Hiding in the Mirror (18 page)

All these applications of relativity to
hypothetical space travel, in fact, involve “sub–light-speed”
travel. Indeed, since special relativity suggests that travel at
the speed of light is an absolute limit, there appears to be no
room for anything else. However, the imaginations of writers and of
scientists have offered up hopeful alternatives, of varying degrees
of credibility. Almost all of these have been centered on the fact
that once one allows for space itself to be dynamic—curving,
expanding, or contracting in the presence of mass and
energy—faster-than-light travel may be feasible. For scientists, it
has been the possible dynamic evolution of space that offers the
most potential. For writers, however, the curvature of space, which
as I have noted is suggestive (although incorrectly so) of an
embedding of our own space in a space of higher dimensions, seems
to have been the primary motivating force.The prolific Australian
(British-born) science fiction writer A. Bertram Chandler was
fascinated with faster-than-light travel as well as alternate
realities and extra dimensions. In his story “Catch the Star Winds”
(1969) he combined both ideas in a single work. The crew of the
Flying Cloud
manipulate space and time to
travel faster than light and back in time, but in so doing they get
hurtled into alternate dimensions from which return is
impossible.

Chandler’s stories may be far removed from any
realistic science, but by the 1960s, physics had in fact produced
some theoretical constructs associated with curved space whose
properties are reminiscent of the fourdimensional objects that had
earlier so fascinated Heinlein: namely, black holes and ultimately
even more exotic objects called wormholes. Black holes are
remarkable not merely because they are so exotic—configurations of
matter and energy so dense that the escape velocity from their
surface exceeds even the speed of light—but because classically, at
least, anything that falls inside one is doomed to encounter a
“singularity” at their origin: A place of infinite density where the
concept of space itself breaks down. Within the context of general
relativity, it seems that nothing can stop the ultimate
gravitational collapse of a black hole, so that the material making
it up gets compressed until it achieves infinite density, at least
if one follows the classical trajectories indefinitely. However, we
expect that general relativity probably gets modified at small
scales and high densities, where the laws of quantum mechanics hold
sway.

Interestingly, however, even the classical
geometry of black holes carries with it certain exotic
possibilities. In particular, mathematically at least, the region
inside what is called the event horizon of a black hole—the volume
out of which nothing that falls in can escape—does not just extend
down to the singularity, but crosses it, and connects it to another
mirror image of all of space outside the event horizon. Is this
just an artifact of the mathematics of classical general
relativity, or could black holes act as portals to another causally
disconnected universe? Both scientists and writers have speculated
about this, although if one had to pass through the singularity to
get there, one probably wouldn’t look too healthy coming out—rather
more like meat after it has been through a grinder.

This practical issue aside, there was a
compelling reason for some physicists, in particular Stephen
Hawking, to have espoused the possibility that black holes are
portals. When things fall through the event horizon into a black
hole, one loses all subsequent information about them. Hawking
showed in 1972 that when one incorporates the laws of quantum
mechanics near the event horizon, black holes can actually radiate
away energy, and in the process may ultimately shrink and
disappear. However, it appeared mathematically that the radiation
that emerged from the black hole would contain no information at
all about what had fallen into it. This is a big problem, because
quantum mechanics requires that this information should be
recoverable, at least in principle, if not in actual practice. If
Hawking radiation really violates this principle, then quantum
mechanics is definitively incompatible with gravity. Indeed, the
so-called information loss paradox has been one of the central
problems driving theoretical physicists to attempt to go beyond
general relativity for a new theory that might be explicitly
compatible with quantum mechanics. Now, if it were really true that
the information that fell down a black hole was lost to our
universe, one might naturally ask where this information
disappeared to. One possibility, which is the one Hawking raised,
is that it would vanish down through the singularity to emerge in
another universe.

Recently, however—indeed, as this book was
being written—Hawking has revised his opinion. He now claims to
have done a calculation that suggests that the Hawking radiation
that comes out of a black hole actually does carry all the
information that fell into it. If this is true, then it is a
profoundly important result, as I shall later discuss, because it
suggests that no significant modifications of general relativity may
be necessary to resolve the information loss paradox. And, as
Hawking himself has pointed out, this would also remove the prime
motivation for considering black holes as portals, a fact he
acknowledged with an apology: “I’m sorry to disappoint
science-fiction fans.”

Whether or not black holes can function as
portals to another universe, the notion that there could be a
potentially infinite space
inside
of objects
that appear from the outside to have a finite size, extending
Heinlein’s “Crooked House” concept to its extreme, is actually not
crazy at all. Indeed, we may be experiencing precisely this
phenomenon in the universe in which we live. As I have discussed,
our universe appears to be accelerating in its expansion, and if
this acceleration is left unchecked, almost everything that
astronomers can now see will recede from view, expanding infinitely
far away in the infinite future. However, as Alan Guth—who in 1980
first recognized the likelihood and potential significance of periods
of acceleration during the history of the universe—has
demonstrated, an initially finite region of the universe that is
inflating on the inside, can actually appear to be contracting when
seen from the outside!

As the universe cools, certain regions can get
stuck in a state that is not the true lowest-energy configuration of
matter and energy, just as when one cools water down while stirring
it, it can remain a liquid well below freezing. In particle physics
such regions are called
false vacua
. Guth
realized that a bubble of false vacuum amidst a sea of true vacuum
would look very different when seen from the inside versus from the
outside. Viewed from inside, the region would appear to be
inflating, expanding with a constant rate of acceleration. From
outside, the bubble would in fact appear to be decreasing in size,
and would eventually disappear from view. Where would everything in
the bubble end up? In a different, causally disconnected, and
otherwise infinite universe!

This is only one of several ways that the
exotic physics of curved space associated with general relativity
can allow seemingly impossible things to happen. A more familiar
example, perhaps, and one borrowed by Carl Sagan from physics (via
his friend Kip Thorne) in his 1985 novel and then movie,
Contact,
involves wormholes. Wormholes are literally
shortcuts through a curved space, much as a tunnel under a mountain
saves you the travel time that would be required to cross over it.
Two otherwise distant regions of space might in principle be
connected via a three-dimensional wormhole if one amassed enough
mass and energy at either of its mouths to produce huge local
curvatures of space. However unlike a tunnel (which connects two
points separated by the same linear distance apart whether or not
the tunnel is there to connect them in this way), a wormhole
literally changes the nature of space connecting them. Before it is
created there is literally no sense in which the two points might
otherwise be considered close to each other.

I have written at length about the fictional fun
one can have with wormholes in
The Physics of
Star Trek,
so I will not repeat these discussions here. Suffice
it to say that wormholes, if they actually were able to exist,
would allow not only distant regions of space to be connected, but
also distant regions of time . . . both past and future! But, they
probably don’t exist, so don’t get too excited about their
potential.
Star Trek,
in fact, has a long
history of using the effects of gravity to achieve exotic results.
In one of the series’s earliest episodes—and even before the
physicist John Wheeler invented the term
black
hole
to describe such gravitationally collapsed objects—its
writers had the
Enterprise
travel too close
to the gravitational field of a “black star,” and, as a result, the
ship was thrown back in time.

While
Star Trek
has
also had its share of wormholes and wormholeinduced travel, it is
best known for its own faster-than-light travel mechanism, warp
drive. While the very name suggests the warping of space, and I and
others have discussed how, within the context of general
relativity, faster-than-light travel is possible in principle (even
though no information is ultimately transmitted faster than light,
avoiding any contradiction with special relativity), it is
interesting that in
Star Trek
lore warp
drive is associated not with the dynamic warping of our own
three-dimensional space, but rather with the possible existence of
extra dimensions. Indeed, while black holes and wormholes are
fascinating implications of the possibility of curved space, which
in some ways can mimic various phenomena one might hope would
result from the existence of extra dimensions, as I have emphasized
already numerous times curved space itself neither implies nor
requires the existence of any extra dimensions. Instead, black
holes and wormholes demonstrate that even a seemingly pedestrian
three-dimensional space can be far stranger than meets the eye.

Nevertheless, as I have just described,
Star Trek
does manage to mix up warped
space and extra dimensions. In fact, at the heart of the
Star Trek
universe is an apparently
infinite
number of extra dimensions. In order to
explain how the crew can communicate instantly with Starfleet when
they are many hundreds if not thousands of light-years away, for
example, the writers invoked “subspace” communication. Using this
imaginary plot device, signals are transmitted into extra subspace
dimensions, where almost instantly they can be beamed back into our
three-dimensional space at a different location.

Star Trek
’s use of
subspace is characteristic of an explosion of interest beginning in
the 1980s, especially in movies and television, in moving beyond
merely a fourth dimension to the idea that many extra dimensions
might exist, and moreover that periodically not only information
but even material objects can leak from one dimension to another.
Interestingly, the things that emerge from other possible
dimensions are almost never benign. A classic
Outer Limits
episode from the 1960s involved an
unfortunate alien inhabitant of another dimension who meant no harm
but who was accidentally sucked into our space as a result of some
wayward scientific experiments, causing a host of problems. By
contrast, the horror film
Poltergeist
(1980)
played off the long-held notion described earlier that somehow the
spirit world inhabits other dimensions that at times intersect with
our own. Inevitably, however, it seems that only evil spirits
choose to cross the border. In one memorable scene during the
movie, reminiscent of the discussion of the magical properties of
motion in higher dimensions pondered by Edwin Abbott in the
nineteenth century, a ball is thrown into a dark closet and
reappears by falling from the ceiling in another location of the
same house.

The notion of evil beings from other dimensions
plays a large part in one of my personal favorite films,
The Adventures of Buckaroo Banzai across the
Eighth Dimension
(1984), whose protagonist
is not only a Nobel Prize–winning particle physicist but also a
skilled neurosurgeon, rock musician, and Zen warrior. Its plot
focuses on the mishaps that can occur when a rocket car that can go
through matter by taking a short cut through the eighth dimension
picks up unwanted alien hitchhikers.

At around this time in the 1980s
Star Trek,
too, began to fixate on multiple extra
spatial dimensions and the aliens that could emerge from them. In
one episode Commander Riker gets kidnapped by aliens from subspace
dimensions and the ship is put in great danger until the
responsible portal can be closed.

Star Trek
also focused
on another common science fiction theme, that of parallel universes.
These involve other three-dimensional spaces, identical to our own,
that somehow coexist with ours, but not necessarily within the
context of a higher-dimensional space. For example, some writers
have taken the many-worlds interpretation of quantum mechanics,
which argues that while true quantum mechanical objects can exist
in many different states simultaneously, each time we make a
measurement of such an object, we immediately force it to exist on
one of what can be an infinite number of parallel branches of the
quantum mechanical “wavefunction” describing the objects. If one
takes this notion literally, it suggests that we somehow define our
reality by the observations we make, but that there could be an
infinite other set of realities with different outcomes. While most
physicists I know view the many-worlds interpretation as merely a
mental crutch to help them deal with phenomena at the quantum level
that simply have no sensible classical analogues, a number of
writers have created stories using many worlds. In one
Star Trek
episode the Klingon Worf finds himself
jumping between different branches of reality, in each of which all
the other characters are slightly different. (Incidentally, the
weird properties of quantum mechanics may have inspired artists as
well as writers. More than one person I know has argued to me that
Jackson Pollock’s abstract “drip” paintings are beautiful
representations of the quantum fluctuations that populate the
vacuum.)