by Paul Davies
Negative quantum vacuum energy also occurs as a by-product of certain gravitational fields. A simple example is the gravitational field of the Earth, which produces a cloud of negative energy around it by dragging some of the virtual photons downwards. In the case of the Earth, the effect is extremely small. But as the gravitational field rises, so the negative energy cloud grows in strength. Near the surface of a black hole it is enormous. Because there is no material surface to the hole, only empty space, this negative energy flows into the black hole in a steady stream. In effect, the black hole vacuums up the quantum vacuum!
A solar-mass black hole with a radius of 3 kilometres sucks up negative energy at a rate of a billion billion billionth of a joule per second. Still pretty feeble. But the smaller the black hole, the stronger the gravity at its surface, and the more intense the negative energy that surrounds it. A black hole the size of an atomic nucleus (and the mass of a mountain) would swallow negative energy at about a billion joules per second, creating a million kilowatt energy sink.
The existence of negative energy near black holes was guessed by Stephen Hawking in 1974. Hawking predicted that a black hole should glow faintly with heat radiation. The radiated energy has to come from somewhere, and since nothing (even energy) can get out of a black hole, it seemed the only explanation must be that negative energy flows into it. The following year, William Unruh, Stephen Fulling and I confirmed this prediction by computing the energy near a black hole in a simplified two-dimensional mathematical model. We found that there is, indeed, a negative energy flux into the hole at a rate that exactly compensates for the heat radiation coming off it.
Stationing our time machine factory near the surface of a black hole to soak up the negative energy is hardly feasible,
but the very existence of negative quantum energy generated by gravitational fields is highly significant. Since the wormhole itself will have a strong gravitational field, it may be that it will generate the required negative energy from the quantum vacuum of its own accord. Nobody yet knows whether this is possible or not. If it is, the wormhole might be induced to self-inflate, with very little exotic matter input. The laser system could be used to start the process, configuring the geometry of the microscopic wormhole to the appropriate shape, and after that nature would do the rest, delivering a large wormhole for free. The wormhole would loom out of the spacetime foam as, so to speak, a ‘free lunch’. If that seems surprising, remember that negative energy has negative mass, so that the total wormhole mass might be close to zero. In other words, there may be little or no overall energy cost in producing a worm-hole: the negative energy parts pay for the positive energy parts. In which case, a large wormhole could generate itself spontaneously, with a little bit of fine-tuning from the inflator factory engineers.
The primary requirement in making a serviceable time machine is keeping the wormhole throat open. But to use a wormhole as an effective transportation device demands that it be more than merely a gateway to other times and places. A human being has to be able to squeeze through and come out smiling. To avoid spaghettifying its users, a wormhole's gravitational field needs to be gentle. Also, the duration of the ride should be reasonable. A journey into the past that takes the time traveller 100 years to complete would not be very attractive. So long wormholes are out.
These two additional requirements impose further restrictions on the exotic matter in the wormhole. Experts quarrel over just how exotic the exotic matter must be, whether it should be confined to a small region deep in the throat of the wormhole or allowed to emanate from the mouths, how it can be so confined, whether radiation issuing from one mouth could enter the other and endlessly cycle back on itself, and a host of other technicalities.
Assuming all these difficulties can be overcome, and we have a safe, short wormhole in the storage bay of the inflator fact-ry, the final step is to convert it into a time machine. That is the job of the differentiator.
The differentiator
To turn a wormhole into a time machine you have to establish a permanent time difference between the two ends. The simplest technique is to use the ordinary time dilation – or twins – effect. To do this, the wormhole is given an electric charge (e.g. by firing electrons into it) when it is still quite small – say, the size of a subatomic particle. One mouth of the wormhole is then fed into an ordinary circular particle accelerator and whirled around at very near the speed of light, while the other is held still. This produces a growing temporal discrepancy between the two mouths of the wormhole. The process is allowed to continue for, say, 10 years, at which time the moving mouth is brought to rest, and allowed to approach the other wormhole mouth. The wormhole is now able to send particles of matter back in time for up to 10 years. In the final step of the process, the wormhole is returned to the inflator factory to be expanded to a size large enough for a human being to traverse – say, 10 metres in diameter. Meanwhile, the length of the wormhole is kept as short as possible.
Another way to turn the wormhole into a time machine is to use the gravitational field of a neutron star rather than an accelerator as a differentiator. This is how it works. Imagine a rather short wormhole, let's say 10 metres in length. Tow one mouth – call it A – to the close vicinity of a neutron star a few light years away, and leave the other end, B, parked in the solar system. Keep them in place until the gravity timewarp of the neutron star accumulates to the required amount, then tow A back to the solar system and park it next to B. The time machine is now ready for use.
To see why this procedure works, imagine identical clocks placed at each mouth of the wormhole. The gravity of the neutron star stretches time at mouth A; the clock there will run slow. What about the clock at B? Being some light years from the star, its rate should not be affected by the star's gravity, so it should tick considerably faster than the clock at A. But there's a catch. Suppose we look through the wormhole from mouth A, located near the star. We then see clock B just a few metres away. So by one route the clock at B is very far from the neutron star, by another it is very near. If it is regarded as very near, then time at B should be slowed by the star's gravity, too. There should be very little difference between the clocks' rates at A and B. So which view is right? The answer is, both. Time is, after all, relative, and the situation here is that, viewed through the wormhole, time is about the same at both ends but, viewed across the ‘outer’ space, there is a substantial time difference between A and B (clock B is ahead of A). If you now jump through the wormhole from A to B, you will jump back 10 years into the past. By returning to A through ‘normal’ space, you could get back to your starting point before you leave. So, once again, by executing a closed loop in space, you also perform a closed loop in time. This time machine is two-way. By going through the wormhole in the other direction – from B to A – you can jump 10 years into the future.
Wormhole time travel differs in two crucial respects from the version H.G. Wells presents. In The Time Machine, the intrepid time traveller throws a lever, and in effect fast-forwards the universe, like a video player, accelerating ‘the cosmic movie’ relative to his mental time. When he gets where he wants to go
(see H. G. Wells on page 102)
Caption
H.G. Wells
he simply hits the stop button. He travels back in time by fast rewinding. The time machine shares in the temporal transport, going back and forth in time with the driver. That is quite unlike the wormhole time machine, which doesn't itself move through time; it is simply part of the cosmic architecture.
Secondly, in Wells's story, the time traveller doesn't go anywhere in space. But a moment's thought exposes the ambiguity of this arrangement, for in the time spans over which he travels, the Earth will have moved many light years across the galaxy. And the galaxy moves relative to others. Since there is no absolute frame of rest against which to measure these movements, the whereabouts of the time machine in space after the temporal gymnastics is completely indeterminate. The wormhole
time machine operates quite differently. Rather than inducing time to run backwards, the time traveller embarks on a journey into space that ends in the past.
4 How to make sense of it all
* * *
Time present and time past
Are both perhaps present in time future
And time future contained in time past.
T.S. Eliot
As nobody has yet produced a knock-down argument to show that time travel is impossible – however daunting the practical difficulties of constructing a time machine may be – the consequences of backward time travel need to be confronted. Writers of science fiction are familiar with the outlandish, even paradoxical, consequences that can ensue if people are able to visit the past. So can two-way time travel be incorporated into real science?
How to avoid time tourists
A much-voiced objection to travel backwards in time is that we don't encounter anybody from the future. If it were possible to visit the past, we might expect that our descendants, perhaps thousands of years from now, would build a time machine and come back to observe us, or even to tell us about themselves. Key historical events such as the crucifixion would have been crowded by throngs of eager witnesses. Discounting reports of ghosts, UFOs and the like, the apparent absence of time tourists is something of a problem for time travel enthusiasts.
Fortunately this objection is easily met in the case of worm-hole time machines. Although wormholes could be used to go back and forth in time, it is not possible to use one to visit a time before the wormhole was constructed. If we built one now, and established, say, a 100 year time difference between the two ends, then in a 100 years someone could revisit 2001. But you couldn't use the wormhole to go back and see the dinosaurs. Only if wormhole time machines already exist in nature – or were made long ago by an alien civilization – could we visit epochs before the present. So if the first wormhole time machine were built in the year 3000, there could not be any time tourists in the year 2000.
Time paradoxes
Changing the past
Perhaps the most famous of all the time travel paradoxes is the one in which the time traveller goes back in time and murders one of his ancestors, e.g. his mother. The problem is then obvious. If mother dies before giving birth, then the time traveller would never have existed. But in that case he would not be able to carry out the murder. So if the woman lives, she dies, but if she dies, she lives! Either way contradictory nonsense results.
Many time travel stories have come up against this obvious and thorny problem. In the movie Back to the Future, the time traveller, Marty McFly, does not attempt to kill his mother as a young woman. Rather, he becomes embroiled in her love life, and risks interfering with her marriage plans, as a result of which he teeters on the edge of obliteration. Of course, his disappearance would not resolve the paradox either, because he would then not have been able to visit the past to interfere in history.
Paradoxes like this arise because the past is causally linked to the present. You cannot change the past without changing the present, too; this creates a causal loop. Because the behaviour of many physical systems is very sensitive to small changes, even modest tinkering with the past could lead to wholesale changes of the present. Imagine how different the world would be if Adolf Hitler were assassinated in 1939, or if the tiny genetic mutation that produced the first human hadn't taken place because the hominid concerned was persuaded to move one centimetre to the left, thus avoiding the crucial cosmic ray that was destined to bring about a species transformation. In Ray Bradbury's story ‘A Sound of Thunder’, a time traveller journeying back to see the dinosaurs kills a single butterfly, but thereby sets in train a series of events that transforms the entire course of history.
Causal loops are not intrinsically paradoxical, so long as they are consistent. Changing the past is obviously paradoxical; the past is, after all, past. But affecting the past is logically unobjectionable, by which I mean there is no logical impediment to some events being caused by later events, or by a mixture of later and earlier events. For example, imagine a rich venture capitalist whose vast inherited wealth derives from a mysterious benefactor who befriended his great grandmother a century before. He finances a time machine project, and then uses the prototype machine to go back and discover the source of his wealth. He can't resist proving his time-travel credentials by taking a newspaper with him, which he duly presents to his young great grandmother. Being an enterprising soul, the lady scans the newspaper's stock prices and, with the help of her foreknowledge, makes some shrewd investments. These investments are, of course, the source of her, and her great grandson's, immense fortune, and the time traveller himself is the mysterious benefactor. No paradox ensues here because the causal loop is self-consistent, and everything fits together neatly.
Paradox looms only when we combine causal loops with unfettered free will. But if the time traveller finds he or she is simply unable or unwilling to carry out the mischievous deeds that produce inconsistent historical sequences – like murdering his mother – then this particular paradox is avoided.
Why should free will be limited? It may be that you can visit the past, but when you arrive you find yourself continually stymied in what you try to do. If you attempt to kill your mother, perhaps the gun will jam, or you will be arrested first for suspicious behaviour, etc. Or maybe the wishes that determine your acts during the visit to the past are simply shaped by what is consistent with the future world from which you have come. In any case, free will is a slippery concept, hard to reconcile with the laws of physics even without time travel. Many scientists and philosophers dismiss it as an illusion.
It's not necessary for a human being to travel back in time for paradoxical consequences to be triggered. In principle, just a single particle (or any minute physical influence) sent into the past can unleash mayhem. Suppose a sensitive device is programmed to explode if, and only if, it receives a signal from one hour in the future – say, the arrival of a photon with a particular frequency. The device is placed next to the photon emitter. Then sending one such photon back in time would trigger the device and destroy the emitter. But if the emitter is destroyed, the photon is never sent. Again, we get inconsistent accounts.
Even if it is impracticable to build a time machine that could convey humans into the past, it may still be possible to send signals back in time. An early speculation of this sort is based on hypothetical particles called ‘tachyons’, that can travel faster than light. It is often stated that nothing can go faster than light, but this isn't strictly true. As I explained in chapter 1 (see p. 14), the theory of relativity introduces a light barrier that can't be crossed. A particle of ordinary matter can never be accelerated to a speed faster than light: if you try to do it, the particle just gets heavier and heavier, rather than faster and faster. But the light barrier operates both ways: if something goes faster than light it can never be slowed below the speed of light. A tachyon is just such an entity stuck on the far side of the light barrier, obliged to travel always at superluminal speed.
If tachyons exist, and can be manipulated, they could be used to send a signal into the past. To do this you would need the help of an accomplice. First you send a signal to a friend using a tachyon beam travelling at, say, 10 times the speed of light relative to you. Then the friend immediately sends the signal back again at 10 times the speed of light relative to her. If the friend is moving towards you at a large fraction of the speed of light, the return signal will reach you before the outgoing one was sent.
What are the prospects for tachyons really existing? Most physicists are extremely sceptical about them. Quite apart from the lack of experimental evidence, they would have some peculiar properties. For example, they would possess imaginary mass (in the mathematical sense), making them hard to reconcile with quantum mechanics. There is no guarantee that they would interact with ordinary matter, in which case it would be impossible to use them to send signals anyway.
; Even if tachyons do not exist, wormholes or other devices might be used to send particles back in time. You can then imagine a billiard ball version of the mother paradox. Kip Thorne and his colleagues studied the idea of time-loop billiards. In the modified game, the pockets of the billiard table represent the entrance and exit of a wormhole time machine. Imagine a ball heading for an end pocket, going down, and emerging a few moments earlier from a side pocket in such a way that the ball collides with its earlier self. The collision will then deflect the ball from its initial path and prevent it from entering the end pocket. There is no free will to complicate matters, but, just as in the ‘matricide’ paradox, the described sequence is inconsistent and so won't happen.
But the paradox can be resolved. We can also imagine a slightly different story. Here, the ball starts out moving in such a way that it would just miss the end pocket; however it suffers a glancing blow from a ball emerging from a side pocket. The collision serves to deflect the ball so that it now enters the end pocket, and emerges from the side pocket a short while earlier in the guise of the ball that delivers the glancing blow. Thorne showed that this sequence – a ball colliding with its earlier self in a manner designed to create a self-consistent causal loop – is perfectly consistent with the laws of physics. Disturbingly, though, he also showed that there is more than one self-consistent sequence of events. When causal loops are present, the laws of Newtonian mechanics no longer predict a unique reality.
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Travel into the past takes on an air of absurdity when the time traveller meets his younger self, for then there will be two of him. Note that you would not be surprised to meet your younger self this way, because you would already remember the encounter from your youth.
The age difference need not be great. In principle it could be, say, a day. In this case, there would be two virtually identical copies of you. That would be very weird. And it needn't stop there. You could invite your (slightly) younger self to accompany you in a similar trip back another day, when there will be three of you Nothing prevents this process being repeated again and again. By making successive hops back in time, the time traveller could accumulate many copies of himself in one place.