The Physics of Star Trek (3 page)

The standard resolution of these paradoxes, at least among many physicists, is to argue a
priori that such possibilities must not be allowed in a sensible universe, such as the one
we presumably live in. However, the problem is that Einstein's equations of general
relativity not only do not directly forbid such possibilities, they encourage them.

Within thirty years of the development of the equations of general relativity, an explicit
solution in which time travel could occur was developed by the famous mathematician Kurt
Gšdel, who worked at the Institute for Advanced Study in Princeton along with Einstein. In
Star Trek language, this solution allowed the creation of a “temporal causality loop,”
such as the one the
Enterprise
got caught in after being hit by the
Bozeman.
The dryer terminology of modern physics labels this a “closed timelike curve.” In either
case, what it implies is that you can travel on a round-trip and return to your starting
point in both space
and
time! Gšdel's solution involved a universe that, unlike the one we happen to live in, is
not expanding but instead is spinning uniformly. In such a universe, it turns out that one
could in principle go back in time merely by traveling in a large circle in space. While
such a hypothetical universe is dramatically different than the one in which we live, the
mere fact that this solution exists at all indicates clearly that time travel is possible
within the context of general relativity.

There is a maxim about the universe which I always tell my students: That which is not
explicitly forbidden is guaranteed to occur. Or, as Data said in the episode “Parallels,”
referring to the laws of quantum mechanics, “All things which can occur, do occur.” This
is the spirit with which I think one should approach the physics of Star Trek. We must
consider the distinction not between what is practical and what is not, but between what
is possible and what is not.

This fact was not, of course, lost on Einstein himself, who wrote, “Kurt Gšdel's [time
machine solution raises] the problem [that] disturbed me already at the time of the
building up of the general theory of relativity, without my having succeeded in clarifying
it.... It will be interesting to weigh whether these [solutions] are not to be excluded on
physical grounds.”
1

The challenge to physicists ever since has been to determine what if any “physical
grounds” exist that would rule out the possibility of time travel, which the form of the
equations of general relativity appears to foreshadow. To discuss such things will require
us to travel beyond the classical world of general relativity to a murky domain where
quantum mechanics must affect even the nature of space and time. On the way, we, like the
Enterprise,
will encounter black holes and wormholes. But first we ourselves must travel back in time
to the latter half of the nineteenth century.

The marriage of space and time that heralded the modern era began with the marriage, in
1864, of electricity and magnetism. This remarkable intellectual achievement, based on the
cumulative efforts of great physicists such as AndrŽ-Marie Amp�re, Charles-Augustin de
Coulomb, and Michael Faraday, was capped by the brilliant British physicist James Clerk
Maxwell. He discovered that the laws of electricity and magnetism not only displayed an
intimate relationship with one another but together implied the existence of
“electromagnetic waves,” which should travel throughout space at a speed that one could
calculate based on the known properties of electricity and magnetism. The speed turned out
to be identical to the speed of light, which had previously been measured.

Now, since the time of Newton there had been a debate about whether light was a wavethat
is, a traveling disturbance in some background mediumor a particle, which travels
regardless of the presence of a background medium. The observation of Maxwell that
electromagnetic waves must exist and that their speed was identical to that of light ended
the debate: light was an electromagnetic wave.

Any wave is just a traveling disturbance. Well, if light is an electromagnetic
disturbance, then what is the medium that is being disturbed as the wave travels? This
became the hot topic for investigation at the end of the nineteenth century. The proposed
medium had had a name since Aristotle. It was called the aether, and had thus far escaped
any attempts at direct detection. In 1887, however, Albert A. Michelson and Edward Morley,
working at the institutions that later merged in 1967 to form my present home, Case
Western Reserve University, performed an experiment guaranteed to detect not the aether
but the aether's effects: Since the aether was presumed to fill all of space, the Earth
was presumed to be in motion through it. Light traveling in different directions with
respect to the Earth's motion through the aether ought therefore to show variations in
speed. This experiment has since become recognized as one of the most significant of the
last century, even though Michelson and Morley never observed the effect they were
searching for. In fact, it is precisely because they failed to observe the effect of the
Earth's motion through the aether that we remember their names today. (A. A. Michelson
actually went on to become the first American Nobel laureate in physics for his
experimental investigations into the speed of light, and I feel privileged to hold a
position today which he held more than a hundred years ago. Edward Morley continued as a
renowned chemist and determined the atomic weight of helium, among other things.)

The nondiscovery of the aether did send minor ripples of shock throughout the physics
community, but, like many watershed discoveries, its implications were fully appreciated
only by a few individuals who had already begun to recognize several paradoxes associated
with the theory of electromagnetism. Around this time, a young high school student who had
been eight years old at the time of the Michelson-Morley experiment independently began to
try to confront these paradoxes directly. By the time he was twenty-six, in the year 1905,
Albert Einstein had solved the problem. But as also often occurs whenever great leaps are
made in physics, Einstein's results created more questions than they answered.

Einstein's solution, forming the heart of his special theory of relativity, was based on a
simple but apparently impossible fact: the only way in which Maxwell's theory of
electromagnetism could be self-consistent would be if the observed speed of light was
independent of the observer's speed relative to the light. The problem, however, is that
this completely defies common sense. If a probe is released from the
Enterprise
when the latter is traveling at impulse speed, an observer on a planet below will see the
probe whiz past at a much higher speed than would a crew member looking out an observation
window on the
Enterprise.
However, Einstein recognized that Maxwell's theory would be self-consistent only if light
waves behaved differentlythat is, if their speed as measured by both observers remained
identical, independent of the relative motion of the observers. Thus, if I shoot a phaser
beam out the front of the
Enterprise,
and it travels away from the ship at the speed of light toward the bridge of a Romulan
Warbird, which itself is approaching the
Enterprise
at an impulse speed of 3/4 the speed of light, those on the enemy bridge will observe the
beam to be heading toward them just at the speed of light and not at 13/4 times the speed
of light. This sort of thing has confused some trekkers, who imagine that if the
Enterprise
is moving at near light speed and another ship is moving in the opposite direction at near
light speed, the light from the
Enterprise
will never catch up with the other ship (and therefore the
Enterprise
will not be visible to it). Instead, those on the other ship will see the light from the
Enterprise
approaching at the speed of light.

This realization alone was not what made Einstein's a household name. More important was
the fact that he was willing to explore the implications of this realization, all of which
on the surface seem absurd. In our normal experience, it is time and space that are
absolute, while speed is a relative thing: how fast something is perceived to be moving
depends upon how fast you yourself are moving. But as one approaches light speed, it is
speed that becomes an absolute quantity, and therefore
space and time must become relative!

This comes about because speed is literally defined as distance traveled during some
specific time. Thus, the only way observers in relative motion can measure a single light
ray to traverse the same distancesay, 300 million metersrelative to each of them in, say,
one second is if each of their “seconds” is different or each of their “meters” is
different! It turns out that in special relativity, the “worst of both worlds” happensthat
is, seconds and meters both become relative quantities.

From the simple fact that the speed of light is measured to be the same for all observers,
regardless of their relative motion, Einstein obtained the four following consequences for
space, time, and matter:

(a) Events that occur for one observer
at the same time in two different places
need not be simultaneous to another observer moving with respect to the first.
Each person's “now” is unique to themselves. “Before” and “after” are relative for
distant events.

(b) All clocks on starships that are moving relative to me will appear to me to be ticking
more slowly than my clock.
Time is measured to slow down for objects in motion.

(c) All yardsticks on starships that are moving relative to me will appear shorter than
they would if they were standing still in my frame.
Objects, including starships, are measured to contract if they are moving.

(d)All massive objects get heavier the faster they travel. As they approach the speed of
light, they become infinitely heavy.
Thus, only massless objects, like light, can actually travel at the speed of light.

This is not the place to review all of the wonderful apparent paradoxes that relativity
introduces into the world. Suffice it to say that, like it or not, consequences (a)
through (d) are truethat is, they have been tested. Atomic clocks have been carried aloft
in high-speed aircraft and have been observed to be behind their terrestrial counterparts
upon their return. In high-energy physics laboratories around the world, the consequences
of the special theory of relativity are the daily bread and butter of experiment. Unstable
elementary particles are made to

move near the speed of light, and their lifetimes are measured to increase by huge
factors. When electrons, which at rest are 2000 times less massive than protons, are
accelerated to near light speed, they are measured to carry a momentum equivalent to that
of their heavier cousins. Indeed, an electron accelerated to
.999999999999999999999999999999999999999999999999999999 99999999 times the speed of light
would hit you with the same impact as a Mack truck traveling at normal speed.

Of course, the reason all these implications of the relativity of space and time are so
hard for us to accept at face value is that we happen to live and move at speeds far
smaller than the speed of light. Each of the above effects becomes noticeable only when
one is moving at “rel-ativistic” speeds. For example, even at half the speed of light,
clocks would slow and yardsticks would shrink by only about 15 percent. On NASA's space
shuttle, which moves at about 5 miles per second around the Earth, clocks tick less than
one ten-millionth of a percent slower than their counterparts on Earth.

However, in the high-speed world of the
Enterprise
or any other starship, relativity would have to be confronted on a daily basis. Indeed, in
managing a Federation, one can imagine the difficulties of synchronizing clocks across a
large segment of the galaxy when a great many of these clocks are moving at close to light
speed. As a result, Starfleet apparently has a rule that normal impulse operations for
starships are to be limited to a velocity of 0.25
c
that is, 1/4 light speed, or a mere 75,000 km/sec.
2

Even with such a rule, clocks on ships traveling at this speed will slow by slightly over
3 percent compared with clocks at Starfleet Command. This means that in a month of travel,
clocks will have slowed by almost one day. If the
Enterprise
were to return to Starfleet Command after such a trip, it would be Friday on the ship but
Saturday back home. I suppose the inconvenience would not be any worse than resetting your
clocks after crossing the international date line when traveling to the Orient, except in
this case the crew would
actually be
one. day younger after the round-trip, whereas on a round-trip to the Orient you gain one
day going in one direction and lose one going in the other.

You can now see how important warp drive is to the
Enterprise.
Not only is it designed to avoid the ultimate speed limitthe speed of lightand so allow
practical travel across the galaxy, but it is also designed to avoid the problems of time
dilation, which result when the ship is traveling close to light speed.

I cannot overemphasize how significant these facts are. The fact that clocks slow down as
one approaches the speed of light has been taken by science fiction writers (and indeed by
all those who have dreamed of traveling to the stars) as opening the possibility that one
might cross the vast distances between the stars in a human lifetimeat least a human
lifetime for those aboard the spaceship. At close to the speed of light, a journey to,
say, the center of our galaxy would take more than 25,000 years of Earth time. For those
aboard the spaceship, if it were moving sufficiently close to light speed, the trip might
take less than 10 yearsa long time, but not impossibly so. Nevertheless, while this might
make individual voyages of discovery possible, it would make the task of running a
Federation of civilizations scattered throughout the galaxy impossible. As the writers of
Star Trek have correctly surmised, the fact that a 10-year journey for the
Enterprise
would correspond to a 25,000-year period for Starfleet Command would wreak havoc on any
command operation that hoped to organize and control the movements of many such craft.
Thus it is absolutely essential that (a) light speed be avoided, in order not to put the
Federation out of synchronization,
and
(b) faster-than-light speed be realized, in order to move practically about the galaxy.