Physicist Thomas Roman of Central Connecticut State University
offers the following response:
Animation: Kenneth Jones
FASTER-THAN-LIGHT TRAVEL, depicted in
series such as Star Trek, is not possible--except for maybe
inside a spacetime or Alcubierre warp bubble.
theory of relativity predicts that nothing can exceed the speed of
light. But special relativity applies when spacetime is flat. When
spacetime is curved, the theory applies only "locally"--that is, over
regions of spacetime small enough to be considered flat. Consider the
analogy of a plane that is tangent to a sphere. The flat geometry of the
plane is a good approximation to the geometry of the sphere when the size
of the plane is very small compared to the sphere's radius of curvature.
In curved spacetimes, when we compare two observers at large separation,
we can no longer use the "locally flat" approximation. In the plane-and-sphere
analogy, this situation would correspond to comparing two observers on the
sphere separated by a distance comparable to the sphere's radius of
curvature. Although each observer could approximate the geometry in his or
her local region as a plane, there is no single plane that would be
applicable to both observers. Consequently, the two observers in curved
spacetime can each apply special relativity in their own local region, but
A similar situation arises in an
expanding universe. Here one should not think of the galaxies as
moving through space, but rather that the space between the galaxies is
expanding. Einstein's general theory of relativity, on which such models
are based, imposes no restrictions on the rate
at which the expansion of space can drive the galaxies apart. But special
relativity still applies locally, in the sense that a particle chasing a
light ray can never catch up to it. An analogy is to imagine bugs crawling
on a rubber sheet. By stretching the sheet we can make the bugs recede
from each other at arbitrarily high speeds, but no bug can crawl across
the sheet faster than a light beam.
In serious proposals for "warp drive,"
such as the Alcubierre warp bubble, space is flat inside the bubble and
special relativity applies. In this region, nothing can travel faster than
light--relative to observers inside the bubble. Outside the bubble,
spacetime is also flat and no particle can travel faster than light--relative
to observers outside the bubble. But because of the large expansion and
contraction of the spacetime in the wall of the bubble, the inside of the
bubble can move faster than light relative to the outside. This would also
be true of light rays inside the bubble; they would be carried along by
the spacetime warp, too. What causes this mismatch of the two flat
spacetime regions is the large spacetime curvature in the bubble wall that
separates the regions.
Cosmologist Martin Bucher of the University of
Cambridge adds this insight:
Image: Slim Films
WORMHOLE. If nature allowed them,
wormholes would appear as spherical openings to an otherwise distant
part of the cosmos. This doctored photograph shows a wormhole in
Times Square that opens onto the Sahara Desert one city block away.
In the pre-Einsteinian conception of the nature of space and time,
there is no limit in principle to how fast an object can travel. But in
Einstein's special theory of relativity, the notion of causality--of the
past completely determining the future--would break down if any type of
matter, energy or signal were able to travel faster than light.
In the pre-Einsteinian framework, time has an absolute character. The
time of an event--and thus its time ordering--is the same to all observers;
velocities add according to ordinary addition. For very small velocities (small
compared to the velocity of light), the same holds in relativity, but for
large velocities significant modifications occur. Early in the 20th
century the Michelson-Morley
experiment established that the speed of light is the same to all
observers whatever their relative motion. Therefore the law for adding
velocities must be modified. The relative velocity of two objects, one
traveling at the same of light and the other traveling at sublight speeds,
must equal the speed of light. When both are traveling at sublight speeds,
the relative velocity must be less than the speed of light.
One surprising consequence is that time loses its absolute character.
The times perceived by observers moving with respect to each other do not
coincide. But observers always agree on the ordering of events. If we
admit the possibility of faster-than-light speeds, some observers would
perceive one event as occurring before another, others would perceive them
as occurring simultaneously, and a third group would perceive the reverse
order. The time ordering is invariant only when the two events can be
linked by a signal traveling at a speed slower than or equal to the speed
In the context of an expanding universe, it is often stated that widely
separated points move apart faster than the speed of light. At first sight
this would seem impossible. But an expanding universe must be considered
within Einstein's general theory of relativity, a generalization of the
special theory of relativity. In general relativity, motion relative to
the speed of light is defined locally. The separation between two distant
points can increase faster than the speed of light as a result of the
swelling of the intervening spacetime. Nothing can pass through the space
faster than light, but space itself can carry things apart superluminally.
Answer posted December 13, 1999
relativity and faster-than-light travel
The Inflationary Universe, by Alan H. Guth. Addison Wesley (1997). See
the footnote on page 183.
The Physics of Star Trek, by Lawrence M. Krauss. Basic Books (1995).
See Chapter 4.
Beyond Star Trek, by Lawrence M. Krauss. Basic Books (1997). See pages
Darkness at Night, by Edward Harrison. Harvard University Press (1987).
See pages 180-181.
Cosmology, by Edward Harrison. Cambridge University Press (1981). See
General Relativity, by Robert M. Wald. University of Chicago Press
(1984). See page 98.