The Physics of Star Trek (6 page)

Not even a diehard trekker might be willing to suspend disbelief long enough to accept the
idea of matter with “negative energy”; however, as noted, in curved space one's normal
expectations are often suspect. When you compound this with the exotica forced upon us by
the laws of quantum mechanics, which govern the behavior of matter on small scales, quite
literally almost all bets are off.

BLACK HOLES AND DR. HAWKING: Enter Stephen Hawking. He first became well known among
physicists

working on general relativity for his part in proving general theorems related to
singularities in spacetime, and then, in the 1970s, for his remarkable theoretical
discoveries about the behavior of black holes. These objects are formed from material that
has collapsed so utterly that the local gravitational field at their surface prevents even
light from escaping.

Incidentally, the term “black hole,” which has so captivated the popular imagination, was
coined by the theoretical physicist John Archibald Wheeler of Princeton University, in the
late fall of 1967. The date here is very interesting, because, as far as I can determine,
the first Star Trek episode to refer to a black hole, which it called a “black star,” was
aired in 1967 before Wheeler ever used the term in public. When I watched this episode
early in the preparation of this book, I found it amusing that the Star Trek writers had
gotten the name wrong. Now I realize that they very nearly invented it!

Black holes are remarkable objects for a variety of reasons. First, all black holes
eventually hide a spacetime singularity at their center, and anything that falls into the
black hole must inevitably encounter it. At such a singularityan infinitely curved “cusp”
in spacetimethe laws of physics as we know them break down. The curvature near the
singularity is so large over such a small region that the effects of gravity are governed
by the laws of quantum mechanics. Yet no one has yet been able to write down a theory that
consistently accommodates both general relativity (that is, gravity) and quantum
mechanics. Star Trek writers correctly recognized this tension between quantum mechanics
and gravity, as they usually refer to all spacetime singularities as “quantum
singularities.” One thing is certain, however: by the time the gravitational field at the
center of a black hole reaches a strength large enough for our present picture of physics
to break down, any ordinary physical object will be torn apart beyond recognition. Nothing
could survive intact.

You may notice that I referred to a black hole as “hiding” a singularity at its center.
The reason is that at the outskirts of a black hole is a mathematically defined surface we
call the “event horizon,” which shields our view of what happens to objects that fall into
the hole. Inside the event horizon, everything must eventually hit the ominous
singularity. Outside the event horizon, objects can escape. While an observer unlucky
enough to fall into a black hole will notice nothing special at all as he or she (soon to
be “it”) crosses the event horizon, an observer watching the process from far away sees
something very different. Time slows down for the observer freely falling in the vicinity
of the event horizon, relative to an observer located far away. As a result, the falling
observer appears from the outside to slow down as he or she nears the event horizon. The
closer the falling observer gets to the event horizon, the slower is his or her clock
relative to the outside observer's. While it may take the falling observer a few moments
(local time) to cross the event horizonwhere, I repeat, nothing special happens and
nothing special sitsit will take an eternity as observed by someone on the outside. The
infalling object appears to become frozen in time.

Moreover, the light emitted by any infalling object gets harder and harder to see from the
outside. As an object approaches the event horizon, the object gets dimmer and dimmer
(because the observable radiation from it gets shifted to frequencies below the visible).
Finally, even if you could see, from the outside, the object's transit of the event
horizon (which you cannot, in any finite amount of time), the object would disappear
completely once it passed the horizon, because any light it emitted would be trapped
inside, along with the object. Whatever falls inside the event horizon is lost forever to
the outside world. It appears that this lack of communication is a one- way street: an
observer on the outside can send signals
into
the black hole, but no signal can ever be returned.

For these reasons, the black holes encountered in Star Trek tend to produce impossible
results. The fact that the event horizon is not a tangible object, but rather a
mathematical marker that we impose on our description of a black hole to delineate the
region inside from that outside, means that the horizon cannot have a “crack,” as required
by the crew of the
Voyager
when they miraculously escape from a black hole's interior. (Indeed, this notion is so
absurd that it makes it onto my ten-best list of Star Trek mistakes described in the last
chapter.) And the “quantum singularity life-forms” encountered by the crew of the
Enterprise
as they, and a nearby Romulan Warbird, travel backward and forward in time have a rather
unfortunate nesting place for their young: apparently they place them inside natural black
holes (which they incorrectly mistake the “artificial” quantum singularity inside the
Romulan engine core for). This may be a safe nursery, but it must be difficult to retrieve
your children afterward. I remind you that nothing inside a black hole can ever
communicate with anything outside one.

Nevertheless, black holes, for all their interesting properties, need not be that exotic.
The only black holes we have any evidence for in the universe today result from the
collapse of stars much more massive than the Sun. These collapsed objects are so dense
that a teaspoon of material inside would weigh many tons. However, it is another
remarkable property of black holes that the more massive they are, the less dense they
need be when they form. For example, the density of the black hole formed by the collapse
of an object 100 million times as massive as our Sun need only be equal to the density of
water. An object of larger mass will collapse to form a black hole at a point when it is
even less dense. If you keep on extrapolating, you will find that the density required to
form a black hole with a mass equal to the mass of the observable universe would be
roughly the same as the average density of matter in the universe! We may be living inside
a black hole.

In 1974, Stephen Hawking made a remarkable discovery about the nature of black holes. They
aren't completely black! Instead, they will emit radiation at a characteristic
temperature, which depends on their mass. While the nature of this radiation will give no
information whatsoever on what fell into the black hole, the idea that radiation could be
emitted from a black hole was nevertheless astounding, and appeared to violate a number of
theoremssome of which Hawking had earlier provedholding that matter could only fall into
black holes, not out of them. This remains true, except for the source of the black-hole
radiation, which is not normal matter. Instead, it is empty space, which can behave quite
exoticallyespecially in the vicinity of a black hole.

Ever since the laws of quantum mechanics were made consistent with the special theory of
relativity, shortly after the Second World War, we have known that empty space is not so
empty. It is a boiling, bubbling sea of quantum fluctuations. These fluctuations
periodically spit out elementary particle pairs, which exist for time intervals so short
that we cannot measure them directly, and then disappear back into the vacuum from which
they came. The uncertainty principle of quantum mechanics tells us that there is no way to
directly probe empty space over such short time intervals and thus no way to preclude the
brief existence of these so-called virtual particles. But although they cannot be measured
directly, their presence does affect certain physical processes that we
can
measure, such as the rate and energy of transitions between certain energy levels in
atoms. The predicted effect

of virtual particles agrees with observations as well as any prediction known in physics.

This brings us back to Hawking's remarkable result about black holes. Under normal
circumstances, when a quantum fluctuation creates a virtual particle pair, the pair will
annihilate and disappear back into the vacuum in a time short enough so that the violation
of conservation of energy (incurred by the pair's creation from nothing) is not
observable. However, when a virtual particle pair pops out in the curved space near a
black hole, one of the particles may fall into the hole, and then the other can escape and
be observed. This is because the particle that falls into the black hole can in principle
lose more energy in the process than the amount required to create it from nothing. It
thus contributes “negative energy” to the black hole, and the black hole's own energy is
therefore decreased. This satisfies the energy-conservation law's balance-sheet, making up
for the energy that the escaping particle is observed to have. This is how the black hole
emits radiation. Moreover, as the black hole's own energy decreases bit by bit in this
process, there is a concomitant decrease in its mass. Eventually, it may completely
evaporate, leaving behind only the radiation it produced in its lifetime.

Hawking and many others have gone beyond a consideration of quantum fluctuations of matter
in a background curved space to something even more exotic and less well defined. If
quantum mechanics applies not merely to matter and radiation but to gravity as well, then
on sufficiently small scales quantum fluctuations in spacetime itself must occur.
Unfortunately, we have no workable theory for dealing with such processes, but this has
not stopped a host of tentative theoretical investigations of phenomena that might result.
One of the most interesting speculations is that quantum mechanical processes might allow
the spontaneous creation not just of particles but of whole new baby universes. The
quantum mechanical formalism describing how this might occur is, at least mathematically,
very similar to the wormhole solutions discovered in ordinary general relativity. Via such
“Euclidean” wormholes, a temporary “bridge” is created, from which a new universe springs.
The possibilities of Euclidean wormhole processes and baby universes are sufficiently
exciting that quantum fluctuations were mentioned during Hawking's poker game with
Einstein and Newton in the
Next Generation
episode “Descent.”
1
If the Star Trek writers were confused, they had a right to be. These issues are
unfortunately currently very murky. Until we discover the proper mathematical framework to
treat such quantum gravitational processes, all such discussions are shots in the dark.

What is most relevant to us here is not the phenomenon of black-hole evaporation, or even
baby universes, as interesting as they may be, but rather the discovery that quantum
fluctuations of empty space can, at least in the presence of strong gravitational fields,
become endowed with properties reminiscent of those required to hold open a worm-hole. The
central question, which also has no definitive answer yet, is whether quantum fluctuations
near a wormhole can behave sufficiently exotically to allow one to keep a wormhole open.

(By the way, once again, I find the Star Trek writers remarkably prescient in their choice
of nomenclature. The Bajoran and Barzan wormholes are said to involve “verteron” fields. I
have no idea whether this name was plucked out of a hat or not. However, since virtual
particlesthe quantum fluctuations in otherwise empty space are currently the best
candidate for Kip Thorne's “exotic matter,” I think the Star Trek writers deserve credit
for their intuition, if that's what it was.)

More generally, if quantum fluctuations in the vacuum can be exotic, is it possible that
some other nonclassical configuration of matter and radiationlike, say, a warp core
breach, or perhaps Scotty's “intermix” imbalance in the warp drivemight also fill the
bill? Questions such as this remain unanswered. While by no means circumventing the
incredible implausibility of stable wormholes in the real universe, they do leave open the
larger question of whether wormhole travel is impossible or merely almost impossible. The
wormhole issue is not just one of science fact versus science fiction: it is a key that
can open doors which many would prefer to leave closed.

TIME MACHINES REVISITED: Wormholes, as glorious as they would be for tunneling through
vast distances in space, have an even more remarkable potential, glimpsed most recently in
the
Voyager
episode “Eye of the Needle.” In this episode, the
Voyager
crew discovered a small wormhole leading back to their own “alpha quadrant” of the galaxy.
After communicating through it, they found to their horror that it led not to the alpha
quadrant they knew and loved but to the alpha quadrant of a generation earlier. The two
ends of the wormhole connected space at two different times!

Well, this is another one of those instances in which the
Voyager
writers got it right. If wormholes exist, they can

and will be time machines! This startling realization has grown over the last decade, as
various theorists, for lack of anything more interesting to do, began to investigate the
physics of wormholes a little more seriously. Worm- hole time machines are easy to design:
perhaps the simplest example (due again to Kip Thorne) is to imagine a wormhole with one
end fixed and the other end moving at a fast but sublight speed through a remote region of
the galaxy. In principle, this is possible
even if
the length of the wormhole remains unchanged. In my earlier two- dimensional wormhole
drawing, just drag the bottom half of the sheet to the left, letting space “slide” past
the bottom mouth of the wormhole while this mouth stays fixed relative to the wormhole's
other mouth: