The Physics of Star Trek (4 page)

The kicker is that, in the context of special relativity alone, the latter possibility
cannot be realized.
Physics becomes full of impossibilities if super light speed is allowed. Not least among
the problems is that because objects get more massive as they approach the speed of light,
it takes progressively more and more energy to accelerate them by a smaller and smaller
amount. As in the myth of the Greek hero Sisyphus, who was condemned to push a boulder
uphill for all eternity only to be continually thwarted near the very top, all the energy
in the universe would not be sufficient to allow us to push even a speck of dust, much
less a starship, past this ultimate speed limit.

By the same token, not just light but all massless radiation
must
travel at the speed of light. This means that the many types of beings of “pure energy”
encountered by the
Enterprise,
and later by the
Voyager,
would have difficulty existing as shown. In the first place, they wouldn't be able to sit
still. Light cannot be slowed down, let alone stopped in empty space. In the second place,
any form of intelligent-energy being (such as the “photonic”

energy beings in the
Voyager
series; the energy beings in the Beta Renna cloud, in
The Next Generation;
the Zetarians, in the original series; and the Dal'Rok, in
Deep Space Nine),
which is constrained to travel at the speed of light, would have clocks that are
infinitely slowed compared to our own. The entire history of the universe would pass by in
a single instant. If energy beings could experience anything, they would experience
everything at once! Needless to say, before they could actually interact with corporeal
beings the corporeal beings would be long dead.

Speaking of time, I think it is time to introduce the Picard Maneuver. Jean-Luc became
famous for introducing this tactic while stationed aboard the
Stargazer.
Even though it involves warp travel, or super light speed, which I have argued is
impossible in the context of special relativity alone, it does so for just an instant and
it fits in nicely with the discussions here. In the Picard Maneuver, in order to confuse
an attacking enemy vessel, one's own ship is accelerated to warp speed for an instant. It
then appears to be in two places at once. This is because, traveling faster than the speed
of light for a moment, it
overtakes
the light rays that left it the instant before the warp drive was initiated. While this is
a brilliant stategyand it appears to be completely consistent as far as it goes (that is,
ignoring the issue of whether it is possible to achieve warp speed)I think you can see
that it opens a veritable Pandora's can of worms. In the first place, it begs a question
that has been raised by many trekkers over the years: How can the
Enterprise
bridge crew “see” objects approaching them at warp speed? Just as surely as the
Stargazer
overtook its own image, so too will all objects traveling at warp speed; one shouldn't be
able to see the moving image of a warp-speed object until long after it has arrived. One
can only assume that when Kirk, Picard, or Janeway orders up an image on the viewscreen,
the result is an image assembled by some sort of long-range “subspace” (that is,
super-light-speed communication) sensors. Even ignoring this apparent oversight, the Star
Trek universe would be an interesting and a barely navigable one, full of ghost images of
objects that long ago arrived where they were going at warp speed.

Moving back to the sub-light-speed world: We are not through with Einstein yet. His famous
relation between

mass and energy,
E=mc
2
,
which is a consequence of special relativity, presents a further challenge to space travel
at impulse speeds. As I have described it in chapter 1, a rocket is a device that propels
material backward in order to move forward. As you might imagine, the faster the material
is propelled backward, the larger will be the forward impulse the rocket will receive.
Material cannot be propelled backward any faster than the speed of light. Even propelling
it at light speed is not so easy: the only way to get propellant moving backward at light
speed is to make the fuel out of matter and antimatter, which (as I describe in a later
chapter) can completely annihilate to produce pure radiation moving at the speed of light.

However, while the warp drive aboard the
Enterprise
uses such fuel, the impulse drive does not. It is powered

instead by nuclear fusionthe same nuclear reaction that powers the Sun by turning hydrogen
into helium. In fusion reactions, about 1 percent of the available mass is converted into
energy. With this much available energy, the helium atoms that are produced can come
streaming out the back of the rocket at about an eighth of the speed of light. Using this
exhaust velocity for the propellant, we then can calculate the amount of fuel the
Enterprise
needs in order to accelerate to, say, half the speed of light. The calculation is not
difficult, but I will just give the answer here. It may surprise you. Each time the
Enterprise
accelerates to half the speed of light, it must burn 81
TIMES ITS ENTIRE MASS
in hydrogen fuel. Given that a Galaxy Class starship such as Picard's
Enterprise-D
would weigh in excess of 4 million metric tons,
3
this means that over 300 million metric tons of fuel would need to be used each time the
impulse drive is used to accelerate the ship to half light speed! If one used a
matter-antimatter propulsion system for the impulse drive, things would be a little
better. In this case, one would have to burn merely
twice
the entire mass of the
Enterprise
in fuel for each such acceleration.

It gets worse. The calculation I described above is correct for a single acceleration. To
bring the ship to a stop at its destination would require the same factor of 81 times its
mass in fuel. This means that just to go somewhere at half light speed and stop again
would require fuel in the amount of 81x81= 6561 TIMES
THE ENTIRE SHIP'S MASS!
Moreover, say that one wanted to achieve the acceleration to half the speed of light in a
few hours (we will assume, of course, that the inertial dampers are doing their job of
shielding the crew and ship from the tremendous G-forces that would otherwise ensue). The
power radiated as propellant by the engines would then be about 10
22
wattsor about a billion times the total average power presently produced and used by all
human

activities on Earth!

Now, you may suggest (as a bright colleague of mine did the other day when I presented him
with this argument) that there is a subtle loophole. The argument hinges on the
requirement that you carry your fuel along with the rocket. What if, however, you harvest
your fuel as you go along? After all, hydrogen is the most abundant element

in the universe. Can you not sweep it up as you move through the galaxy? Well, the average
density of matter in our galaxy is about one hydrogen atom per cubic centimeter. To sweep
up just one gram of hydrogen per second, even moving at a good fraction of the speed of
light, would require you to deploy collection panels with a diameter of over 25 miles. And
even turning all this matter into energy for propulsion would provide only about a
hundred- millionth of the needed propulsion power!

To paraphrase the words of the Nobel prizewinning physicist Edward Purcell, whose
arguments I have adapted and extended here:

If this sounds preposterous to you, you are right. Its preposterousness follows from the
elementary laws of classical mechanics and special relativity. The arguments presented
here are as inescapable as the fact that a ball will fall when you drop it at the Earth's
surface. Rocket-propelled space travel through the galaxy at near light speed
is not physically practical,
now or ever!

So, do I end the book here? Do we send back our Star Trek memorabilia and ask for a
refund? Well, we are still not done with Einstein. His final, perhaps greatest discovery
holds out a glimmer of hope after all.

Fast rewind back to 1908: Einstein's discovery of the relativity of space and time heralds
one of those “Aha!” experiences that every now and then forever change our picture of the
universe. It was in the fall of 1908 that the mathematical physicist Hermann Minkowski
wrote these famous words: “Henceforth, space by itself, and time by itself, are doomed to
fade away into mere shadows, and only a kind of union of the two will preserve an
independent reality.”

What Minkowski realized is that even though space and time are relative for observers in
relative motionyour clock can tick slower than mine, and my distances can be different
from yoursif space and time are instead merged as part of a four-dimensional whole (three
dimensions of space and one of time), an “absolute” objective reality suddenly reappears.

The leap of insight Minkowski had can be explained by recourse to a world in which
everyone has monocular vision and thus no direct depth perception. If you were to close
one eye, so that your depth perception was reduced, and I were to hold a ruler up for you
to see, and I then told someone else, who was observing from a different angle, to close
one eye too, the ruler I was holding up would appear to the other observer to be a
different length than it would appear to be to youas the following bird's-eye view shows.

Each observer in the example above, without the direct ability to discern depth, will
label “length” (L or L') to be the two-dimensional projection onto his or her plane of
vision of the actual three-dimensional length of the ruler. Now, because we know that
space has three dimensions, we are not fooled by this trick. We know that viewing
something from a different angle does not change its real length, even if it changes its
apparent length. Minkowski showed that the same idea can explain the various paradoxes of
relativity, if we now instead suppose that our perception of space is merely a
three-dimensional slice of what is actually a four-dimensional manifold in which space and
time are joined. Two different observers in relative motion perceive
different
three-dimensional slices of the underlying four-dimensional space in much the same way
that the two rotated observers pictured here view
different
two-dimensional slices of a three-dimensional space.

Minkowski imagined that the spatial distance measured by two observers in relative motion
is a projection of an underlying
four-dimensional spacetime distance
onto the three-dimensional space that they can sense; and, similarly, that the temporal
“distance” between two events is a projection of the four-dimensional spacetime distance
onto their own timeline. Just as rotating something in three dimensions can mix up width
and depth, so relative motion in four-dimensional space can mix up different observers'
notions of “space” and “time.” Finally, just as the length of an object does not change
when we rotate it in space, the four-dimensional spacetime distance between two events is
absoluteindependent of how different observers in relative motion assign “spatial” and
“temporal” distances.

So the crazy invariance of the speed of light for all observers provided a key clue to
unravel the true nature of the four-dimensional universe of spacetime in which we actually
live.
Light displays the hidden connection between space and time.
Indeed, the speed of light
defines
the connection.

It is here that Einstein returned to save the day for Star Trek. Once Minkowski had shown
that spacetime in special relativity was like a four-dimensional sheet of paper, Einstein
spent the better part of the next decade flexing his mathematical muscles until he was
able to bend that sheet, which in turn allows us to bend the rules of the game. As you may
have guessed, light was again the key.

Shows His Hand
“How little do you mortals understand time. Must you be so linear, Jean-Luc?”

Q
to Picard, in "All Good Things... .

The planet Vulcan, home to Spock, actually has a venerable history in twentieth-century
physics. A great puzzle in astrophysics in the early part of this century was the fact
that the perihelion of Mercurythe point of its closest approach to the Sunwas precess-ing
around the Sun each Mercurian year by a very small amount in a way that was not consistent
with Newtonian gravity. It was suggested that a new planet existed inside Mercury's orbit
which could perturb it in such a way as to fix the problem. (In fact, the same solution to
an anomaly in the orbit of Uranus had earlier led to the discovery of the planet Neptune.)
The name given to the hypothetical planet was Vulcan.

Alas, the mystery planet Vulcan is not there. Instead, Einstein proposed that the flat
space of Newton and Minkowski had to be given up for the curved spacetime of general
relativity. In this curved space, Mercury's orbit would deviate slightly from that
predicted by Newton, explaining the observed discrepancy. While this removed the need for
the planet Vulcan, it introduced possibilities that are much more exciting. Along with
curved space come black holes, wormholes, and perhaps even warp speeds and time travel.

Indeed, long before the Star Trek writers conjured up warp fields, Einstein warped
spacetime, and, like the Star Trek writers, he was armed with nothing other than his
imagination. Instead of imagining twenty-second-century starship technology, however,
Einstein imagined an elevator. He was undoubtedly a great physicist, but he probably never
would have sold a screenplay.

Nonetheless, his arguments remain intact when translated aboard the
Enterprise.
Because light is the thread that weaves together space and time, the trajectories of light
rays give us a map of spacetime just as surely as warp and weft threads elucidate the
patterns of a tapestry. Light generally travels in straight lines. But what if a Romulan
commander aboard a nearby Warbird shoots a phaser beam at Picard as he sits on the bridge
of his captain's yacht
Calypso,
having just engaged the impulse drive (we will assume the inertial dampers are turned off
for this example)? Picard would accelerate forward, narrowly missing the brunt of the
phaser blast. When viewed in Picard's frame of reference, things would look like the
figure at the top of the following page.