the last chapter discussed why we see time go forward:

why disorder increases and why we remember the past butnot the future. time was treated as if it were a straight railwayline on which one could only go one way or the other.

but what if the railway line had loops and branches so thata train could keep going forward but come back to a station ithad already passed? in other words, might it be possible forsomeone to travel into the future or the past?

h. g. wells in the time machine explored these possibilitiesas have countless other writers of science fiction. yet many ofthe ideas of science fiction, like submarines and travel to themoon, have become matters of science fact. so what are theprospects for time travel?

the first indication that the laws of physics might really allowpeople to travel in time came in 1949 when kurt godeldiscovered a new space-time allowed by general relativity. godelwas a mathematician who was famous for proving that it isimpossible to prove all true statements, even if you limityourself to trying to prove all the true statements in a subjectas apparently cut and dried as arithmetic. like the uncertaintyprinciple, godel’s incompleteness theorem may be a fundamentallimitation on our ability to understand and predict the universe,but so far at least it hasn’t seemed to be an obstacle in oursearch for a complete unified theory.

godel got to know about general relativity when he andeinstein spent their later years at the institute for advancedstudy in princeton. his space-time had the curious propertythat the whole universe was rotating. one might ask: “rotatingwith respect to what?” the answer is that distant matter wouldbe rotating with respect to directions that little tops orgyroscopes point in.

this had the side effect that it would be possible forsomeone to go off in a rocket ship and return to earth beforehe set out. this property really upset einstein, who hadthought that general relativity wouldn’t allow time travel.

however, given einstein’s record of ill-founded opposition togravitational collapse and the uncertainty principle, maybe thiswas an encouraging sign. the solution godel found doesn’tcorrespond to the universe we live in because we can showthat the universe is not rotating. it also had a non-zero valueof the cosmological constant that einstein introduced when hethought the universe was unchanging. after hubble discoveredthe expansion of the universe, there was no need for acosmological constant and it is now generally believed to bezero. however, other more reasonable space-times that areallowed by general relativity and which permit travel into thepast have since been found. one is in the interior of a rotatingblack hole. another is a space-time that contains two cosmicstrings moving past each other at high speed. as their namesuggests, cosmic strings are objects that are like string in thatthey have length but a tiny cross section. actually, they aremore like rubber bands because they are under enormoustension, something like a million million million million tons. acosmic string attached to the earth could accelerate it from 0to 60 mph in 1/30th of a second. cosmic strings may soundlike pure science fiction but there are reasons to believe theycould have formed in the early universe as a result ofsymmetry-breaking of the kind discussed in chapter 5. becausethey would be under enormous tension and could start in anyconfiguration, they might accelerate to very high speeds whenthey straighten out.

the godel solution and the cosmic string space-time start outso distorted that travel into the past was always possible. godmight have created such a warped universe but we have noreason to believe he did. observations of the microwavebackground and of the abundances of the light elementsindicate that the early universe did not have the kind ofcurvature required to allow time travel. the same conclusionfollows on theoretical grounds if the no boundary proposal iscorrect. so the question is: if the universe starts out withoutthe kind of curvature required for time travel, can wesubsequently warp local regions of space-time sufficiently toallow it?

a closely related problem that is also of concern to writersof science fiction is rapid interstellar or intergalactic travel.

according to relativity, nothing can travel faster than light. if wetherefore sent a spaceship to our nearest neighboring star,alpha centauri, which is about four light-years away, it wouldtake at least eight years before we could expect the travelers toreturn and tell us what they had found. if the expedition wereto the center of our galaxy, it would be at least a hundredthousand years before it came back. the theory of relativitydoes allow one consolation. this is the so-called twins paradoxmentioned in chapter 2.

because there is no unique standard of time, but ratherobservers each have their own time as measured by clocksthat they carry with them, it is possible for the journey toseem to be much shorter for the space travelers than forthose who remain on earth. but there would not be much joyin returning from a space voyage a few years older to findthat everyone you had left behind was dead and gonethousands of years ago. so in order to have any humaninterest in their stories, science fiction writers had to supposethat we would one day discover how to travel faster than light.

what most of thee authors don’t seem to have realized is thatif you can travel faster than light, the theory of relativity impliesyou can also travel back in the, as the following limerick says:

there was a young lady of wightwho traveled much faster than light.

she departed one day,in a relative way,and arrived on the previous nightthe point is that the theory of relativity says hat there is nounique measure of time that all observers will agree on rather,each observer has his or her own measure of time. if it ispossible for a rocket traveling below the speed of light to getfrom event a (say, the final of the 100-meter race of theolympic games in 202) to event b (say, the opening of the100,004th meeting of the congress of alpha centauri), then allobservers will agree that event a happened before event baccording to their times. suppose, however, that the spaceshipwould have to travel faster than light to carry the news of therace to the congress. then observers moving at differentspeeds can disagree about whether event a occurred before bor vice versa. according to the time of an observer who is atrest with respect to the earth, it may be that the congressopened after the race. thus this observer would think that aspaceship could get from a to b in time if only it could ignorethe speed-of-light speed limit. however, to an observer at alphacentauri moving away from the earth at nearly the speed oflight, it would appear that event b, the opening of thecongress, would occur before event a, the 100-meter race. thetheory of relativity says that the laws of physics appear thesame to observers moving at different speeds.

this has been well tested by experiment and is likely toremain a feature even if we find a more advanced theory toreplace relativity thus the moving observer would say that iffaster-than-light travel is possible, it should be possible to getfrom event b, the opening of the congress, to event a, the100-meter race. if one went slightly faster, one could even getback before the race and place a bet on it in the sureknowledge that one would win.

there is a problem with breaking the speed-of-light barrier.

the theory of relativity says that the rocket power needed toaccelerate a spaceship gets greater and greater the nearer itgets to the speed of light. we have experimental evidence forthis, not with spaceships but with elementary particles in particleaccelerators like those at fermilab or cern (european centrefor nuclear research). we can accelerate particles to 99.99percent of the speed of light, but however much power wefeed in, we can’t get them beyond the speed-of-light barrier.

similarly with spaceships: no matter how much rocket powerthey have, they can’t accelerate beyond the speed of light.

that might seem to rule out both rapid space travel andtravel back in time. however, there is a possible way out. itmight be that one could warp space-time so that there was ashortcut between a and b one way of doing this would be tocreate a wormhole between a and b. as its name suggests, awormhole is a thin tube of space-time which can connect twonearly flat regions far apart.

there need be no relation between the distance through thewormhole and the separation of its ends in the nearly hatbackground. thus one could imagine that one could create orfind a wormhole that world lead from the vicinity of the solarsystem to alpha centauri. the distance through the wormholemight be only a few million miles even though earth and alphacentauri are twenty million million miles apart in ordinary space.

this would allow news of the 100-meter race to reach theopening of the congress. but then an observer moving toward6e earth should also be able to find another wormhole thatwould enable him to get from the opening of the congress onalpha centauri back to earth before the start of the race. sowormholes, like any other possible form of travel faster thanlight, would allow one to travel into the past.

the idea of wormholes between different regions ofspace-time was not an invention of science fiction writers butcame from a very respectable source.

in 1935, einstein and nathan rosen wrote a paper in whichthey showed that general relativity allowed what they called“bridges,” but which are now known as wormholes. theeinstein-rosen bridges didn’t last long enough for a spaceshipto get through: the ship would run into a singularity as thewormhole pinched off. however, it has been suggested that itmight be possible for an advanced civilization to keep awormhole open. to do this, or to warp space-time in anyother way so as to permit time travel, one can show that oneneeds a region of space-time with negative curvature, like thesurface of a saddle. ordi-nary matter, which has a positiveenergy density, gives space-time a positive curvature, like thesurface of a sphere. so what one needs, in order to warpspace-time in a way that will allow travel into the past, ismatter with negative energy density.

energy is a bit like money: if you have a positive balance,you can distribute it in various ways, but according to theclassical laws that were believed at the beginning of the century,you weren’t allowed to be overdrawn. so these classical lawswould have ruled out any possibility of time travel. however, ashas been described in earlier chapters, the classical laws weresuperseded by quantum laws based on the uncertaintyprinciple. the quantum laws are more liberal and allow you tobe overdrawn on one or two accounts provided the totalbalance is positive. in other words, quantum theory allows theenergy density to be negative in some places, provided that thisis made up for by positive energy densities in other places, sothat the total energy re-mains positive. an example of howquantum theory can allow negative energy densities is providedby what is called the casimir effect. as we saw in chapter 7,even what we think of as “empty” space is filled with pairs ofvirtual particles and antiparticles that appear together, moveapart, and come back together and annihilate each other. now,suppose one has two parallel metal plates a short distanceapart. the plates will act like mirrors for the virtual photons orparticles of light. in fact they will form a cavity between them,a bit like an organ pipe that will resonate only at certain notes.

this means that virtual photons can occur in the spacebetween the plates only if their wavelengths (the distancebetween the crest of one wave and the next) fit a wholenumber of times into the gap between the plates. if the widthof a cavity is a whole number of wavelengths plus a fraction ofa wave-length, then after some reflections backward andforward between the plates, the crests of one wave will coincidewith the troughs of another and the waves will cancel out.

because the virtual photons between the plates can haveonly the resonant wavelengths, there will be slightly fewer ofthem than in the region outside the plates where virtualphotons can have any wavelength. thus there will be slightlyfewer virtual photons hitting the inside surfaces of the platesthan the outside surfaces. one would therefore expect a forceon the plates, pushing them toward each other. this force hasactually been detected and has the predicted value. thus wehave experimental evidence that virtual particles exist and havereal effects.

the fact that there are fewer virtual photons between theplates means that their energy density will be less thanelsewhere. but the total energy density in “empty” space faraway from the plates must be zero, because otherwise theenergy density would warp the space and it would not bealmost flat. so, if the energy density between the plates is lessthan the energy density far away, it must be negative.

we thus have experimental evidence both that space-timecan be warped (from the bending of light during eclipses) andthat it can be curved in the way necessary to allow time travel(from the casimir effect). one might hope therefore that as weadvance in science and technology, we would eventually manageto build a time machine. but if so, why hasn’t anyone comeback from the future and told us how to do it? there mightbe good reasons why it would be unwise to give us the secretof time travel at our present primitive state of development, butunless human nature changes radically, it is difficult to believethat some visitor from the future wouldn’t spill the beans. ofcourse, some people would claim that sightings of ufos areevidence that we are being visited either by aliens or by peoplefrom the future. (if the aliens were to get here in reasonabletime, they would need faster-than-light travel, so the twopossibilities may be equivalent.)however, i think that any visit by aliens or people from thefuture would be much more obvious and, probably, much moreunpleasant. if they are going to reveal themselves at all, whydo so only to those who are not regarded as reliablewitnesses? if they are trying to warn us of some great danger,they are not being very effective.

a possible way to explain the absence of visitors from thefuture would be to say that the past is fixed because we haveobserved it and seen that it does not have the kind of warpingneeded to allow travel back from the future. on the otherhand, the future is unknown and open, so it might well havethe curvature required. this would mean that any time travelwould be confined to the future. there would be no chance ofcaptain kirk and the starship enterprise turning up at thepresent time.

this might explain why we have not yet been overrun bytourists from the future, but it would not avoid the problemsthat would arise if one were able to go back and changehistory. suppose, for example, you went back and killed yourgreat-great-grandfather while he was still a child. there aremany versions of this paradox but they are essentiallyequivalent: one would get contradictions if one were free tochange the past.

there seem to be two possible resolutions to the paradoxesposed by time travel. one i shall call the consistent historiesapproach. it says that even if space-time is warped so that itwould be possible to travel into the past, what happens inspace-time must be a consistent solution of the laws of physics.

according to this viewpoint, you could not go back in timeunless history showed that you had already arrived in the pastand, while there, had not killed your great-great-grandfather orcommitted any other acts that would conflict with your currentsituation in the present. moreover, when you did go back, youwouldn’t be able to change recorded history. that means youwouldn’t have free will to do what you wanted. of course, onecould say that free will is an illusion anyway. if there really is acomplete unified theory that governs everything, it presumablyalso determines your actions. but it does so in a way that isimpossible to calculate for an organism that is as complicatedas a human being. the reason we say that humans have freewill is because we can’t predict what they will do. however, ifthe human then goes off in a rocket ship and comes backbefore he or she set off, we will be able to predict what he orshe will do because it will be part of recorded history. thus, inthat situation, the time traveler would have no free will.

the other possible way to resolve the paradoxes of timetravel might be called the alternative histories hypothesis. theidea here is that when time travelers go back to the past, theyenter alternative histories which differ from recorded history.

thus they can act freely, without the constraint of consistencywith their previous history. steven spiel-berg had fun with thisnotion in the back to the future films: marty mcfly was ableto go back and change his parents’ courtship to a moresatisfactory history.

the alternative histories hypothesis sounds rather like richardfeynman’s way of expressing quantum theory as a sum overhistories, which was described in chapters 4 and 8. this saidthat the universe didn’t just have a single history: rather it hadevery possible history, each with its own probability. however,there seems to be an important difference between feynman’sproposal and alternative histories. in feynman’s sum, eachhistory comprises a complete space-time and everything in it.

the space-time may be so warped that it is possible to travelin a rocket into the past. but the rocket would remain in thesame space-time and therefore the same history, which wouldhave to be consistent. thus feynman’s sum over historiesproposal seems to support the consistent histories hypothesisrather than the alternative histories.

the feynman sum over histories does allow travel into thepast on a microscopic scale. in chapter 9 we saw that thelaws of science are unchanged by combinations of theoperations c, p, and t. this means that an antiparticle spinningin the anticlockwise direction and moving from a to b can alsobe viewed as an ordinary particle spinning clockwise andmoving backward in time from b to a. similarly, an ordinaryparticle moving forward in time is equivalent to an antiparticlemoving backward in time. as has been discussed in thischapter and chapter 7, “empty” space is filled with pairs ofvirtual particles and antiparticles that appear together, moveapart, and then come back together and annihilate each other.

so, one can regard the pair of particles as a single particlemoving on a closed loop in space-time. when the pair ismoving forward in time (from the event at which it appears tothat at which it annihilates), it is called a particle. but when theparticle is traveling back in time (from the event at which thepair annihilates to that at which it appears), it is said to be anantiparticle traveling forward in time.

the explanation of how black holes can emit particles andradiation (given in chapter 7) was that one member of avirtual particle/ antiparticle pair (say, the antiparticle) might fallinto the black hole, leaving the other member without a partnerwith which to annihilate. the forsaken particle might fall intothe hole as well, but it might also escape from the vicinity ofthe black hole. if so, to an observer at a distance it wouldappear to be a particle emitted by the black hole.

one can, however, have a different but equivalent intuitivepicture of the mechanism for emission from black holes. onecan regard the member of the virtual pair that fell into theblack hole (say, the antiparticle) as a particle traveling backwardin time out of the hole. when it gets to the point at which thevirtual particle/antiparticle pair appeared together, it is scatteredby the gravitational field into a particle traveling forward in timeand escaping from the black hole. if, instead, it were theparticle member of the virtual pair that fell into the hole, onecould regard it as an antiparticle traveling back in time andcoming out of the black hole. thus the radiation by black holesshows that quantum theory allows travel back in time on amicroscopic scale and that such time travel can produceobservable effects.

one can therefore ask: does quantum theory allow timetravel on a macroscopic scale, which people could use? at firstsight, it seems it should. the feynman sum over historiesproposal is supposed to be over all histories. thus it shouldinclude histories in which space-time is so warped that it ispossible to travel into the past. why then aren’t we in troublewith history? suppose, for example, someone had gone backand given the nazis the secret of the atom bomb?

one would avoid these problems if what i call thechronology protection conjecture holds. this says that the lawsof physics conspire to prevent macroscopic bodies from carryinginformation into the past. like the cosmic censorship conjecture,it has not been proved but there are reasons to believe it istrue.

the reason to believe that chronology protection operates isthat when space-time is warped enough to make travel into thepast possible, virtual particles moving on closed loops inspace-time can become real particles traveling forward in timeat or below the speed of light. as these particles can go roundthe loop any number of times, they pass each point on theirroute many times. thus their energy is counted over and overagain and the energy density will become very large. this couldgive space-time a positive curvature that would not allow travelinto the past. it is not yet clear whether these particles wouldcause positive or negative curvature or whether the curvatureproduced by some kinds of virtual particles might cancel thatproduced by other kinds. thus the possibility of time travelremains open. but i’m not going to bet on it. my opponentmight have the unfair advantage of knowing the future.