workings of the brain. Many scientists, most notably Roger Penrose of Oxford University, suspect it has some thing to do with quantum mechanics and the so-called collapse of the wave func tion ("Escape from the quantum whirlpool", New Scientist, 26 April, p 38). The link between quantum physics and consciousness is a deep and contentious one. The basis of quantum mechanics, which describes the behaviour of matter at the atomic level, is uncertainty. Given a particular atomic state, you cannot generally predict how it will change. For example, if you have an [email protected] atom, you cannot know in advance exactly when it will decay; all you know are the betting odds. A fancy way to describe this indecision is to say that there are two alternative universes, one with an excited atom, one with a decayed atom. According to the weird rules of quantum mechanics, an atomic state will generally involve both universes coexisting and overlapping each other in a sort of hybrid reality. Human beings, however, always observe just one universe, so somehow the act of making an observation provokes nature into making a choice be tween contending realities. To use the jargon, the wave function collapses into one possibility. It is as if the act of inspecting the world projects one of the ghostly alternative universes into concrete actuality. The nature of this process is not fully understood, but all investigators accept that it seems to move only one way in time. Once the choice of reality has been made, it can't be unmade. So, the argument goes, our perception of the flow of time could arise from the ways that our consciousness resolves ambigu ous quantum states. Even if time doesn't literally flow from past to future, it still seems that the world is strongly lopsided in time. If you take a movie of a typical every day scene and run it in reverse, every body laughs. They have no trouble spotting the deception. In real life, raindrops don't rise into the sky and broken eggs don't mend themselves.
A lopsided world
But this time asymmetry doesn't depend on time flowing: you don't actually have to run the movie to find it. A vertical stack of still frames would display a structural directionality People grow old, cars rust, eggs break, snowmen melt, radio waves spread out from transmitters. Physicists often use the term "the arrow of time" to denote the asymmetry between past and future directions of time. It can be misinterpreted though, because arrows also fly, and so the term could also refer to time flowing. The correct way to picture the arrow of time is by analogy with a compass needle or weather vane, which point in a direction but do not move towards it. So where does this directionality come from? Well, most irreversible processes are examples of the second law of thermodynamics. This says that in an isolated system heat will flow from hot to cold, never the other way. The end result is a state called thermodynamic equilibrium, with the heat distributed evenly at a uniform temperature. Thermodynamic equilibrium is the state of maximum disorder, and as long ago as the 1850s physicists realised that the second iaw meant that the Universeis stuck on a one-way slide towards degeneration and chaos. A clear-cut example of the thermodynamic arrow of time is the way that a bottle of perfume evaporates if the stopper is removed. The process is irreversible because you would never see all the perfume molecules go back into the bottle on their own. Once they are mixed up with air molecules, the original state is irretrievable. The transition is best thought of as a change from an ordered state (perfume neatly in the bottle) to a disordered state (perfume spread around the room).
Back and forth
Mystery sets in, however, when you try to trace the source of this directionality. The molecular agitation that jumbles up the perfume and air molecules involves lots of intermolecular collisions. But the collision of two molecules is a reversible process: run the movie backwards and the molecules retrace their trajectories. This reflects the symmetry in time of the laws goveming molecular behaviour. Indeed, almost all the laws of physics are tirnereversible. The puzzle is how temporally lopsided processes can emerge from timesymmetric laws. A possible answer given in the 1950s by German philosopher Hans Reichenbach lies with the initial conditions. Imagine unwrapping a new pack of cards arranged in suits and numerical sequence. This highly ordered state is soon destroyed with a bit of shuffling. There is nothing intrinsically directional about the shuffling process. The asymmetry arises only because you started out with the cards in a very special state, and then randomly disturbed it. So too with the perfume molecules. Order gives way to disorder not because there is a directionality in the underlying laws, but simply because there are many more disordered states than ordered states. Disturbing an ordered state will therefore very probably produce a less-ordered state. So to work out the ultimate origin of the arrow of time, we have to ask how the Universe got itself into an ordered state in the first place. The obvious place to look is in the big bang. But looking there yields a strange paradox. We know that the early Universe was in fact highly disordered. The big bang was accompanied by a flash of heat that filled space with radiation. A remnant of this primeval heat radiation survives in a background of n-dcrowaves that still bathes the cosmos today. Satellite observations show that the spectrum of the microwave radiation is precisely the "black body" form associated with uniform temperature and complete microscopic disorder. So, while the second law of thermodynamics requires that the arrow of time point from order to chaos, from disequilibrium to equilibrium, it seemf, that the early Universe started at equilibrium and is now far from equilibrium-all of which seems to point the arrow in the wrong direction. How can this be? This is where gravity comes in. Remember the caveat in the second law: it applies only to isolated systems. In the Universe, matter and heat radiation are not isolated, because they are free to engage in large-scale motion. This activity is subject to gravitational forces, and so we must include the gravitational field as part of the total system. In the lab, where gravity is negligible, the equilibrium end state of a gas is a uniform distribution. But taking gravity into account changes everything. Gravity is an attractive force that tries to pull matter into clumps. The ultimate triumph of this process is when material falls together completely to form a black hole. Applying thermodynamics to gravity, the black hole can be seen as the equilibrium end state. Attempting to find the equations that link gravity with thermodynamics is taxing the best brains in physics. But for a clue to how these two processes might be related from the standpoint of the arrow of time, it helps to think of order and disorder not in terms of clumpiness and smoothness, but in terms of information. A totally disordered state needs only a few bits of information to describe it. For example, the macroscopic state of a flask of gas in thermodynamic equilibrium can be completely described simply by giving its temperature and volume. But a gas with lots of hot spots and swirling eddies would take a lot more information to describe. As a system approaches equilibrium, it loses information irreversibly. When a body collapses into a black hole, it loses information. The escalating gravitational field of the body traps light, and because information cannot travel faster than light, it is trapped too. Ultimately, an event horizon forms around the body, preventing any information from getting out. To an external observer, the information content of the collapsing body disappears irreversibly down the hole. Not surprisingly, therefore, black holes obey a set of laws identical to the normal laws of thermodynamics. The second law of thermodynamics can be thought of as nature's way of driving systems towards equilibrium. If this law is taken to embrace gravitating systems, it describes a trend from smooth to clumpy. The microwave background radiation reveals that the early Universe was in fact extremely smooth-with only the merest hint of clumping showing up in the satellite observations. While this was very close to equilibrium in terms of matter and heat energy alone, it is very far from equilibrium in terms of gravitation. Because of this, the matter and radiation could be driven away from their own equilibrium without violating the second law. As the Universe developed, it gained thermal order, but also gained gravitational disorder, so the second law was satisfied throughout. So the arrow of time ultimately stems from the gravitational arrangement of the Universe at the beginning. This still begs the question of why the Universe began in such a gravitationally ordered state. Why didn't the big bang cough out black holes-which, gravitationally, represent a much more natural state than smooth gas? In recent years, cosmologists have sought an explanation for the primordial state of the Universe by investigating highenergy particle physics, and the quantum processes that occurred during the first fraction of a second. Although these investigations are highly speculative, a common feature is inflationan abrupt and enormous jump in the size of the Universe about one trilliontrillion-trillionth of a second after the big bang. This could have created the very smooth state reflected in the cosmic microwave background radiation. However, as it turns out, inflation solves only part of the problem. To see why, consider the situation that would arise if, as some theories suggest, the Universe eventually ceases expanding, and starts to collapse towards a big crunch, rather like the big bang in reverse. If the Universe did this, its gross motion would be symmetric in time-starting and ending in similar dense states. Where's the thermodynamic arrow in that? This large-scale symmetry reflects the underlying time-symmetry of the laws of gravitation and it prompts the question of why one temporal extremity should differ from the other. If the big bang was followed by a period of inflation, couldn't the big crunch be preceded by a period of "deflation", making the Universe symmetric in time, not just in its gross motion but in its fine details too? Such a theory was suggested by Thomas Gold in the 1960s. He proposed that if the Universe contracted, the arrow of time would be reversed. Heat would flow from cold to hot, raindrops would rise and people would grow younger. In short, the movie would be played backwards. Any inhabitants of this contracting phase would have their mental processes reversed too, and would not notice anything unusual. However, if the arrow of time reversed like this, I believe that it would produce conspicuous phy sical effects-which no body has r instance, radiation from the Sun escapes from the Galaxy and heads off into the void of intergalactic space. In 1995, Jason Twamley, then at the University of Adelaide, and I calculated that much of this ra diation would remain undis turbed until long after the Uni verse began recontracting When the radiation eventually encountered matter, it would find that all thermodynamic processes had been reversed.
Likewise, radiation emitted in the contracting phase should travel back in time and reach our region of the Universe now, all of which would play havoc with causality. What's more, the presence of a large amount of "radiation from the future" would almost certainly show up in cosmological observations, and yet nobody has detected it.
A more promising explanation, proposed a few years ago by Murray Gell-Mann from Caltech and James Hartle from the University of California at Santa Barbara, accepts that the observed Universe is asymmetric, and appeals to quantum theory to explain it. Quantum physics implies that a given quantum state of the Universe could evolve in many different ways. Some of these possibilities correspond to a Universe that starts out smooth and grows clumpy, while others correspond to the reverse process. Yet others are universes which remain clumpy and chaotic throughout. A few quantum alternatives involve a universe that start out smooth, grows clumpy, and the reverses, ending up smooth agai Although individual possible universe are generally lopsided, the collection as whole does not favour one direction time over the other, thus maintaining th underlying time symmetry of nature.
Galaxies point in many directions so the universe's arrow of time could also be one of many.
But only a few of these many quantum alternatives could actually be perceived by living creatures. Life depends on a thermodynamic disequilibrium, so it is no surprise that we observe a universe with one smooth temporal extremity, which we term "the beginning". However, we are much less likely to observe a time-symmetric universe. Only a tiny fraction of the possible universes have both smooth initial and final states, and the over whelming majority of possible universes are lopsided in time. So living creatures are most likely to witness a universe that begins smooth and ends clumpy. And if the Universe does reverse its expansion, this implies the big bang would be smooth, but the big crunch would be a messy collapse of clumpy material and black holes. If these ideas are correct-and they are admittedly based on some very shaky calculationss then the arrow of time has a simple spatial analogue. just as the laws of physics do not favour a direction of time, neither do they favour a direction of space. Nevertheless, many physical systems have a definite a orientation in space. For example, the Milky Way galaxy has rotation axis that points to a particular part of the Universe. However, the rotation axes of other galaxies point in different directions, and overall there is no preferred alignment. So laws can have symmetries that are broken by actual physi cal systems. If our Universe didn't break the time symmetry of the laws and so produce an arrow of time, wouldn't be here to notice.
Paul Davies is a physicist and writer living in South Australia
Further reading: The Arrow of Time by P. Coveney and R Highfield (W. H. Allen, 1990). About Time by Paul Davies (Penguin, 1995). Time's Arrow. Our and Archimedes' Point by Huw Price (OUP, 1996).
This is followed by an article considering the possibility of multiple time dimensions - hypertime. This is a suggestion also once intuitively made by J W Dunne in "An Experiment with Time" in the 1930s. For example several Kaluza-Klein type theories can be enhanced to a 12-dimensional M-theory by adding an extra time-like dimension, but this may be an artifact of the theoretical construct, rather than necessarily being a genuine physical realization, and has very counter-intuitive implications. There is for example no consistent description of the future or past, unless the time dimensions are linked into a single parameter.