Page 79 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 10
the Congress on Alpha Centauri back to earth before the start of the race. So wormholes, like any other
possible form of travel faster than light, would allow one to travel into the past.

The idea of wormholes between different regions of space-time was not an invention of science fiction writers
but came from a very respectable source.

In 1935, Einstein and Nathan Rosen wrote a paper in which they showed that general relativity allowed what
they called “bridges,” but which are now known as wormholes. The Einstein-Rosen bridges didn’t last long
enough for a spaceship to get through: the ship would run into a singularity as the wormhole pinched off.
However, it has been suggested that it might be possible for an advanced civilization to keep a wormhole open.
To do this, or to warp space-time in any other way so as to permit time travel, one can show that one needs a
region of space-time with negative curvature, like the surface of a saddle. Ordi-nary matter, which has a
positive energy density, gives space-time a positive curvature, like the surface of a sphere. So what one needs,
in order to warp space-time in a way that will allow travel into the past, is matter 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
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earlier chapters, the classical laws were superseded by quantum laws based on the uncertainty principle.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 re-mains
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
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

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