Negative Energy, Worm Holes, and Warp Drives

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."