The Physics of Star Trek (11 page)

In any case, one can perform a calculation, given that the
Enterprise
is using radiation with a wavelength of less than a billionth of a centimeter and scanning
an object 40,000 kilometers away with atomic-scale resolution. I find that in order to do
this, the ship would need a telescope with a lens greater than approximately 50,000
kilometers in diameter! Were it any smaller, there would be no possible way even in
principle to resolve single atoms. I think it is fair to say that while the
Enterprise-D
is one large mother, it is not that large.

As promised, thinking about transporters has led us into quantum mechanics, particle
physics, computer science, Einstein's mass-energy relation, and even the existence of the
human soul. We should therefore not be too disheartened by the apparent impossibility of
building a device to perform the necessary functions. Or, to put it less negatively,
building a transporter would require us to heat up matter to a temperature a million times
the temperature at the center of the Sun, expend more energy in a single machine than all
of humanity presently uses, build telescopes larger than the size of the Earth, improve
present computers by a factor of 1000 billion billion, and avoid the laws of quantum
mechanics. It's no wonder that Lieutenant Barclay was terrified of beaming! I think even
Gene Roddenberry, if faced with this challenge in real life, would probably choose instead
to budget for a landable starship.

The Most Bang for Your Buck

Nothing Unreal Exists.
Kir-kin-tha's First Law of Metaphysics
(Star Trek IV: The Voyage Home,)

If you are driving west on Interstate 88 out of Chicago, by the time you are 30 miles out
of town, near Aurora, the hectic urban sprawl gives way to the gentle Midwestern prairie,
which stretches forward and flat as far as you can see. Located slightly north of the
interstate at this point is a ring of land marked by what looks like a circular moat.
Inside the property, you may see buffalo grazing and many species of ducks and geese in a
series of ponds.

Twenty feet below the surface, it is a far cry from the calm pastoral atmosphere above
ground. Four hundred thousand times a second, an intense beam of antiprotons strikes a
beam of protons head on, producing a shower of hundreds or thousands of secondary
particles: electrons, positrons, pions, and more.

This is the Fermi National Accelerator Laboratory, or Fermilab for short. It contains the
world's highest-energy particle accelerator. But more germane for our purposes is the fact
that it is also the world's largest repository of antiprotons. Here, antimatter is not the
stuff of science fiction. It is the bread and butter of the thousands of research
scientists who use the Fermilab facilities.

It is in this sense that Fermilab and the
U.S.S. Enterprise
bear a certain kinship. Antimatter is crucial to the functioning of a starship: it powers
the warp drive. As I mentioned earlier, there is no more efficient way to power a
propulsion system (though the warp drive is not, in fact, based on rocket propulsion).
Antimatter and matter, when they come into contact, can completely annihilate and produce
pure radiation, which travels out at the speed of light.

Obviously, great pains must be taken to make sure that antimatter is “contained” whenever
it is stored in bulk. When antimatter containment systems fail aboard starships, as when
the
Enterprise's
system failed after its collision with the
Bozeman,
or when the containment system aboard the
Yamato
failed due to the Iconian computer weapon, total destruction inevitably follows soon
afterward. In fact, antimatter containment would be so fundamental to starship operation
that it is hard to understand why Federation Lieutenant Commander Deanna Troi was ignorant
of the implications of containment loss when she temporarily took over command of the
Enterprise
in the
Next Generation
episode “Disaster,” after the ship collided with two “quantum filaments.” The fact that
she was formally trained only as a psychologist should have been no excuse!

The antimatter containment system aboard starships is plausible, and in fact uses the same
principle that allows Fermilab to store antiprotons for long periods. Antiprotons and
antielectrons (called positrons) are electrically charged particles. In the presence of a
magnetic field, charged particles will move in circular orbits. Thus, if the particles are
accelerated in electric fields, and then a magnetic field of appropriate strength is
applied, the antiparticles will travel in circles of prescribed sizes. In this way, for
example, they can travel around inside a doughnut-shaped container without ever touching
the walls. This principle is also used in so-called Tokomak devices to contain the
high-temperature plasmas in studies of controlled nuclear fusion.

The Antiproton Source for the Fermilab collider contains a large ring of magnets. Once
antiprotons are produced, in medium-energy collisions, they are steered into this ring,
where they can be stored until they are needed for the highest-energy collisions, which
take place in the Tevatronthe Fermilab high-energy collider. The Teva-tron is a much
larger ring, about four miles in circumference. Protons are injected into the ring and
accelerated in one direction, and antiprotons are accelerated in the other. If the
magnetic field is carefully adjusted, these two beams of particles can be kept apart
throughout most of the tunnel. At specified points, however, the two beams converge and
the collisions are studied.

Besides containment, another problem faces us immediately if we want to use a
matter-antimatter drive: where to get the antimatter. As far as we can tell, the universe
is made mostly of matter, not antimatter. We can confirm that this is the case by
examining the content of high-energy cosmic rays, many of which originate well outside our
own galaxy. Some antiparticles should be created during the collisions of high-energy
cosmic rays with matter, and if one explores the cosmic-ray signatures over wide energy
ranges, the antimatter signal is completely consistent with this phenomenon alone; there
is no evidence of a primordial antimatter component.

Another possible sign of antimatter in the universe would be the annihilation signature of
antiparticle-particle collisions. Wherever the two coexist, one would expect to see the
characteristic radiation emitted during the annihilation process. Indeed, this is exactly
how the
Enterprise
searched for the Crystalline Entity after it had destroyed a new Federation outpost.
Apparently the Entity left behind a trace antiproton trail. By looking for the
annihilation radiation, the
Enterprise
trailed the Entity and overtook it before it could attack another planet.

While the Star Trek writers got this idea right, they got the details wrong. Dr. Marr and
Data search for a sharp “gamma radiation” spike at “10 keV”a reference to 10 kilo-electron
volts, which is a unit of energy of radiation. Unfortunately, this is the wrong scale of
energy for the annihilation of protons and antiprotons, and in fact corresponds to no
known annihilation signal. The lightest known particle with mass is the electron. If
electrons and positrons annihilate, they produce a sharp spike of gamma radiation at 511
keV, corresponding to the mass of the electron. Protons and antiprotons would produce a
sharp spike at an energy corresponding to the rest energy of the proton, or about 1 GeV
(Giga-electron volt)roughly a hundred thousand times the energy searched for by Marr and
Data. (Incidentally, 10 keV is in the X-ray band of radiation, not the gamma-ray band,
which generally corresponds to radiation in excess of about 100 keV, but this is perhaps
too fine a detail to complain about.)

In any case, astronomers and physicists have looked for diffuse background signals near
511 keV and in the GeV range as signals of substantial matter-antimatter conflagrations
but have not found such signals. This and the cosmic-ray investigations indicate that even
if substantial distributions of antimatter were to exist in the universe, they would not
be interspersed with ordinary matter.

As most of us are far more comfortable with matter than antimatter, it may seem quite
natural that the universe should be made of the former and not the latter. However, there
is nothing natural at all about this. In fact, the origin of the excess of matter over
antimatter is one of the most interesting unsolved problems in physics today, and is a
subject of intense research at the present time. This excess is very relevant to our
existence, and thus to Star Trek's, so it seems appropriate to pause to review the problem
here.

When quantum mechanics was first developed, it was applied successfully to atomic physics
phenomena; in particular, the behavior of electrons in atoms was wonderfully accounted
for. However, it was clear that one of the limitations of this testing ground was that
such electrons have velocities that are generally much smaller than the speed of light.
How to accommodate the effects of special relativity with quantum mechanics remained an
unsolved problem for almost two decades. Part of the reason for the delay was that unlike
special relativity, which is quite straightforward in application, quantum mechanics
required not just a whole new world view but a vast array of new mathematical techniques.
The best young minds in physics were fully occupied in the first three decades of this
century with exploring this remarkable new picture of the universe.

One of those minds was Paul Adrien Maurice Dirac. Like his successor Stephen Hawking, and
later Data, he would one day hold the Lucasian Professorship in Mathematics at Cambridge
University. Educated by Lord Rutherford, and later training with Niels Bohr, Dirac was
better prepared than most to extend quantum mechanics to the realm of the ultrafast. In
1928, like Einstein before him, he wrote down an equation that would change the world. The
Dirac equation correctly describes the relativistic behavior of electrons in fully quantum
mechanical terms.

Shortly after writing down this equation, Dirac realized that to retain consistency, the
mathematics required another particle of equal but opposite charge to the electron to
exist in nature. Of course, such a particle was known alreadynamely, the proton. However,
Dirac's equation suggested that this particle should have the same mass as the electron,
whereas the proton is almost two thousand times heavier. This discrepancy between
observation and the “naive” interpretation of the mathematics remained a puzzle for four
years, until the American physicist Carl Anderson discovered, among the cosmic rays
bombarding the Earth, a new particle whose mass was identical to the electron's but whose
charge was the oppositethat is, positive. This “antielectron” soon became known as the
positron.

Since then, it has become clear that one of the inevitable consequences of the merger of
special relativity and quantum mechanics is that all particles in nature must possess
antiparticles, whose electric charge (if any) and various other properties should be the
opposite of their particle partners. If all particles possess antiparticles, then which
particles we call particles and which we call antiparticles is completely arbitrary, as
long as no physical process displays any bias for particles over antiparticles. In the
classical world of electromagnetism and gravity, no such biased process exists.

Now we are left in a quandary. If particles and antiparticles are on an identical footing,
why should the initial conditions of the universe have determined that what we call
particles should comprise the dominant form of matter? Surely a more sensible, or at least
a more symmetric, initial condition would be that in the beginning the

number of particles and antiparticles would have been identical. In this case, we must
explain how the laws of physics, which apparently do not distinguish particles from
antiparticles, could somehow contrive to produce more of one type than the other. Either
there exists a fundamental quantity in the universethe ratio of particles to
antiparticleswhich was fixed at the beginning of time and about which the laws of physics
apparently have nothing to say, or we must explain the paradoxical subsequent dynamical
creation of more matter than antimatter.

In the 1960s, the famous Soviet scientist and later dissident Andrei Sakharov made a
modest proposal. He argued that it was possible, if three conditions were fulfilled in the
laws of physics during the early universe, to dynamically generate an asymmetry between
matter and antimatter even if there was no asymmetry to start with. At the time this
proposal was made, there were no physical theories that satisfied the conditions Sakharov
laid down. However, in the years since, particle physics and cosmology have both made
great strides. Now we have many theories that can, in principle, explain directly the
observed difference in abundance between matter and antimatter in nature. Unfortunately,
they all require new physics and new elementary particles in order to work; until nature
points us in the right direction, we will not know which of them to choose from.
Nevertheless, many physicists, myself included, find great solace in the possibility that
we may someday be able to calculate from first principles exactly why the matter
fundamental to our existence itself exists.

Now, if we had the correct theory, what number would it need to explain? In the early
universe, what would the extra number of protons compared to antiprotons need to have been
in order to explain the observed excess of matter in the universe today? We can get a clue
to this number by comparing the abundance of protons today to the abundance of photons,
the elementary particles that make up light. If the early universe began with an equal
number of protons and antiprotons, these would annihilate, producing radiationthat is,
photons. Each proton- antiproton annihilation in the early universe would produce, on
average, one pair of photons. However, assuming there was a small excess of protons over
antiprotons, then not all the protons would be annihilated. By counting the number of
protons left over after the annihilations were completed, and comparing this with the
number of photons produced by those annihilations (that is, the number of photons in the
background radiation left over from the big bang), we can get an idea of the fractional
excess of matter over antimatter in the early universe.