How to Build a Time Machine

by Paul Davies

  (see Making Successive hops back in time on page 112)

  Such a scenario suggests a get-rich-quick strategy. Take along a gold bar and give it to your earlier self to keep until he

  Caption

  Making successive hops back in time

  or she embarks on the time travel; then there will be two gold bars. You will have effortlessly doubled your investment. It's just as easy to duplicate gold bars as people this way.

  From the physicist's point of view, duplicating entities is very disturbing, for it violates all sorts of so-called conservation laws. Suppose the gold bar were replaced by an electrically charged particle? Then two electric charges would appear from one. This violates the law of conservation of electric charge. Again, paradox is avoided by sticking to self-consistent loops. For example, a positively charged particle taken through a wormhole will leave its electric field threading the hole, giving the wormhole an effective positive charge at the entrance (in the future) and a negative charge at the exit (in the past). The negative charge precisely cancels the additional positive charge that the trip back in time has created, thus rescuing the cherished law of change conservation.

  How to pluck knowledge out of thin air

  The most baffling of all the time travel paradoxes is illustrated by the following parable. A professor builds a time machine in the year 2005, and decides to go forward (no problem there) to 2010. When he arrives, he seeks out the university library and browses through the current journals. In the mathematics section he notices a splendid new theorem, and jots down the details. Then he returns to 2005, summons a clever student, and outlines the theorem. The student goes away, tidies up the argument, writes a paper, and publishes it in a mathematics journal. It was, of course, in this very journal that the professor read the paper in 2010.

  Once more, there is no contradiction: the story involves a self-consistent causal loop so, strictly speaking, it is not a paradox but simply a very weird state of affairs. Rather, the problem concerns the origin of information. Where, exactly, did the theorem come from? Not from the professor, for he merely read it in a journal. But not the student either, since he copied it from the professor. It's as if the information about the theorem just came out of thin air.

  This paradox has a familiar ring to it. Something-for-nothing scenarios have long been pursued by eccentric inventors in search of perpetual motion. All such machines fail for reasons related to the first and second laws of thermodynamics which, roughly, state that you can never get out of a closed system more than you put in. Proposed perpetual motion machines always generate some waste heat through friction and other inefficiencies, and eventually grind to a halt. Entropy (waste heat) and information are closely related (technically, rising entropy is the same as falling information). So getting information for free is, from the physicist's point of view, equivalent to heat flowing backwards, from cold to hot.

  Time travel expert David Deutsch believes that information

  entering the universe from nowhere is tantamount to a miracle, and therefore strikes at the very heart of the orderly rationality of nature. For that reason he believes the third paradox is probably the most disturbing of the three. Perhaps we should place it alongside perpetual motion and cosmic censorship on our list of paradoxes, since all involve uncaused information entering the universe ‘from nowhere’.

  How to make another universe

  At the heart of time travel paradoxes is the problem of causality – what happened yesterday affects what happens today. Go back and try to change yesterday and you threaten to change today, too, making causal loops inherently problematic. But maybe there's a more comprehensive let-out than restricting all time loops to detailed self-consistency.

  Causality is not quite the rigid linkage that most people suppose. It's true that in daily life, the connection between cause and effect is inescapable. However, the familiar world of tables and chairs and human beings conceals the shadowy micro-realm of quantum mechanics in which causation is somewhat fuzzy (see p. 82).

  The game of billiards provides a good example of commonsense causation at work. Hit the cue ball at a certain velocity so it collides with another ball In the absence of causal loops, the motion of the two balls after the collision is completely determined by the initial speed and direction of the cue ball. Using Newton's laws of motion, you could work out in advance what will happen after the collision, because those laws are strictly deterministic the initial state suffices to determine completely the final state. That is, if the experiment is repeated under identical conditions, the outcome should be exactly the same. If the struck ball drops in a particular pocket today, it will do so tomorrow, all else being equal. Thus is the orderly operation of the macro-cosmos ensured.

  Things are very different, however, if you try playing billiards with atoms, or particles like electrons and protons. Today, an electron may collide with a proton and bounce to the left. Tomorrow, under identical conditions, it may bounce to the right. Newton's laws of motion don't apply here, and must be replaced by the rules of quantum mechanics, which are indeterministic. That is to say, the state of a physical system at one moment will not usually suffice to determine what will happen at the next moment. The uncertainty of the micro-realm is encapsulated in Heisenberg's uncertainty principle (see p. 82). So prediction is a hazardous business in atomic theory. Generally, the best that can be done is to give the betting odds for this or that outcome. An electron colliding with a proton might bounce off at one among a whole range of angles, some more likely than others. Quantum mechanics gives an accurate account of the probabilities, but it usually won't tell you what will happen in any given case.

  (See Quantum uncertainty on page 118)

  Caption

  Quantum uncertainty

  Physicists are convinced that quantum uncertainty is intrinsic to nature, and not just the result of human ignorance of the processes involved. In other words, even the electron doesn't know which way it will bounce until the collision actually happens. So although it remains true to say in a general sense that a collision with a proton causes the electron to be deflected in its path, the causal link is rather nebulous because the actual final path of the electron is undetermined.

  It is not only simple collisions that are uncertain in atomic physics, but all processes. For example, a given nucleus of the radioactive element uranium may or may not decay next year. An atom hitting a barrier may bounce back, or it may appear on the far side, having mysteriously tunnelled through the barrier, because it is uncertain about precisely where it should be at any moment.

  Among atoms and subatomic particles, quantum uncertainty is very conspicuous. However, for larger systems the fuzziness is less severe. When it comes to big molecules, quantum effects are rarely very important. But quantum uncertainty never completely disappears; in principle, it applies even to billiard balls.

  If events in the microworld aren't completely nailed down by cause and effect, the whole complexion of the causal loop paradoxes associated with time travel changes. One way to think about quantum uncertainty is in terms of possible worlds. An electron hits a proton and may bounce either to left or right. There are then two possible worlds: one with a left-moving electron, the other with a right-moving electron. More generally, an atomic or subatomic process will have many possible outcomes – perhaps even an infinite number of them – so there will be many alternative universes on offer almost every time something happens to a subatomic particle.

  The issue of quantum uncertainty then forces itself upon us if we want to ask in any particular case: Which of the many possible universes will correspond to the actual universe? Of course, we cannot know in advance – that being the nature of quantum uncertainty – but most people suppose that there can be only one real world, all the others representing failed potential worlds. If that is so, there is then a deep problem about connecting smoothly between the quantum realm of multiple potential realities, and the so-called classical (or everyday) r
ealm of just a single reality.

  In fact, there is no agreement about how to make this connection, but a growing number of physicists believe the best way to approach the problem is to suppose that each of those alternative universes is every bit as real as the others. In other words, there is no need to make a transition from many possible worlds to one actual world, because all the possible quantum worlds really exist. In this ‘many-universes’ interpretation of quantum mechanics, there is an infinity of parallel universes, with each possible quantum alternative represented in a universe somewhere. There will be universes in which some atoms of your body are located in slightly different places, a universe in which President Kennedy wasn't assassinated, others which have no planet Earth, and so on. Every possible universe will be there somewhere, except ‘there’ doesn't mean out in space, but in some sense ‘alongside’ our space and time (hence ‘parallel’ universes). Zillions of these other universes will have copies of you, each of whom feels unique and assumes he or she inhabits the one true reality.

  (see Many universes? on page 122)

  Solving the time travel paradoxes by invoking parallel realities has long been a device used by writers of science fiction. The basic idea is that when the time traveller interferes with history, the universe forks into two or more branches. Among scientists who propose this escape route is David Deutsch, who points out that the many-universes interpretation of quantum mechanics naturally resolves the time travel paradoxes. Take the matricide paradox. Suppose the time traveller goes back and carries out the murder. This time there is no mistake; mother is dead. But which mother? Remember, there is a vast collection of mothers amid the stupendous number of parallel realities. In the multiverse of parallel quantum worlds, you could change the past of a parallel world, while leaving your own world untouched. In effect, the act of murder divides reality in two sets, one with a dead mother, another with a live mother. Both possibilities co-exist side-by-side in the vastness

  Caption

  Many universes?

  of the quantum multiverse. Any given ‘branch’ of the multiverse (i.e. any specific observed reality) is thoroughly selfconsistent, but causal interactions between branches need not respect a definite chronological order. In Deutsch's scheme you can have your cake and eat it: time travel and unfettered free will are apparently both allowed.

  Scientists are divided about the desirability of invoking the quantum multiverse to solve time travel paradoxes. Some believe that parallel realities are even more absurd than time loops and would rather have neither. But whether or not one buys the many-universes interpretation of quantum mechanics, nature is quantum-mechanical, and any final analysis of a physical situation must be carried out at the quantum level. It seems that causal loops arising from time travel have the effect of amplifying quantum phenomena – normally confined to the atomic realm – to the level of everyday life. So we cannot avoid adding the weirdness of quantum reality to the strangeness of time travel.

  Chronology protection

  Time travel may seem like fun to fans of science fiction, but the idea is positively scary for many physicists. The problem lies partly with the plethora of paradoxes that travel into the past would unleash. In addition, the possibility that causal loops may be imminent seems to be so physically pathological that it would produce profound physical effects; so profound, in fact, that they may stymie any attempt to actually create a time machine. Among theorists who have expressed serious doubts that wormholes or other time machines would work as advertised is Stephen Hawking. He has proposed a ‘chronology protection conjecture’ which, in simplified terms, says that nature always comes up with an obstacle to prevent travel backwards in time – ‘making the universe safe for historians’ was the way he expressed it.

  What might go wrong, then, if a supercivilization attempted to build a wormhole time machine? One possibility is that antigravity is too fickle a phenomenon to harness in realistic wormhole scenarios. It is one thing to demonstrate that nega-tive energy is physically possible under some unusual circumstances, quite another to expect it to arise inside a wormhole or other time machine set-up, with the strength necessary to achieve time travel. The jury remains out on this one. Mathematical studies suggest that antigravity states in quantum fields occur under a fairly wide range of circumstances, but at present there is no general theorem to indicate precisely what the limits are.

  Even granted that antigravity could be deployed in some suitable manner (or the necessary exotic matter obligingly put there by nature), other problems loom. The exotic matter pervading the wormhole's throat might interact with any normal matter attempting to traverse the wormhole and impede or destroy it.

  Another difficulty concerns the behaviour of the quantum vacuum in the vicinity of a wormhole, or any other sort of time machine. The problem centres on what happens at the join between the region of spacetime that permits time loops, and ‘normal’ spacetime where past and future don't get entangled. The interface between the two regions is called the chronology horizon. Crossing the chronology horizon entails entering a region of spacetime where particles can go round and round in endless causal loops. This includes the virtual photons of the quantum vacuum state. Crudely speaking, each time a virtual photon does a circuit in time, it doubles the (borrowed) energy. Calculations show that as the horizon is approached, virtual photons circulate around almost closed causal loops, and the nearer to the horizon they get, the closer to closure the loops risk becoming. Given the inherent uncertainties in the behaviour of quantum particles like photons, the horizon does not act as a sharp boundary. The mere threat of impending causal closure is enough to boost the virtual photons without limit, piling up more and more energy as the horizon is approached. This runaway energy escalation would probably generate a huge gravitational field that would warp the spacetime and wreck the time machine. I say probably, because we do not yet have a good enough theory of quantum gravity to check what would actually happen under these extreme circumstances. So the quantum vacuum catastrophe argument is suggestive, but so far not fatal. At the time of writing, the chronology protection conjecture remains in limbo, a hope for some, a party-pooper for others.

  Alternative models of time machines

  The wormhole remains the favoured design of time machine, but it is by no means the only one. I have already mentioned the early work of van Stockum and Gödel on rotating matter (see pp. 35–6). A quite different proposal for a time machine has been made by J. Richard Gott III, based on the use of hypothetical entities called ‘cosmic strings’. A cosmic string is an astronomically long thread that contains a vast amount of mass; each kilometre of cosmic string would weigh about the same as the Earth. Some cosmologists believe cosmic strings may have formed in the hot big bang, when the intense primordial energy pervading space became trapped inside thin tubes and was preserved for posterity.

  Cosmic strings would be made of exotic matter, but in this case what makes string matter exotic concerns not energy but pressure. Normally we do not notice that pressure is a source of gravity, but according to Einstein's general theory of relativity pressure creates a gravitational field too. If it is truly enormous, pressure can rival energy in its gravitating power. It turns out that the pressure inside a cosmic string is enormous and negative, which is to say that the string is in tension. Because pressure gravitates, tension (negative pressure) antigravitates. In the case of a straight segment of string, the antigravity of the tension exactly cancels the gravity of the mass-energy, with the result that the string would exert no gravitational force on a nearby body, in spite of its colossal mass.

  Nevertheless, the string still alters the geometry of space in its vicinity, in a rather distinctive manner, best illustrated by analogy with a maypole. When a May Day dancer cavorts once around a maypole, he will turn through exactly 360 degrees. If the maypole were a cosmic string instead, the dancer would find he got back to his starting-point after turning through less than 360 degrees. A circle drawn arou
nd a cosmic string does not contain four right angles as does a circle drawn on a blackboard.

  The angular deficit caused by a cosmic string is predicted to be only a few seconds of arc, but, nevertheless, it leads to some distinctive effects. For example, a pair of parallel straight lines that straddle the string will end up converging. If the lines represent light rays from, for example, a quasar or distant galaxy, an observer will see two copies of either if the string interposes itself between it and the observer. Double images of this sort are known to astronomers, but they can be produced in other ways too, and there is no hard evidence that cosmic strings actually exist.

  (see Double quasar images on page 128)

  Caption

  Double quasar images

  In spite of this, they are much studied. Gott has pointed out that photons from a distant source that straddle the string and converge need not arrive at the crossover point at the same moment if the string, source and observer are not precisely aligned or are in relative motion. As a result, it would be possible for an astronaut travelling very close to the speed of light around one side of the string to reach the convergence point ahead of the photon coming round the other way. In effect, the astronaut will have outpaced the slower light pulse by taking an alternative route through space, just as in the case of the wormhole. This physical argument suggests that time travel may be possible using cosmic strings, too. Gott proved mathematically that, if a pair of parallel cosmic strings are moving apart at very close to the speed of light, there will exist a region in which an astronaut could travel back in time by executing a loop around the strings.