*Prepared by***
**

*Bob Seitz***
**

*April 8, 2000*

Among the blue-sky loopholes in the laws of physics that might be invoked to effectively permit faster-than-light travel are worm holes and negative energy concepts. The following passages are taken from, "Negative Energy, Wormholes, and Warp Drive" by Lawrence H. Ford and Tom Roman, in the January, 2000, Issue of Scientific American (pg. 46).

__Worm
Holes:__

"The black hole is
not the only curved region of space-time where negative energy seems to
play a role. Another is the wormhole—a hypothesized type of tunnel that
connects one region of space and time to aother. Physicists used to think
that wormholes exist only on the very finest length scales, bubbling in
and out of existence like virtual particles [see "Quantum Gravity," by
Bryce S. DeWitt, SCIENTIFIC AMERICAN, December, 1983]. In the early 1960s,
physicists Robert Fuller and John A. Wheeler showed that larger wormholes
would collapse under their own gravity so rapidly that even a beam of light
would not have enough time to travel through them. But in the late 1980s
various researchers notably Michael S. Morris and Kip S. Thorne of the
California Institute of Technology found otherwise. Certain wormholes could
in fact be made large enough for a person or spaceship. Someone might enter
the mouth of a wormhole stationed on Earth, walk a short distance inside
the wormhole, and exit the other mouth in, say, the Andromeda galaxy. The
catch is that traversable wormholes require negative energy. Because negative
energy is gravitationally repulsive, it would prevent the wormhole from
collapsing.

"For a wormhole to
be traversable, it ought to (at a bare minimum) allow signals, in the form
of light rays, to pass through it. Light rays entering one mouth of a wormhole
are converging but to emerge from the other mouth, they must go from converging
to diverging somewhere in between [*see illustration below*] This
defocusing requires negative enery, Whereas the curvature of space produced
by the attractive gravitational field of ordinary matter acts like a converging
lens, negative energy acts like a diverging lens.

"When applied to wormholes
and warp drives, the quantum inequalities typically imply that such structures
must either be limited to submicroscopic sizes, or if they are macroscopic
the negative energy must be confined to incredibly thin bands. In 1996,
we showed that a submicroscopic wormhole would have a throat radius of
no more than about 10^{-32} meters. This is
only slightly larger than the Planck length, 10^{-35}
meter, the smallest distance that has definite meaning. We found that it
is possible to have models of wormholes of macroscopic sizee but
only at the price of confining the negative energy to an extremely thin
band around the throat. For example, in one model, a throat radius of 1
meter requires the negative energy to be in a band no thicker than 10^{-21}
meter, a millionth the size of the proton. Visser has estimated that__
the negative energy required for this size of wormhole has a magnitude
equivalent to the total energy output of a star over its 10,000,000,000-year
lifespan__. The situation does not improve much for larger wormholes.
For the same model, the maximum allowed thickness of the negative
energy band is proportional to the cube root of the throat radius. Even
if the throat radius is increased to a size of one light-year, the negative
enegy must still be confined to a region smaller than a proton radius,
and the total amount required increases linearly with the throat size.

"It seems that wormhole
engineers face daunting problems. They must find a mechanism for confining
large amounts of negative energy to extremely thin volumes. So-called cosmic
strings, hypothesized in some coxmological theories, involve very large
energy densities in long, narrow lines. But all known physically reasonable
cosmic-string models have positive energy densities."

__Warp
Drives__

"Such space-time contortions
would enable another staple of science fiction as well: faster-than-light
travel. In 1994, Miguel Alcubiere Moya, then at the University of Wales
at Cardiff, discovered a solution to Einstein's equations that has many
of the desired features of warp drive. It describes a space-time bubble
that transports a starship at arbitrarily high speeds relative to observers
outside the bubble, Calculations show that negative energy is required.

"Warp drives might appear
to violate Einstein's special theory of relativity. Bu special relativity
says that you cannot outrun a light signal in a fair race in which you
and the signal follow the same route. When space-time is warped, it might
be possible to beat a light signal by taking a different route, a shortcut.
The contraction of space-time in front of the bubble and the expansion
behind it create such a shortcut [see illustration above].

"One problem with Alcubierre's
original model, pointed out by Sergei V. Krasnikov of the Central Astronomical
Observatory at Pulkovo near St. Petersburg, is that the interior of the
warp bubble is causally disconnected from its forward edge. A starship
captain on the inside cannot steer the bubble or turn it on or off; some
external agency must set it up ahead of time. To get around this problem,
Krasnikov proposed a "superluminal subway," a tube of modified space-time
(not the same as a wormhole) connecting Earth and a distant star. Within
the tube, superluminal travel in one direction is possible. During the
outbound journey at sublight speeds, a spaceship crew would create such
a tube. On the return journey, they could travel through it at warp speed.
Like warp bubbles, the subway involves negative energy. It has since been
shown by Ken D. Olum of Tufts University and by Visser, together with Bruce
Bassett of Oxford and Stefano Liberati of the Intenational School for Avanced
Studies in Triests, that any scheme for faster-than-light travel involves
the use of negative energy.

"If one can construct
wormholes or warp drives, time travel might become possible. The passage
of time is relative; it depends upon the observer's velocity. A person
who leaves Earth in a spaceship, travels at near lightspeed and returns
will have aged less than someone who remains on Earth. If the traveler
manages to outrun a light ray, perhaps by taking a shortcut through a wormhole
or a warp bubble, he may return before he left.

"Warp drives are even more
tightly constrained than wormholes, as shown by Pfenning and Allen Everett
of Tufts, working with us. In Alcubierre's model, a warp bubble traveling
at 10 times lightspeed (warp factor 2, in the parlance of *Star Trek,
The Next Generation*) must have a wall thickness of no more than 10^{-32}
meter. A bubble large enough to enclose a starship 200 meters across would
require a total amount of negative energy equal to __10 billion times
the mass of the observable universe__. Similar constraints apply to Krasnikov's
superluminal subway. A modification of Alcubierre's model was reecently
constructed by Chris Van Den Broeck of the Catholic University of Louvain
in Belgium. It requires much less negative energy but places the starship
in a curved space-time bottle whose neck is about 10^{-32} meters
across, a difficult feat. These results would seem to make it rather unlikely
that one could constuct wormholes and warp drives using negative energy
generated by quantum effects."