Parallel Worlds (21 page)

Last, it turns
out that a black hole also has negative energy, near its event horizon. As
shown by Jacob Bekenstein and Stephen Hawking, a black hole is not perfectly
black because it slowly evaporates energy. This is because the uncertainty
principle makes possible the tunneling of radiation past the enormous gravity
of a black hole. But because an evaporating black hole loses energy, the event
horizon gradually gets smaller with time. Usually, if positive matter (like a
star) is thrown into a black hole, the event horizon expands. But if we throw
negative matter into the black hole, its event horizon will contract. Thus,
black hole evaporation creates negative energy near the event horizon. (Some
have advocated putting the mouth of the wormhole next to the event horizon in
order to harvest negative energy. However, harvesting such negative energy
would be extraordinarily difficult and dangerous, since you would have to be
extremely close to the event horizon.)

Hawking has
shown that in general negative energy is required to stabilize all wormhole
solutions. The reasoning is quite simple. Usually, positive energy can create
an opening of a wormhole that concentrates matter and energy. Thus, light rays
converge as they enter the mouth of the wormhole. However, if these light rays
emerge from the other side, then somewhere in the center of the wormhole light
rays should defocus. The only way this can happen is if negative energy is
present. Furthermore, negative energy is repulsive, which is required to keep
the wormhole from collapsing under gravity. So the key to building a time
machine or wormhole may be to find sufficient amounts of negative energy to
keep the mouth open and stable. (A number of physicists have shown that, in the
presence of large gravitational fields, negative energy fields are rather
common. So perhaps one day gravitational negative energy may be used to drive a
time machine.)

Another obstacle
facing such a time machine is: where do we find a wormhole? Thorne relied upon
the fact that wormholes occur naturally, in what is called the space-time
foam. This goes back to a question asked by the Greek philosopher Zeno over two
thousand years ago: what is the smallest distance one can travel?

Zeno once proved
mathematically that it was impossible to cross a river. He first observed that
the distance across a river can be subdivided into an infinite number of
points. But since it took an infinite amount of time to move across an
infinite number of points, it was therefore impossible to cross the river. Or,
for that matter, it was impossible for anything to move at all. (It would take
another two thousand years, and the coming of calculus, to finally resolve this
puzzle. It can be shown that an infinite number of points can be crossed in a
finite amount of time, making motion mathematically possible after all.)

John Wheeler of
Princeton analyzed Einstein's equations to find the smallest distance. Wheeler found
that at incredibly small distances, on the order of the Planck length (10
^-33
cm), Einstein's theory predicted that the curvature of space could be quite
large. In other words, at the Planck length, space was not smooth at all but
had large curvature—that is, it was kinky and "foamy." Space becomes
lumpy and actually froths with tiny bubbles that dart in and out of the vacuum.
Even empty space, at the tiniest distances, is constantly boiling with tiny
bubbles of space-time, which are actually tiny wormholes and baby universes.
Normally, "virtual particles" consist of electron and antielectron
pairs that pop into existence momentarily before annihilating each other. But
at the Planck distance, tiny bubbles representing entire universes and
wormholes may spring into existence, only to vanish back into the vacuum. Our
own universe may have started as one of these tiny bubbles floating in the
space-time foam that suddenly inflated, for reasons we don't understand.

Since wormholes
are found naturally in the foam, Thorne assumed that an advanced civilization
could somehow pick wormholes out of the foam and then expand and stabilize them
with negative energy. Although this would be a very difficult process, it is
within the realm of the laws of physics.

While Thorne's
time machine seems theoretically possible, although exceedingly difficult to
build from an engineering viewpoint, there is a third nagging question: does
time travel violate a fundamental law of physics?

A UNIVERSE IN
YOUR BEDROOM

In 1992, Stephen
Hawking tried to resolve this question about time travel once and for all.
Instinctively, he was against time travel; if journeys through time were as
common as Sunday picnics, then we should see tourists from the future gawking
at us and taking pictures.

But physicists
often quote from T. H. White's epic novel
The Once and Future King,
where a society of ants declares, "Everything not forbidden
is compulsory." In other words, if there isn't a basic principle of
physics forbidding time travel, then time travel is necessarily a physical
possibility. (The reason for this is the uncertainty principle. Unless
something is forbidden, quantum effects and fluctuations will eventually make
it possible if we wait long enough. Thus, unless there is a law forbidding it,
it will eventually occur.) In response, Stephen Hawking proposed a
"chronology protection hypothesis" that would prevent time travel
and hence "make history safe for historians." According to this
hypothesis, time travel is not possible because it violates specific physical
principles.

Since wormhole
solutions are extremely difficult to work with, Hawking began his argument by
analyzing a simplified universe discovered by Charles Misner of the University
of Maryland which had all the ingredients of time travel. Misner space is an
idealized space in which your bedroom, for example, becomes the entire
universe. Let's say that every point on the left wall of your bedroom is identical
to the corresponding point on the right wall. This means that if you walk
toward the left wall, you will not get a bloody nose, but will instead walk
through the wall and reappear from the right wall. This means that the left and
right wall are joined, in some sense, as in a cylinder.

In addition, the
points on the front wall are identical to the points on the back wall, and the
points on the ceiling are identical to the points on the floor. Thus, if you
walk in any direction, you pass right through your bedroom walls and return
back again to your bedroom. You cannot escape. In other words, your bedroom
truly is the entire universe!

In a Misner space, the entire universe is contained in your
bedroom. The opposite walls are all identified with each other, so entering
one wall you immediately emerge from the opposite wall. The ceiling is
likewise identified with the floor. Misner space is often studied because it
has the same topology as a wormhole but is much simpler to handle
mathematically. If the walls move, then time travel might be possible within the
Misner universe.

What is really
bizarre is that, if you look carefully at the left wall, you see that it is
actually transparent and there is a carbon copy of your bedroom on the other
side of this wall. In fact, there is an exact clone of yourself standing in the
other bedroom, although you can only see your back side, never your front side.
If you look below or above, you also see carbon copies of yourself. In fact,
there is an infinite sequence of yourselves standing in front, behind, below,
and above you.

Making contact
with yourself is quite difficult. Every time you turn your head to catch a
glimpse of the clones' faces, you find that they have also turned away, so you
never see their faces. But if the bedroom is small enough, you might pass your
hand through the wall and grab the shoulder of the clone in front of you. Then
you might be shocked to find that the clone behind you has reached out and
grabbed your shoulder as well. Also, you can reach out with your left and right
hands, grabbing hold of the clones to your side, until there is an infinite
sequence of yourselves holding hands. In effect, you have reached completely
around the universe to grab ahold of yourself. (It is not advisable to harm
your clones. If you take a gun and point it at the clone in front of you, you
might reconsider pulling the trigger, because the clone behind you is pointing
a gun at you as well!)

In Misner space,
assume that the walls are collapsing around you. Now things become very
interesting. Let's say the bedroom is being squeezed, with the right wall
slowly coming toward you at 2 miles per hour. If you now walk through the left
wall, you will return back from the moving right wall, but boosted by an
additional 2 miles per hour, so you are now traveling at 4 miles per hour. In
fact, each time you make a complete circuit into the left wall, you get an
additional boost of 2 miles per hour emerging from the right wall, so you are
now traveling at 6 miles per hour. After repeated trips around the universe,
you travel 6, 8, 10 miles per hour, until you gradually approach incredible
velocities close to the speed of light.

At a certain
critical point, you are traveling so fast in this Misner universe that you
travel back in time. In fact, you can visit any previous point in space-time.
Hawking analyzed this Misner space carefully. He found that the left wall and
right wall, mathematically speaking, are almost identical to the two mouths of
a wormhole. In other words, your bedroom resembles a wormhole, where the left
wall and the right wall are the same, similar to the two mouths of a wormhole,
which are also identical.

Then he pointed
out that this Misner space was unstable both classically and quantum
mechanically. If you shine a flashlight at the left wall, for example, the light
beam gains energy every time it emerges from the right wall. The light beam
becomes blue-shifted— that is, it becomes more energetic, until it reaches
infinite energy, which is impossible. Or, the light beam becomes so energetic
that it creates a monstrous gravitational field of its own which collapses the
bedroom/wormhole. Thus, the wormhole collapses if you try to walk through it.
Also, one can show that something called the energy- momentum tensor, which
measures the energy and matter content of space, becomes infinite because
radiation can pass an infinite number of times through the two walls.

To Hawking, this
was the coup de grace for time travel—quantum radiation effects built up until
they became infinite, creating a divergence, killing the time traveler and
closing the wormhole.

Since Hawking's
paper, the divergence question he raised has generated a lively discussion in
the physics literature, with scientists taking both pro and con positions with
regard to chronology protection. In fact, several physicists began to find
loopholes in Hawking's proof by making suitable choices for wormholes, by
changing their size, length, and so on. They found that in some wormhole
solutions, the energy-momentum tensor did, in fact, diverge, but in others it
was well defined. Russian physicist Sergei Krasnikov examined this divergence
question for different types of wormholes and concluded that "there is not
a grain of evidence to suggest that the time machine must be unstable."

The tide has
swung so far in the other direction against Hawking that Princeton physicist
Li-Xin Li even proposed an
anti
chronology protection conjecture: "There is no law of
physics preventing the appearance of closed timelike curves."

In 1998, Hawking
was forced to make a retreat of sorts. He wrote, "The fact that the
energy-momentum tensor fails to diverge [in certain cases] shows that the back
reaction does not enforce chronology protection." This does not mean that
time travel is possible, only that our understanding is still incomplete.
Physicist Matthew Visser sees the failure of Hawking's conjecture is "not
as a vindication for time travel enthusiasts, but rather as an indication that
resolving issues of chronology protection requires a fully developed theory of
quantum gravity."

Today, Hawking
no longer says that time travel is absolutely impossible, only that it is
highly unlikely and impractical. The odds are overwhelmingly against time
travel. But one cannot rule it out entirely. If one can somehow harness large
quantities of positive and negative energy and solve the stability problem,
time travel may indeed be possible. (And perhaps the reason we are not flooded
by tourists from the future is that the earliest time they can go back to is
when the time machine was created, and perhaps time machines haven't been
created yet.)

GOTT TIME MACHINE

In 1991, J.
Richard Gott III of Princeton proposed yet another solution to Einstein's
equations which allowed for time travel. His approach was interesting because
he started from an entirely fresh approach, abandoning spinning objects,
wormholes, and negative energy entirely.

Gott was born in
Louisville, Kentucky, in 1947, and he still speaks in a gentle southern accent
that seems a bit exotic in the rarefied, rough-and-tumble world of theoretical
physics. He got his start in science as a child when he joined an amateur
astronomy club and enjoyed stargazing.

While in high
school, he won the prestigious Westinghouse Science Talent Search contest and
has been associated with that contest ever since, acting as chairman of the
judges for many years. After graduating from Harvard in mathematics, he went to
Princeton, where he still works.