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
wave-length, 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 Spiel-berg 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.
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PREVIOUS NEXT
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CHAPTER 11
THE UNIFICATION OF PHYSICS
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As 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 Gottingen 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
