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 lumpy anddisordered state. in that case, the universe would already be ina state of complete disorder, so disorder could not increasewith time. it would either stay constant, in which case therewould be no well-defined thermodynamic arrow of time, or itwould decrease, in which case the thermodynamic arrow oftime would point in the opposite direction to the cosmologicalarrow. neither of these possibilities agrees with what weobserve. however, as we have seen, classical general relativitypredicts its own downfall. when the curvature of space-timebecomes large, quantum gravitational effects will becomeimportant and the classical theory will cease to be a gooddescription of the universe. one has to use a quantum theoryof gravity to understand how the universe began.

in a quantum theory of gravity, as we saw in the lastchapter, in order to specify the state of the universe one wouldstill have to say how the possible histories of the universewould behave at the boundary of space-time in the past. onecould avoid this difficulty of having to describe what we do notand cannot know only if the histories satisfy the no boundarycondition: they are finite in extent but have no boundaries,edges, or singularities. in that case, the beginning of time wouldbe a regular, smooth point of space-time and the universewould have begun its expansion in a very smooth and orderedstate. it could not have been completely uniform, because thatwould violate the uncertainty principle of quantum theory. therehad to be small fluctuations in the density and velocities ofparticles. the no boundary condition, however, implied thatthese fluctuations were as small as they could be, consistentwith the uncertainty principle.

the universe would have started off with a period ofexponential or “inflationary” expansion in which it would haveincreased its size by a very large factor. during this expansion,the density fluctuations would have remained small at first, butlater would have started to grow. regions in which the densitywas slightly higher than average would have had theirexpansion slowed down by the gravitational attraction of theextra mass. eventually, such regions would stop expanding andcollapse to form galaxies, stars, and beings like us. the universewould have started in a smooth and ordered state, and wouldbecome lumpy and disordered as time went on. this wouldexplain the existence of the thermodynamic arrow of time.

but what would happen if and when the universe stoppedexpanding and began to contract? would the thermodynamicarrow reverse and disorder begin to decrease with time? thiswould lead to all sorts of science-fiction-like possibilities forpeople who survived from the expanding to the contractingphase. would they see broken cups gathering themselvestogether off the floor and jumping back onto the table? wouldthey be able to remember tomorrow’s prices and make afortune on the stock market? it might seem a bit academic toworry about what will happen when the universe collapsesagain, as it will not start to contract for at least another tenthousand million years. but there is a quicker way to find outwhat will happen: jump into a black hole. the collapse of astar to form a black hole is rather like the later stages of thecollapse of the whole universe. so if disorder were to decreasein the contracting phase of the universe, one might also expectit to decrease inside a black hole. so perhaps an astronautwho fell into a black hole would be able to make money atroulette by remembering where the ball went before he placedhis bet. (unfortunately, however, he would not have long toplay before he was turned to spaghetti. nor would he be ableto let us know about the reversal of the thermodynamic arrow,or even bank his winnings, because he would be trappedbehind the event horizon of the black hole.)at first, i believed that disorder would decrease when theuniverse recollapsed. this was because i thought that theuniverse had to return to a smooth and ordered state when itbecame small again. this would mean that the contractingphase would be like the time reverse of the expanding phase.

people in the contracting phase would live their lives backward:

they would die before they were born and get younger as theuniverse contracted.

this idea is attractive because it would mean a nicesymmetry between the expanding and contracting phases.

however, one cannot adopt it on its own, independent of otherideas about the universe. the question is: is it implied by theno boundary condition, or is it inconsistent with that condition?

as i said, i thought at first that the no boundary condition didindeed imply that disorder would decrease in the contractingphase. i was misled partly by the analogy with the surface ofthe earth. if one took the beginning of the universe tocorrespond to the north pole, then the end of the universeshould be similar to the beginning, just as the south pole issimilar to the north. however, the north and south polescorrespond to the beginning and end of the universe inimaginary time. the beginning and end in real time can bevery different from each other. i was also misled by work ihad done on a simple model of the universe in which thecollapsing phase looked like the time reverse of the expandingphase. however, a colleague of mine, don page, of penn stateuniversity, pointed out that the no boundary condition did notrequire the contracting phase necessarily to be the time reverseof the expanding phase. further, one of my students, raymondlaflamme, found that in a slightly more complicated model, thecollapse of the universe was very different from the expansion.

i realized that i had made a mistake: the no boundarycondition implied that disorder would in fact continue toincrease during the contraction. the thermodynamic andpsychological arrows of time would not reverse when theuniverse begins to recontract, or inside black holes.

what should you do when you find you have made amistake like that? some people never admit that they arewrong and continue to find new, and often mutuallyinconsistent, arguments to support their case - as eddingtondid in opposing black hole theory. others claim to have neverreally supported the incorrect view in the first place or, if theydid, it was only to show that it was inconsistent. it seems tome much better and less confusing if you admit in print thatyou were wrong. a good example of this was einstein, whocalled the cosmological constant, which he introduced when hewas trying to make a static model of the universe, the biggestmistake of his life.

to return to the arrow of time, there remains the question:

why do we observe that the thermodynamic and cosmologicalarrows point in the same direction? or in other words, whydoes disorder increase in the same direction of time as that inwhich the universe expands? if one believes that the universewill expand and then contract again, as the no boundaryproposal seems to imply, this becomes a question of why weshould be in the expanding phase rather than the contractingphase.

one can answer this on the basis of the weak anthropicprinciple. conditions in the contracting phase would not besuitable for the existence of intelligent beings who could ask thequestion: why is disorder increasing in the same direction oftime as that in which the universe is expanding? the inflationin the early stages of the universe, which the no boundaryproposal predicts, means that the universe must be expandingat very close to the critical rate at which it would just avoidrecollapse, and so will not recollapse for a very long time. bythen all the stars will have burned out and the protons andneutrons in them will probably have decayed into light particlesand radiation. the universe would be in a state of almostcomplete disorder. there would be no strong thermodynamicarrow of time. disorder couldn’t increase much because theuniverse would be in a state of almost complete disorderalready. however, a strong thermodynamic arrow is necessaryfor intelligent life to operate. in order to survive, human beingshave to consume food, which is an ordered form of energy,and convert it into heat, which is a disordered form of energy.

thus intelligent life could not exist in the contracting phase ofthe universe. this is the explanation of why we observe thatthe thermodynamic and cosmological arrows of time point inthe same direction. it is not that the expansion of the universecauses disorder to increase. rather, it is that the no boundarycondition causes disorder to increase and the conditions to besuitable for intelligent life only in the expanding phase.

to summarize, the laws of science do not distinguishbetween the forward and backward directions of time. however,there are at least three arrows of time that do distinguish thepast from the future. they are the thermodynamic arrow, thedirection of time in which disorder increases; the psychologicalarrow, the direction of time in which we remember the pastand not the future; and the cosmological arrow, the direction oftime in which the universe expands rather than contracts. ihave shown that the psychological arrow is essentially the sameas the thermodynamic arrow, so that the two would alwayspoint in the same direction. the no boundary proposal for theuniverse predicts the existence of a well-defined thermodynamicarrow of time because the universe must start off in a smoothand ordered state. and the reason we observe thisthermodynamic arrow to agree with the cosmological arrow isthat intelligent beings can exist only in the expanding phase.

the contracting phase will be unsuitable because it has nostrong thermodynamic arrow of time.

the progress of the human race in understanding theuniverse has established a small corner of order in anincreasingly disordered universe. if you remember every wordin this book, your memory will have recorded about two millionpieces of information: the order in your brain will haveincreased by about two million units. however, while you havebeen reading the book, you will have converted at least athousand calories of ordered energy, in the form of food, intodisordered energy, in the form of heat that you lose to the airaround you by convection and sweat. this will increase thedisorder of the universe by about twenty million million millionmillion units - or about ten million million million times theincrease in order in your brain - and that’s if you remembereverything in this book. in the next chapter but one i will tryto increase the order in our neck of the woods a little furtherby explaining how people are trying to fit together the partialtheories i have described to form a complete unified theorythat would cover everything in the universe.