The Physics of Star Trek (7 page)

Because the bottom mouth of the wormhole will be moving with respect to the space in which
it is situated, while the top mouth will not, special relativity tells us that clocks will
tick at different rates at each mouth. On the other hand, if the length of the wormhole
remains fixed, then as long as one is inside the wormhole the two ends appear to be at
rest relative to each other. In this frame, clocks at either end should be ticking at the
same rate. Now slide the bottom sheet back to where it used to be, so that the bottom
mouth of the wormhole ends up back where it started relative to the background space.
Let's say that this process takes a day, as observed by someone near the bottom mouth. But
for an observer near the top mouth, this same process could appear to have taken ten days.
If this second observer were to peer through the top mouth to look at the observer located
near the bottom mouth, he would see on the wall calendar next to the observer a date nine
days earlier! If he now decides to go through the worm-hole for a visit, he will travel
backward in time.

If stable wormholes exist, we must therefore concede that time machines are possible. We
now return finally to Einstein's remarks early in the last chapter. Can time travel, and
thus stable wormholes, and thus exotic matter with negative energy, be “excluded on
physical grounds”?

Wormholes are after all merely one example of time machines that have been proposed in the
context of general relativity. Given our previous discussion about the nature of the
theory, it is perhaps not so surprising that time travel becomes a possibility. Let's
recall the heuristic description of Einstein's equations which I gave earlier:

The left-hand side of this equation fixes the geometry of spacetime. The right-hand side
fixes the matter and energy distribution. Generally we would ask: For a given distribution
of matter and energy, what will be the resulting curvature of space? But we can also work
backward: For any given geometry of space, including one with “closed timelike curves”that
is, the “causality loops,” which allow you to return to where you began in space and time,
like the loop the
Enterprise
was caught in before, during, and after crashing into the
Boze-man
Einstein's equations tell you exactly what distribution of matter and energy must be
present. So in principle you can design any kind of time-travel universe you want;
Einstein's equations will tell you what matter and energy distribution is necessary. The
key question then simply becomes: Is such a matter and energy distribution physically
possible?

We have already seen how this question arises in the context of wormholes. Stable
wormholes require exotic matter with negative energy. Kurt Gšdel's time-machine solution
in genera! relativity involves a universe with constant uniform energy density and zero
pressure which spins but does not expand. More recently, a proposed time machine involving
“cosmic strings” was shown to require a negative-energy configuration. In fact, it was
recently proved that any configuration of matter in general relativity which might allow
time travel must involve

exotic types of matter with negative energy as viewed by at least one observer.

It is interesting that almost all the episodes in Star Trek involving time travel or
temporal distortions also involve some catastrophic form of energy release, usually
associated with a warp core breach. For example, the temporal causality loop in which the
Enterprise
was trapped resulted only after (although the concepts of “before” and “after” lose their
meaning in a causality loop) a collision with the
Bozeman,
which caused the warp core to breach and thereby caused the destruction of the
Enterprise,
a series of events that kept repeating over and over, until finally in one cycle the crew
managed to avoid the collision. The momentary freezing of time aboard the
Enterprise,
discovered by Picard, Data, Troi, and LaForge in the episode “Timescape,” also appears to
have been produced by a nascent warp core breach combined with a failure of the engine
core aboard a nearby Romulan vessel. In “Time Squared,” a vast “energy vortex” propelled
Picard back in time. In the original example of Star Trek time travel, “The Naked Time,”
the
Enterprise
was thrown back three days following a warp core implosion. And the mammoth spacetime
distortion in the final episode of
The Next Generation,
which travels backward in time and threatens to engulf the entire universe, was caused by
the simultaneous explosion of three different temporal versions of the
Enterprise,
which converged at the same point in space.

So, time travel in the real universe, as in the Star Trek universe, seems to hinge on the
possibility of exotic configurations of matter. Could some sufficiently advanced alien
civilization construct a stable wormhole? Or can we characterize
all
mass distributions that might lead to time travel and then exclude them, as a set, “on
physical grounds,” as Einstein might have wished? To date, we do not know the answer. Some
specific time machines such as Gšdel's, and the cosmic-string-based systemhave been shown
to be unphysical. While wormhole time travel has yet to be definitively ruled out,
preliminary investigations suggest that the quantum gravitational fluctuations themselves
may cause wormholes to self-destruct before they could lead to time travel.

Until we have a theory of quantum gravity, the final resolution of the issue of time
travel is likely to remain unresolved. Nevertheless, several brave individuals, including
Stephen Hawking, have already tipped their hand. Hawking is convinced that time machines
are impossible, because of the obvious paradoxes that might result, and he has proposed a
“chronology-protection conjecture,” to wit: “The laws of physics do not allow the
appearance of closed timelike curves.”

I am personally inclined to agree with Hawking in this case. Nevertheless, physics is not
done by fiat. As I have stated earlier, general relativity often outwits our naive
expectations. As a warning, I provide two historical precedents. Twice before (that I know
of), eminent theorists have argued that a proposed phenomenon in general relativity should
be dismissed because the laws of physics must forbid it:

1. When the young astrophysicist Subrahmanyan Chandrasekhar proposed that stellar cores
more massive than 1.4 times the mass of the Sun cannot, after burning all their nuclear
fuel, settle down as white dwarfs but must continue to collapse due to gravity, the
eminent physicist Sir Arthur Eddington dismissed the result in public, stating, “Various
accidents may intervene to save the star, but I want more protection than that. I think
there should be a law of nature to prevent a star from behaving in this absurd way!” At
the time, much of the astrophysics community sided with Eddington. A half century later,
Chandrasekhar shared the Nobel Prize for his insights, which have long since been verified.

2. Slightly over 20 years after Eddington dismissed Chan-drasekhar's claim, a remarkably
similar event ocurred at a conference in Brussels. J. Robert Oppenheimer, the
distinguished American theoretical physicist and father of the atomic bomb, had calculated
that objects called neutron starsleft over after supernovae and even more dense than white
dwarfscould not be larger than about twice the mass of the Sun without collapsing further
to form what we would now call a black hole. The equally distinguished John Archibald
Wheeler argued that this result was impossible, for precisely the reason Eddington had
given for his earlier rejection of Chandrasekhar's claim: somehow the laws of physics must
protect objects from such an absurd fate. Within a decade, Wheeler would completely
capitulate and, ironically, would become known as the man who gave black holes their name.

DATA

Ends the Game
For I dipt into the future, far as human eye could see, Saw the Vision of the world, and
all the wonder that would

be.
From “Locksley Hall, ” by Alfred Lord Tennyson (posted aboard the starship
Voyager,)

Whether or not the Star Trek future can include a stable worm-hole, and whether or not the
Enterprise
crew could travel back in time to nineteenth-century San Francisco, the real stakes in
this cosmic poker game derive from one of the questions that led us to discuss curved
spacetime in the first place: Is warp drive possible? For, barring the unlikely
possibility that our galaxy is riddled with stable wormholes, it is abundantly clear from
our earlier discussions that without something like it, most of the galaxy will always
remain beyond our reach. It is finally time to address this vexing question. The answer is
a resounding “Maybe!”

Once again we are guided by the linguistic perspicacity of the Star Trek writers. I have
described how no rocket

propulsion mechanism can ever get around the three roadblocks to interstellar travel set
up by special relativity: First, nothing can travel faster than the speed of light in
empty space. Second, objects that travel near the speed of light will have clocks that are
slowed down. Third, even if a rocket could accelerate a spacecraft to near the speed of
light, the fuel requirements would be prohibitive.

The idea is not to use any sort of rocket at all for propulsion, but instead to use
spacetime itselfby warping it. General relativity requires us to be a little more precise
in our statements about motion. Instead of saying that nothing can travel faster than the
speed of light, we must state that nothing can travel
locally
any faster than the speed of light. This means that nothing can travel faster than the
speed of light
with respect to local distance markers.
However, if spacetime is curved, local distance markers need not be global ones.

Let me use the universe itself as an example. Special relativity tells me that all
observers who are at rest with respect to their local surroundings will have clocks that
tick at the same rate. Thus, as I move throughout the universe, I can periodically stop
and place clocks at regular intervals in space and expect that they will all keep the same
time. General relativity does not change this result. Clocks that are locally at rest will
all keep the same time. However, general relativity allows spacetime itself to expand.
Objects on opposite sides of the observable universe are flying apart at almost the speed
of light, yet they remain at rest relative to their local surroundings. In fact, if the
universe is expanding uniformly and if it is large enoughboth of which appear to be the
casethere exist objects we cannot yet see which are at this very moment moving away from
us far faster than the speed of light, even though any civilizations in these far reaches
of the universe can be locally at rest with respect to their surroundings.

The curvature of space therefore produces a loophole in special relativistic argumentsa
loophole large enough to drive a Federation starship through. If spacetime itself can be
manipulated, objects can travel locally at very slow velocities, yet an accompanying
expansion or contraction of space could allow huge distances to be traversed in short time
intervals. We have already seen how an extreme manipulationnamely, cutting and pasting
distant parts of the universe together with a wormholemight create shortcuts through
space-time. What is argued here is that even if we do not resort to this surgery,
faster-than-light travel might globally be possible, even if it is not locally possible.

A proof in principle of this idea was recently developed by a physicist in Wales, Miguel
Alcubierre, who for fun decided to explore whether a consistent solution in general
relativity could be derived which would correspond to “warp travel.” He was able to
demonstrate that it was possible to tailor a spacetime configuration wherein a spacecraft
could travel between two points in an arbitrarily short time. Moreover, throughout the
journey the spacecraft could be moving with respect to its local surroundings at speeds
much less than the speed of light, so that clocks aboard the spacecraft would remain
synchronized with those at its place of origin and at its destination. General relativity
appears to allow us to have our cake and eat it too.

The idea is straightforward. If spacetime can locally be warped so that it expands behind
a starship and contracts in front of it, then the craft will be propelled along with the
space it is in, like a surfboard on a wave. The craft will never travel locally faster
than the speed of light, because the light, too, will be carried along with the expanding
wave of space.

One way to picture what is happening is to imagine yourself on the starship. If space
suddenly expands behind you by a huge amount, you will find that the starbase you just
left a few minutes ago is now many light-years away. Similarly, if space contracts in
front of you, you will find that the starbase you are heading for, which formerly was a
few light-years away, is now close to you, within reach by normal rocket propulsion in a
matter of minutes.

It is also possible to arrange the geometry of spacetime in this solution so that the huge
gravitational fields necessary to expand and contract space in this way are never large
near the ship or any of the star-bases. In the vicinity of the ship and the bases, space
can be almost flat, and therefore clocks on the ship and the starbases remain
synchronized. Somewhere in between the ship and the bases, the tidal forces due to gravity
will be immense, but that's OK as long as we aren't located there.

This scenario must be what the Star Trek writers intended when they invented warp drive,
even if it bears little resemblance to the technical descriptions they have provided. It
fulfills all the requirements we listed earlier for successful controlled intergalactic
space travel: (1) faster-than-light travel, (2) no time dilation, and (3) no resort to
rocket propulsion. Of course, we have begged a pretty big question thus far. By making
spacetime itself dynamical, general relativity allows the creation of “designer
spacetimes,” in which almost any type of motion in space and time is possible. However,
the cost is that the theory relates these spacetimes to some underlying distribution of
matter and energy. Thus, for the desired spacetime to be “physical,” the underlying
distribution of matter and energy must be attainable. I will return to this question
shortly.