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CHAPTER 10 WORMHOLES AND TIME TRAVEL
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 dens............
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