A Brief History of Time (23 page)

Energy is a bit like money: if you have a positive balance, you can distribute it in various ways, but according to the classical laws that were believed at the beginning of the century, you weren’t allowed to be overdrawn. So these classical laws would have ruled out any possibility of time travel. However, as has been described in earlier chapters, the classical laws were superseded by quantum laws based on the uncertainty principle. The quantum laws are more liberal and allow you to be overdrawn on one or two accounts provided the total balance is positive. In other words, quantum theory allows the energy density to be negative in some places, provided that this is made up for by positive energy densities in other places, so that the total energy remains positive. An example of how quantum theory can allow negative energy densities is provided by what is called the Casimir effect. As we saw in
Chapter 7
, even what we think of as “empty” space is filled with pairs of virtual particles and antiparticles that appear together, move apart, and come back together and annihilate each other. Now, suppose one has two parallel metal plates a short distance apart. The plates will
act like mirrors for the virtual photons or particles 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 space between the plates only if their wavelengths (the distance between the crest of one wave and the next) fit a whole number of times into the gap between the plates. If the width of a cavity is a whole number of wavelengths plus a fraction of a wavelength, then after some reflections backward and forward between the plates, the crests of one wave will coincide with the troughs of another and the waves will cancel out.

Because the virtual photons between the plates can have only the resonant wavelengths, there will be slightly fewer of them than in the region outside the plates where virtual photons can have any wavelength. Thus there will be slightly fewer virtual photons hitting the inside surfaces of the plates than the outside surfaces. One would therefore expect a force on the plates, pushing them toward each other. This force has actually been detected and has the predicted value. Thus we have experimental evidence that virtual particles exist and have real effects.

The fact that there are fewer virtual photons between the plates means that their energy density will be less than elsewhere. But the total energy density in “empty” space far away from the plates must be zero, because otherwise the energy density would warp the space and it would not be almost flat. So, if the energy density between the plates is less than the energy density far away, it must be negative.

We thus have experimental evidence both that space-time can be warped (from the bending of light during eclipses) and that it can be curved in the way necessary to allow time travel (from the Casimir effect). One might hope therefore that as we advance in science and technology, we would eventually manage to build a time machine. But if so, why hasn’t anyone come back from the future and told us how to do it? There might be good reasons why it would be unwise to give us the secret of time travel at our present primitive state of development,
but unless human nature changes radically, it is difficult to believe that some visitor from the future wouldn’t spill the beans. Of course, some people would claim that sightings of UFOs are evidence that we are being visited either by aliens or by people from the future. (If the aliens were to get here in reasonable time, they would need faster-than-light travel, so the two possibilities may be equivalent.)

However, I think that any visit by aliens or people from the future would be much more obvious and, probably, much more unpleasant. If they are going to reveal themselves at all, why do so only to those who are not regarded as reliable witnesses? 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 the future would be to say that the past is fixed because we have observed it and seen that it does not have the kind of warping needed to allow travel back from the future. On the other hand, the future is unknown and open, so it might well have the curvature required. This would mean that any time travel would be confined to the future. There would be no chance of Captain Kirk and the Starship
Enterprise
turning up at the present time.

This might explain why we have not yet been overrun by tourists from the future, but it would not avoid the problems that would arise if one were able to go back and change history. Suppose, for example, you went back and killed your great-great-grandfather while he was still a child. There are many versions of this paradox but they are essentially equivalent: one would get contradictions if one were free to change the past.

There seem to be two possible resolutions to the paradoxes posed by time travel. One I shall call the consistent histories approach. It says that even if space-time is warped so that it would be possible to travel into the past, what happens in space-time must be a consistent solution of the laws of physics. According to this viewpoint, you could not go back in time unless history showed that you had already arrived in the past and, while there, had not killed your great-great-grandfather or
committed any other acts that would conflict with your current situation in the present. Moreover, when you did go back, you wouldn’t be able to change recorded history. That means you wouldn’t have free will to do what you wanted. Of course, one could say that free will is an illusion anyway. If there really is a complete unified theory that governs everything, it presumably also determines your actions. But it does so in a way that is impossible to calculate for an organism that is as complicated as a human being. The reason we say that humans have free will is because we can’t predict what they will do. However, if the human then goes off in a rocket ship and comes back before he or she set off, we
will
be able to predict what he or she will do because it will be part of recorded history. Thus, in that situation, the time traveler would have no free will.

The other possible way to resolve the paradoxes of time travel might be called the alternative histories hypothesis. The idea here is that when time travelers go back to the past, they enter alternative histories which differ from recorded history. Thus they can act freely, without the constraint of consistency with their previous history. Steven Spielberg had fun with this notion in the
Back to the Future
films: Marty McFly was able to go back and change his parents’ courtship to a more satisfactory history.

The alternative histories hypothesis sounds rather like Richard Feynman’s way of expressing quantum theory as a sum over histories, which was described in
Chapters 4
and
8
. This said that the universe didn’t just have a single history: rather it had every possible history, each with its own probability. However, there seems to be an important difference between Feynman’s proposal and alternative histories. In Feynman’s sum, each history comprises a complete space-time and everything in it. The space-time may be so warped that it is possible to travel in a rocket into the past. But the rocket would remain in the same space-time and therefore the same history, which would have to be consistent. Thus Feynman’s sum over histories proposal seems to support the consistent histories hypothesis rather than the alternative histories.

The Feynman sum over histories
does
allow travel into the past on a microscopic scale. In
Chapter 9
we saw that the laws of science are unchanged by combinations of the operations C, P, and T. This means that an antiparticle spinning in the anticlockwise direction and moving from A to B can also be viewed as an ordinary particle spinning clockwise and moving backward in time from B to A. Similarly, an ordinary particle moving forward in time is equivalent to an antiparticle moving backward in time. As has been discussed in this chapter and
Chapter 7
, “empty” space is filled with pairs of virtual particles and antiparticles that appear together, move apart, and then come back together and annihilate each other.

So, one can regard the pair of particles as a single particle moving on a closed loop in space-time. When the pair is moving forward in time (from the event at which it appears to that at which it annihilates), it is called a particle. But when the particle is traveling back in time (from the event at which the pair annihilates to that at which it appears), it is said to be an antiparticle traveling forward in time.

The explanation of how black holes can emit particles and radiation (given in
Chapter 7
) was that one member of a virtual particle/antiparticle pair (say, the antiparticle) might fall into the black hole, leaving the other member without a partner with which to annihilate. The forsaken particle might fall into the hole as well, but it might also escape from the vicinity of the black hole. If so, to an observer at a distance it would appear to be a particle emitted by the black hole.

One can, however, have a different but equivalent intuitive picture of the mechanism for emission from black holes. One can regard the member of the virtual pair that fell into the black hole (say, the antiparticle) as a particle traveling backward in time out of the hole. When it gets to the point at which the virtual particle/antiparticle pair appeared together, it is scattered by the gravitational field into a particle traveling forward in time and escaping from the black hole. If, instead, it were the particle member of the virtual pair that fell into the hole, one could regard it as an antiparticle traveling back in time and coming
out of the black hole. Thus the radiation by black holes shows that quantum theory allows travel back in time on a microscopic scale and that such time travel can produce observable effects.

One can therefore ask: does quantum theory allow time travel on a macroscopic scale, which people could use? At first sight, it seems it should. The Feynman sum over histories proposal is supposed to be over
all
histories. Thus it should include histories in which space-time is so warped that it is possible to travel into the past. Why then aren’t we in trouble with history? Suppose, for example, someone had gone back and given the Nazis the secret of the atom bomb?

One would avoid these problems if what I call the chronology protection conjecture holds. This says that the laws of physics conspire to prevent
macroscopic
bodies from carrying information into the past. Like the cosmic censorship conjecture, it has not been proved but there are reasons to believe it is true.

The reason to believe that chronology protection operates is that when space-time is warped enough to make travel into the past possible, virtual particles moving on closed loops in space-time can become real particles traveling forward in time at or below the speed of light. As these particles can go round the loop any number of times, they pass each point on their route many times. Thus their energy is counted over and over again and the energy density will become very large. This could give space-time a positive curvature that would not allow travel into the past. It is not yet clear whether these particles would cause positive or negative curvature or whether the curvature produced by some kinds of virtual particles might cancel that produced by other kinds. Thus the possibility of time travel remains open. But I’m not going to bet on it. My opponent might have the unfair advantage of knowing the future.

A
s was explained in the first chapter, it would be very difficult to construct a complete unified theory of everything in the universe all at one go. So instead we have made progress by finding partial theories that describe a limited range of happenings and by neglecting other effects or approximating them by certain numbers. (Chemistry, for example, allows us to calculate the interactions of atoms, without knowing the internal structure of an atom’s nucleus.) Ultimately, however, one would hope to find a complete, consistent, unified theory that would include all these partial theories as approximations, and that did not need to be adjusted to fit the facts by picking the values of certain arbitrary numbers in the theory. The quest for such a theory is known as “the unification of physics.” Einstein spent most of his later years unsuccessfully searching for a unified theory, but the time was not ripe: there were partial theories for gravity and the electromagnetic force, but very little was known about the nuclear forces. Moreover, Einstein refused to believe in the reality of quantum mechanics, despite the important role he had played in its development. Yet it seems that
the uncertainty principle is a fundamental feature of the universe we live in. A successful unified theory must, therefore, necessarily incorporate this principle.

As I shall describe, the prospects for finding such a theory seem to be much better now because we know so much more about the universe. But we must beware of overconfidence—we have had false dawns before! At the beginning of this century, for example, it was thought that everything could be explained in terms of the properties of continuous matter, such as elasticity and heat conduction. The discovery of atomic structure and the uncertainty principle put an emphatic end to that. Then again, in 1928, physicist and Nobel Prize winner Max Born told a group of visitors to Göttingen University, “Physics, as we know it, will be over in six months.” His confidence was based on the recent discovery by Dirac of the equation that governed the electron. It was thought that a similar equation would govern the proton, which was the only other particle known at the time, and that would be the end of theoretical physics. However, the discovery of the neutron and of nuclear forces knocked that one on the head too. Having said this, I still believe there are grounds for cautious optimism that we may now be near the end of the search for the ultimate laws of nature.

In previous chapters I have described general relativity, the partial theory of gravity, and the partial theories that govern the weak, the strong, and the electromagnetic forces. The last three may be combined in so-called grand unified theories, or GUTs, which are not very satisfactory because they do not include gravity and because they contain a number of quantities, like the relative masses of different particles, that cannot be predicted from the theory but have to be chosen to fit observations. The main difficulty in finding a theory that unifies gravity with the other forces is that general relativity is a “classical” theory; that is, it does not incorporate the uncertainty principle of quantum mechanics. On the other hand, the other partial theories depend on quantum mechanics in an essential way. A necessary first step, therefore, is to combine general relativity with the
uncertainty principle. As we have seen, this can produce some remarkable consequences, such as black holes not being black, and the universe not having any singularities but being completely self-contained and without a boundary. The trouble is, as explained in
Chapter 7
, that the uncertainty principle means that even “empty” space is filled with pairs of virtual particles and antiparticles. These pairs would have an infinite amount of energy and, therefore, by Einstein’s famous equation
E = mc
²
, they would have an infinite amount of mass. Their gravitational attraction would thus curve up the universe to infinitely small size.