The Physics of Star Trek (19 page)

Federation starships are free to keep finding them.

ANYONS: In the
Next Generation
episode “The Next Phase,” a transporter mix-up with a new Romulan cloaking device that
puts matter “out of phase” with other matter causes Geordi LaForge and Ro Laren to vanish.
They are presumed dead, and remain invisible and incommunicado until Data modifies an
“anyon emitter” for another purpose and miraculously “dŽphasŽs” them.

If the Star Trek writers had never heard of anyons, and I am willing to bet that they
hadn't, their penchant for pulling apt names out of the air is truly eerie. Anyons are
theoretical constructs proposed and named by my friend Frank Wilczek, a physicist at the
Institute for Advanced Study in Princeton, and his collaborators. Incidentally, he also
invented another particlea dark matter candidate he called the axion, after a laundry
detergent. “Axionic chips” also crop up in Star Trek, as part of an advanced machine's
neural network. But I digress.

In the three-dimensional space in which we live, elementary particles are designated as
fermions and bosons, depending on their spin. We associate with each variety of elementary
particle a quantum number, which gives the value of its spin. This number can be an
integer (0,1, 2,... ) or a half integer
(1/2, 3/2, 5/2,...).
Particles with integer spin are called bosons, and particles with half integer spin are
called fermions. The quantum mechanical behavior of fermions and bosons is different: When
two identical fermions are interchanged, the quantum mechanical wavefunction describing
their properties is multiplied by minus 1, whereas in an interchange of bosons nothing
happens to the wavefunction. Therefore, two fermions can never be in the same place,
because if they were, interchanging them would leave the configuration identical but the
wavefunction would have to be multiplied by minus 1, and the only thing that can be
multiplied by minus 1 and remain the same is 0. Thus, the wavefunction must vanish. This
is the origin of the famous Pauli exclusion principleoriginally applied to electronswhich
states that two identical fermions cannot occupy the same quantum mechanical state.

In any case, it turns out that if one allows panicles to move in only two dimensionsas the
two-dimensional beings encountered by the
Enterprise
(see next item) are forced to do;
or,
more relevantly, as happens in the real world when atomic configurations in a crystal are
arranged so that electrons, say, travel only on a two- dimensional plane the standard
quantum mechanical rules that apply in three-dimensional space are changed. Spin is no
longer quantized, and particles can carry any value for this quantity. Hence, instead of
fermi-ons or bos-ons, one can have any-ons. This was the origin of the name, and the idea
that Wilczek and others have explored.

Back to the Star Trek writers: What I find amusing is that the number by which the
wavefunction of particles is multiplied when the particles are interchanged is called a
“phase.” Fermion wavefunctions are multiplied by a phase of minus 1, while bosons are
multiplied by a phase of 1 and hence remain the same. Anyons are multiplied by a
combination of 1 and an imaginary number (imaginary numbers are the square roots of
negative numbers), and hence in a real sense are “out of phase” with normal particles. So
it seems fitting that an “anyon emitter” would change the phase of something, doesn't it?

COSMIC STRINGS: In the
Next Generation
episode “The Loss,” the crew of the
Enterprise
encounters two- dimensional beings who have lost their way. These beings live on a
“cosmic-strings fragment.” In the episode, this is described as an infinitesimally thin
filament in space, with a very strong gravitational pull and vibrating with a
characteristic set of “subspace” frequencies.

In fact, cosmic strings are objects proposed to have been created during a phase
transition in the early universe. One of the world's experts on these theoretical objects
recently joined the faculty at Case Western Reserve, so I hear a lot about cosmic strings
these days. Their properties would be similar in some respects to the object encountered
by the
Enterprise.

During a phase transition in materialsas when water boils, say, or freezesthe
configuration of the material's constituent particles changes. When water freezes, it
forms a crystalline structure. As crystals aligned in various directions grow, they can
meet to form random lines, which create the patterns that look so pretty on a window in
the winter. During a phase transition in the early universe, the configuration of matter,
radiation, and empty space (which, I remind you, can carry energy) changes, too. Sometimes
during these transitions, various regions of the universe relax into different
configurations. As these configurations grow, they too can eventually meet sometimes at a
point, and sometimes along a line, marking a boundary between the regions. Energy becomes

trapped in this boundary line, and it forms what we call a cosmic string.

We have no idea whether cosmic strings actually were created in the early universe, but if
they were and lasted up to the present time they could produce some fascinating effects.
They would be infinitesimally thinthinner than a protonyet the mass density they carry
would be enormous, up to a million million tons per centimeter. They might form the seeds
around which matter collapses to form galaxies, for example. They would also “vibrate,”
producing not subspace harmonics but gravitational waves. Indeed, we may well detect the
gravitational wave signature of a cosmic string before we ever directly observe the string
itself.

So much for the similarities with the Star Trek string. Now for the differences. Because
of the way they are formed, cosmic strings cannot exist in fragments. They have to exist
either in closed loops or as a single long string that winds its way through the universe.
Moreover, in spite of their large mass density, cosmic strings exert no gravitational
force on faraway objects. Only if a cosmic string moves past an object will the object
experience a sudden gravitational force. These are subtle points, however; on the whole,
the Star Trek writers have done pretty well by cosmic strings.

QUANTUM MEASUREMENTS: There was a wonderful episode in the final season of
The Next Generation,
called “Parallels,” in which Worf begins to jump between different “quantum realities.”
The episode touches, albeit incorrectly, on one of the most fascinating aspects of quantum
mechanicsquantum measurement theory.

Since we live on a scale at which quantum mechanical phenomena are not directly observed,
our entire intuitive physical picture of the universe is classical in character. When we
discuss quantum mechanics, we generally use a classical language, so as to try and explain
the quantum mechanical world in terms we understand. This approach, which is usually
referred to as “the interpretation of quantum mechanics” and so fascinates some
philosophers of science, is benighted; what we really should be discussing is “the
interpretation of classical mechanics”that is, how can the classical word we seewhich is
only an approximation of the underlying reality, which in turn is quantum mechanical in
naturebe understood in terms of the proper quantum mechanical variables?

If we insist on interpreting quantum mechanical phenomena in terms of classical concepts,
we will inevitably encounter phenomena that seem paradoxical, or impossible. This is as it
should be. Classical mechanics cannot account properly for quantum mechanical phenomena,
and so there is no reason that classical descriptions should make sense.

Having issued this caveat, I will describe the relevant issues in classical mechanics
terms, because these are the only tools of language I have. While I have the proper
mathematical terms to describe quantum mechanics, like all other physicists I have
recourse only to a classical mental picture, because all my direct experience is classical.

As I alluded to in chapter 5, one of the most remarkable features of quantum mechanics is
that objects observed to have some property cannot be said to have had that property the
instant before the observation. The observation process can change the character of the
physical system under consideration. The quantum mechanical wavefunc-tion of a system
describes completely the configuration of this system at any one time, and this
wavefunction evolves according to deterministic laws of physics. However, what makes
things seem so screwy is that this wavefunction can encompass two or more mutually
exclusive configurations at the same time.

For example, if a particle is spinning clockwise, we say that its spin is “up.” If it is
spinning counterclockwise, we say that its spin is “down.” Now, the quantum mechanical
wavefunction of this particle can incorporate a sum with equal probabilities: spin up and
spin down. If you measure the direction of the spin, you will measure
either
spin up
or
spin down. Once you have made the measurement, the wavefunction of the particle will from
then on include only the component you measured the particle to have; if you measured spin
up, you will go on measuring this same value for this panicle.

This picture presents problems. How, you may ask, can the particle have had both spin up
and spin down before the measurement? The correct answer is that it had neither. The
configuration of its spin was indeterminate before the measurement.

The fact that the quantum mechanical wavefunction that describes objects does not
correspond to unique values for observables is especially disturbing when one begins to
think of living objects. There is a famous paradox called “Schršdinger's cat.” (Erwin
Schršdinger was one of the young Turks in their twenties who, early in this century,
helped uncover the laws of quantum mechanics. The equation describing the time evolution
of the quantum mechanical wavefunction is known as Schršdinger's equation.) Imagine a box,
inside of which is a cat. Inside the box, aimed at the cat, is a gun, which is hooked up
to a radioactive source. The radioactive source has a certain quantum mechanical
probability of decaying at any given time. When the source decays, the gun will fire and
kill the cat. Is the wavefunction describing the cat, before I open the box, a linear
superposition of a live cat and a dead cat? This seems absurd.

Similarly, our consciousness is always unique, never indeterminate. Is the act of
consciousness a measurement? If so, then it could be said that at any instant there is a
nonzero quantum mechanical probability for a number of different outcomes to occur, and
our act of consciousness determines which outcome we experience. Reality then has an
infinite number of branches. At every instant our consciousness determines which branch we
inhabit, but an infinite number of other possibilities exist a priori.

This “many worlds” interpretation of quantum mechanicswhich says that in some other branch
of the quantum mechanical wavefunction Stephen Hawking is writing this book and I am
writing the forewordis apparently the basis for poor Worf's misery. Indeed, Data says as
much during the episode. When Worf's ship traverses a “quantum fissure in spacetime,”
while simultaneously emitting a “subspace pulse,” the barriers between quantum realities
“break down,” and Worf begins to jump from one branch of the wavefunction to another at
random times, experiencing numerous alternative quantum realities. This can never happen,
of course, because once a measurement has been made, the system, including the measuring
apparatus (Worf, in this case), has changed. Once Worf has an experience, there is no
going back ... or perhaps I should say sideways. The experience itself is enough to fix
reality. The very nature of quantum mechanics demands this.

There is one other feature of quantum mechanics touched upon in the same episode. The
Enterprise
crew are able to verify that Worf is from another “quantum reality” at one point by
arguing that his “quantum signature at the atomic level” differs from anything in their
world. According to Data, this signature is unique and cannot change due to any physical
process. This is technobabble, of course; however, it does relate to something interesting
about quantum mechanics. The entire set of all possible states of a system is called a
Hubert space, after David Hubert, the famous German mathematician who, among other things,
came very close to developing general relativity before Einstein. It sometimes happens
that the Hubert space breaks up into separate sectors, called “superselection sectors.” In
this case, no local physical process can move a system from one sector to another. Each
sector is labeled by some quantityfor instance, the total electric charge of the system.
If one wished to be poetic, one could say that this quantity provided a unique “quantum
signature” for this sector, since all local quantum operations preserve the same sector,
and the behavior of the operations and the observables they are associated with is
determined by this quantity.

However, the different branches of the quantum mechanical wave-function of a system must
be in a single superselection sector, because any one of them is physically accessible in
principle. So, unfortunately for Worf, even if he did violate the basic tenets of quantum
mechanics by jumping from one branch to another, no external observable would be likely to
exist to validate his story.

The whole point of the many-worlds interpretation of quantum mechanics (or any other
interpretation of quantum mechanics, for that matter) is that you can never experience
more than one world at a time. And thankfully there are other laws of physics that would
prevent the appearance of millions of
Enterprises
from different realities, as happens at the end of the episode. Simple conservation of
energy a purely classical conceptis enough to forbid it.

SOLITONS: In the
Next Generation
episode “New Ground,” the
Enterprise
assists in an experiment developed by Dr. Ja'Dor, of the planet Bilana III. Here a
“soliton wave,” a nondispersing wavefront of subspace distortion, is used to propel a test
ship into warp speed without the need for warp drive. The system requires a planet at the
far end of the voyage, which will deliver a scattering field to dissipate the wave. The
experiment nearly results in a disaster, which is of course averted at the last instant.