The Physics of Star Trek (18 page)

(a) the dark matter is not just “out there,” it is in this room as you are reading this
book, passing imperceptibly through your body. These exotic elementary particles would not
clump into astronomical objects; they would form a diffuse “gas” streaming throughout the
galaxy. Since they interact at best only very weakly with matter, they would be able to
sail through objects as big as the Earth. Indeed, examples of such particles already exist
in nature notably, neutrinos (particles that should be familiar to trekkers, and which I
will later discuss).

(b) the dark matter might be detected directly here on Earth, using sophisticated
elementary-particle-detection techniques. Various detectors designed with a sensitivity to
various dark matter candidates are currently being constructed.

(c) the detections of such particles might revolutionize elementary particle physics. It
is quite likely that these objects are remnants of production processes in the very early
universe, well before it was 1 second old, and would thus be related to physics at energy
scales comparable to or even beyond those we can directly probe using modern accelerators.

Of course, as exciting as this possibility is, we are not yet certain that the dark matter
may not be made of less exotic stuff. There are many ways of putting protons and neutrons
together so that they do not shine. For example, if we populated the galaxy with
snowballs, or boulders, these would be difficult to detect. Perhaps the most plausible
possibility for this scenario is that there are many objects in the galaxy which are
almost large enough to be stars but are too small for nuclear reactions to start occurring
in their cores. Such objects are known as brown dwarfs, and Data and his colleagues aboard
the
Enterprise
have discussed them (for instance, in “Manhunt”). In fact, there are interesting
experiments going on right now to find out whether or not brown dwarfsknown in this
context as MACHOs (for Massive Astrophysical Compact Halo Objects)make up a significant
component of the dark matter halo around the Milky Way galaxy. While these objects are not
directly observable, if one of them were to pass in front of a star the star's light would
be affected by the MACHO's gravity in such a way as to make the star appear brighter. This
“gravitational lensing” phenomenon was first predicted by Einstein back in the 1930s, and
we now have the technology to detect it. Several experiments are observing literally
millions of stars in our galaxy each night, to see if this lensing phenomenon takes place.
The sensitivity is sufficient to detect a dark matter halo of MACHOS, if they do indeed
make up most of the dark matter surrounding our galaxy. Preliminary data have set upper
limits that tend to suggest that the dark matter halo is not composed of MACHOs, but the
question is still open.

NEUTRON STARS: These objects are, as you will recall, all that is left of the collapsed
cores of massive stars that have undergone a supernova. Although they typically contain a
mass somewhat in excess of the mass of our Sun, they are so compressed that they are about
the size of Manhattan! Once again, the Star Trek writers have outdone themselves in the
nomenclature department. The
Enterprise
has several times encountered material expelled from a neutron stara material that the
writers have dubbed “neutronium.” Since neutron stars are composed almost entirely of
neutrons held so tightly together that the star is basically one huge atomic nucleus, the
name is a good one. The Doomsday machine in the episode of the same name was apparently
made of pure neutronium, which is why it was impervious to Federation weapons. However, in
order for this material to be stable it has to be under the incredibly high pressure
created by the gravitational attraction of a stellar mass of material only 15 kilometers
in radius. In the real world, such material exists only as part of a neutron star.

The
Enterprise
has had several close calls near neutron stars. In the episode “Evolution,” when the
Nanites began eating the ship's computers, the crew was in the act of studying a neutron
star that was apparently about to erupt as it accreted material. In the episode “The
Masterpiece Society,” the
Enterprise
must deflect a stellar core

fragment hurtling toward Moab IV.

There are no doubt millions of neutron stars in the galaxy. Most of these are born with
incredibly large magnetic fields inside them. If they are spinning rapidly, they make
wonderful radio beacons. Radiation is emitted from each of their poles, and if the
magnetic field is tilted with respect to the spin axis, a rotating beacon is created. On
Earth, we detect these periodic bursts of radio waves, and call their sources pulsars.
Rotating out in space, they make the best clocks in the universe. The pulsar signals can
keep time to better than one microsecond per year. Moreover, some pulsars produce more
than 1000 pulses per second. This means that an object that is essentially a huge atomic
nucleus with the mass of the Sun and 10 to 20 kilometers across is rotating over 1000
times each second. Think about that. The rotation speed at the neutron star surface is
therefore almost half the speed of light! Pulsars are one illustration of the fact that
nature produces objects more remarkable than any the Star Trek writers are likely to
invent.

OTHER DIMENSIONS: As James T. Kirk slowly drifts in and out of this universe in “The
Tholian Web,” we find that the cause is a “spatial interphase” briefly connecting
different dimensional planes, which make up otherwise “parallel universes.” Twice before
in the series, Kirk encountered parallel universesone made of antimatter, in “The
Alternative Factor,” and the other accessed via the transporter, in “Mirror, Mirror.” In
The Next Generation,
we have the Q-continuum, Dr. Paul Manheim's nonlinear time “window into other dimensions,”
and of course subspace itself, containing an infinite number of dimensions, which aliens,
like the ones who kidnapped Lieutenant Riker in “Schisms,” can hide in.

The notion that somehow the four dimensions of space and time we live in are not all there
is has had great tenacity in the popular consciousness. Recently a Harvard psychiatrist
wrote a successful book (and apparently got in trouble with the Medical School) in which
he reported on his analysis of a variety of patients, all of whom claimed they had been
abducted by aliens. In an interview, when asked where the aliens came from and how they
got here, he is reported to have suggested, “From another dimension.”

This love affair with higher dimensions no doubt has at its origin the special theory of
relativity. Once three- dimensional space was tied with time to make four-dimensional
spacetime by Hermann Minkowski, it was natural to suppose that the process might continue.
Moreover, once general relativity demonstrated that what we perceive as the force of
gravity can be associated with the curvature of spacetime, it was not outrageous to
speculate that perhaps other forces might be associated with curvature in yet other
dimensions.

Among the first to speculate on this idea were the Polish physicist Theodor Kaluza in 1919
and, independently, the Swedish physicist Oskar Klein in 1926. They proposed that
electromagnetism could be unified with gravity in a five-dimensional universe. Perhaps the
electromagnetic force is related to some “curvature” in a fifth dimension, just as the
gravitational force is due to curvature in four-dimensional spacetime.

This is a very pretty idea, but it has problems. In fact, in any scenario in which one
envisages extra dimensions in the universe, one has to explain
why we don't experience these dimensions as we do space and time.
The proposed answer to this question is very important, because it crops up again and
again when physicists consider the possibility of higher dimensions in the universe.

Consider a cylinder and an intelligent bug. As long as the circumference of the cylinder
is large compared to the size of the bug, then the bug can move along both dimensions and
will sense that it is crawling on a two- dimensional surface.

However, if the circumference of the cylinder becomes very small, then as far as the bug
is concerned it is crawling on a one-dimensional objectnamely, a line or a stringand can
move only up or down:

Now think how such a bug might actually find out that there is another dimension,
corresponding to the circumference of the cylinder. With a microscope, it might be able to
make out the “string's” width. However, the wavelength of radiation needed to resolve
sizes this small would have to be on order of the diameter of the cylinder or smaller,
because, as I noted in chapter 5, waves scatter off only those objects that are at least
comparable to their wavelength. Since the energy of radiation increases as its wavelength
decreases, it would require a certain minimum energy of radiation to resolve this “extra
dimension.”

If somehow a fifth dimension were “curled up” in a tight circle, then unless we focused a
lot of energy at a small point, we would not be able to send waves traveling through it to
probe its existence, and the world would continue to look to us to be effectively
four-dimensional. After all, we know that space is three-dimensional because we can probe
it with waves traveling in all three dimensions.

If the only waves that can be sent into the fifth dimension have much more energy than we
can produce even in high-energy accelerators, then we cannot experience this extra
dimension.

In spite of its intrinsic interest, the Kaluza-Klein theory cannot be a complete theory.
First, it does not explain
why
the fifth dimension would be curled up into a tiny circle. Second, we now know of the
existence of two other

fundamental forces in nature beyond electro-magnetism and gravitythe strong nuclear force
and the weak nuclear force. Why stop at a fifth dimension? Why not include enough extra
dimensions to accommodate all the fundamental forces?

In fact, modern particle physics has raised just such a possibility. The modern effort,
centered around what is called superstring theory, focused initially on extending the
general theory of relativity so that a consistent theory of quantum gravity could be
constructed. In the end, however, the goal of a unified theory of all interactions has
resurfaced.

I have already noted the challenges faced in developing a theory wherein general
relativity is made consistent with quantum mechanics. The key difficulty in this effort is
trying to understand how quantum fluctuations in spacetime can be handled. In elementary
particle theory, quantum excitations in fieldsthe electric field, for exampleare
manifested as elementary particles, or quanta. If one tries to understand quantum
excitations in the gravitational fieldwhich, in general relativity, correspond to quantum
excitations of spacetime the mathematics leads to nonsensical predictions.

The advance of string theory was to suppose that at microscopic levels, typical of the
very small scales (that is, 10
-33
cm) where quantum gravitational effects might be important, what we think of as pointlike
elementary particles actually could be resolved as vibrating strings. The mass of each
particle would correspond in some sense to the energy of vibration of these strings.

The reason for making this otherwise rather outlandish proposal is that it was discovered
as early as the 1970s that such a theory requires the existence of particles having the
properties that quantum excitations in spacetimeknown as gravitonsshould have. General
relativity is thus in some sense imbedded in the theory in a way that may be consistent
with quantum mechanics.

However, a quantum theory of strings cannot be made mathematically consistent in 4
dimensions, or 5, or even 6. It turns out that such theories can exist consistently only
in 10 dimensions, or perhaps only 26! Indeed, Lieutenant Reginald Barclay, while he
momentarily possessed an IQ of 1200 after having been zapped by a Cytherian probe, had
quite a debate with Albert Einstein on the holodeck about which of these two possibilities
was more palatable in order to incorporate quantum mechanics in general relativity.

This plethora of dimensions may seem an embarrassment, but it was quickly recognized that
like many embarrassments it also presented an opportunity. Perhaps all the fundamental
forces in nature could be incorporated in a theory of 10 or more dimensions, in which all
the dimensions but the four we know curl up with diameters on the order of the Planck
scale (10
-33
cm)as Lieutenant Barclay surmised they mustand are thus

unmeasurable today.

Alas, this great hope has remained no more than that. We have, at the present time,
absolutely no idea whether the tentative proposals of string theory can produce a unified
Theory of Everything. Also, just as with the Kaluza- Klein theory, no one has any clear
notion of why the other dimensions, if they exist, would curl up, leaving four-
dimensional spacetime on large scales.

So, the moral of this saga is that Yes, Virginia, there may be extra dimensions in the
universe. In fact, there is now some reason to expect them. However, these extra
dimensions are not the sort that might house aliens who could then abduct psychiatric
patients (or Commander Riker, for that matter). They are not “parallel universes.”

They also cannot be mixed up with the four dimensions of spacetime in a way that would
allow objects to drift from one place to another in space by passing through another
dimension, as “subspace” seems to allow in the Star Trek universe.

Nevertheless, we cannot rule out the possibility that there might exist microscopic or
even macroscopic “bridges” to otherwise disconnected (or parallel) universes. Indeed, in
general relativity, regions of very high curvature inside a black hole, or in a
wormholecan be thought of as connecting otherwise disconnected and potentially very large
regions of spacetime. I know of no reason to expect such phenomena outside black holes and
wormholes, based on our present picture of the universe, but since we cannot rule them
out, I suppose that