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CHAPTER 9 THE ARROW OF TIME
In previous chapters we have seen how our views of thenature of time have changed over the years. Up to thebeginning of this century people believed in an absolute time.
That is, each event could be labeled by a number called “time”
in a unique way, and all good clocks would agree on the timeinterval between two events. However, the discovery that thespeed of light appeared the same to every observer, no matterhow he was moving, led to the theory of relativity - and inthat one had to abandon the idea that there was a uniqueabsolute time. Instead, each observer would have his ownmeasure of time as recorded by a clock that he carried: clockscarried by different observers would not necessarily agree. Thustime became a more personal concept, relative to the observerwho measured it.
When one tried to unify gravity with quantum mechanics,one had to introduce the idea of “imaginary” time. Imaginarytime is indistinguishable from directions in space. If one can gonorth, one can turn around and head south; equally, if onecan go forward in imaginary time, one ought to be able toturn round and go backward. This means that there can beno important difference between the forward and backwarddirections of imaginary time. On the other hand, when onelooks at “real” time, there’s a very big difference between theforward and backward directions, as we all know. Where doesthis difference between the past and the future come from?
Why do we remember the past but not the future?
The laws of science do not distinguish between the past andthe future. More precisely, as explained earlier, the laws ofscience are unchanged under the combination of operations (orsymmetries) known as C, P, and T. (C means changingparticles for antiparticles. P means taking the mirror image, soleft and right are interchanged. And T means reversing thedirection of motion of all particles: in effect, running the motionbackward.) The laws of science that govern the behavior ofmatter under all normal situations are unchanged under thecombination of the two operations C and P on their own. Inother words, life would be just the same for the inhabitants ofanother planet who were both mirror images of us and whowere made of antimatter, rather than matter.
If the laws of science are unchanged by the combination ofoperations C and P, and also by the combination C, P, and T,they must also be unchanged under the operation T alone. Yetthere is a big difference between the forward and backwarddirections of real time in ordinary life. Imagine a cup of waterfalling off a table and breaking into pieces on the floor. If youtake a film of this, you can easily tell whether it is being runforward or backward. If you run it backward you will see thepieces suddenly gather themselves together off the floor andjump back to form a whole cup on the table. You can tell thatthe film is being run backward because this kind of behavior isnever observed in ordinary life. If it were, crockerymanufacturers would go out of business.
The explanation that is usually given as to why we don’t seebroken cups gathering themselves together off the floor andjumping back onto the table is that it is forbidden by thesecond law of thermodynamics. This says that in any closedsystem disorder, or entropy, always increases with time. Inother words, it is a form of Murphy’s law: things always tendto go wrong! An intact cup on the table is a state of highorder, but a broken cup on the floor is a disordered state.
One can go readily from the cup on the table in the past tothe broken cup on the floor in the future, but not the otherway round.
The increase of disorder or entropy with time is oneexample of what is called an arrow of time, something thatdistinguishes the past from the future, giving a direction to time.
There are at least three different arrows of time. First, there isthe thermodynamic arrow of time, the direction of time inwhich disorder or entropy increases. Then, there is thepsychological arrow of time. This is the direction in which wefeel time passes, the direction in which we remember the pastbut not the future. Finally, there is the cosmological arrow oftime. This is the direction of time in which the universe isexpanding rather than contracting.
In this chapter I shall argue that the no boundary conditionfor the universe, together with the weak anthropic principle, canexplain why all three arrows point in the same direction - andmoreover, why a well-defined arrow of time should exist at all.
I shall argue that the psychological arrow is determined by thethermodynamic arrow, and that these two arrows necessarilyalways point in the same direction. If one assumes the noboundary condition for the universe, we shall see that theremust be well-defined thermodynamic and cosmological arrows oftime, but they will not point in the same direction for thewhole history of the universe. However, I shall argue that it isonly when they do point in the same direction that conditionsare suitable for the development of intelligent beings who canask the question: why does disorder increase in the samedirection of time as that in which the universe expands?
I shall discuss first the thermodynamic arrow of time. Thesecond law of thermodynamics results from the fact that thereare always many more disordered states than there areordered ones. For example, consider the pieces of a jigsaw in abox. There is one, and. only one, arrangement in which thepieces make a complete picture. On the other hand, there area very large number of arrangements in which the pieces aredisordered and don’t make a picture.
Suppose a system starts out in one of the small number ofordered states. As time goes by, the system will evolveaccording to the laws of science and its state will change. At alater time, it is more probable that the system will be in adisordered state than in an ordered one because there aremore disordered states. Thus disorder will tend to increase withtime if the system obeys an initial condition of high order.
Suppose the pieces of the jigsaw start off in a box in theordered arrangement in which they form a picture. If youshake the box, the pieces will take up another arrangement.
This will probably be a disordered arrangement in which thepieces don’t form a proper picture, simply because there are somany more disordered arrangements. Some groups of piecesmay still form parts of the picture, but the more you shakethe box, the more likely it is that these groups will get brokenup and the pieces will be in a completely jumbled state inwhich they don’t form any sort of picture. So the disorder ofthe pieces will probably increase with time if the pieces obeythe initial condition that they start off in a condition of highorder.
Suppose, however, that God decided that the universe shouldfinish up in a state of high order but that it didn’t matter whatstate it started in. At early times the universe would probablybe in a disordered state. This would mean that disorder woulddecrease with time. You would see broken cups gatheringthemselves together and jumping back onto the table. However,any human beings who were observing the cups would beliving in a universe in which disorder decreased with time. Ishall argue that such beings would have a psychological arrowof time that was backward. That is, they would rememberevents in the future, and not remember events in their past.
When the cup was broken, they would remember it being onthe table, but when it was on the table, they would notremember it being on the floor.
It is rather difficult to talk about human memory because wedon’t know how the brain works in detail. We do, however,know all about how computer memories work. I shall thereforediscuss the psychological arrow of time for computers. I think itis reasonable to assume that the arrow for computers is thesame as that for humans. If it were not, one could make akilling on the stock exchange by having a computer that wouldremember tomorrow’s prices! A computer memory is basically adevice containing elements that can exist in either of two states.
A simple example is an abacus. In its simplest form, thisconsists of a number of wires; on each wire there are anumber of beads that can be put in one of two positions.
Before an item is recorded in a computer’s memory, thememory is in a disordered state, with equal probabilities for thetwo possible states. (The abacus beads are scattered randomlyon the wires of the abacus.) After the memory interacts withthe system to be remembered, it will definitely be in one stateor the other, according to the state of the system. (Eachabacus bead will be at either the left or the right of the abacuswire.) So the memory has passed from a disordered state toan ordered one. However, in order to make sure that thememory is in the right state, it is necessary to use a certainamount of energy (to move the bead or to power thecomputer, for example). This energy is dissipated as heat, andincreases the amount of disorder in the universe. One canshow that this increase in disorder is always greater than theincrease in the order of the memory itself. Thus the heatexpelled by the computer’s cooling fan means that when acomputer records an item in memory, the total amount ofdisorder in the universe still goes up. The direction of time inwhich a computer remembers the past is the same as that inwhich disorder increases.
Our subjective sense of the direction of time, thepsychological arrow of time, is therefore determined within ourbrain by the thermodynamic arrow of time. Just like acomputer, we must remember things in the order in whichentropy increases. This makes the second law ofthermodynamics almost trivial. Disorder increases with timebecause we measure time in the direction in which disorderincreases You can’t have a safer bet than that!
But why should the thermodynamic arrow of time exist atall? Or, in other words, why should the universe be in a stateof high order at one end of time, the end that we call thepast? Why is it not in a state of complete disorder at all times?
After all, this might seem more probable. And why is thedirection of time in which disorder increases the same as thatin which the universe expands?
In the classical theory of general relativity one cannot predicthow the universe would have begun because all the knownlaws of science would have broken down at the big bangsingularity. The universe could have started out in a verysmooth and ordered state. This would have led to well-definedthermodynamic and cosmological arrows of time, as we observe.
But it could equally well have started out in a very............
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