SpaceTime Hypersurfing

by Michael Szpir

from Volume 82 of American Scientist

In some future history, 1994 may be remembered as the year that the warp drive was first conceived to be a physical possibility. Long a cliche' of science- fiction writing, the warp drive has transported countless fictional characters through light-years of interstellar space in the time it takes for you or me to travel to the market. Unfortunately for real-world travelers, the warp drive has always been thought to be inconsistent with the laws of physics.

But all this has changed. In the May issue of Classical and Quantum Gravity, Miguel Alcubierre, a physicist at the University of Wales describes a space-travel scenario that bears an uncanny resemblance to the warp drive of science fiction. With Alcubierre's warp drive, we could reach any place in the universe in as short a time as we please!

The warp drive envisioned by Alcubierre is made possible by the subleties of Einstein's general theory of relativity. According to Einstein, spacetime (the union of the three dimensions of space with the dimension of time) is not an inert substrate, but rather a dynamical entity that twists and distorts under the influence of concentrations of energy. Alcubierre suggests that it might be possible to exploit this phenomenon to travel from one star to another faster than the speed of light. This could be done by creating a disturbance in spacetime such that the region directly in front of a spaceship is contracted while the region directly behind the spaceship is expanded. This distortion of spacetime would, in effect, propel the spaceship forward like a surfer riding the crest of a breaking wave. At first glance this mechanism would appear to violate Einstein's special theory of relativity, which holds that no object can travel faster than light. Violations of this law lead to causal paradoxes, in which actors in the present can alter their own past. Yet Alcubierre shows that his warp drive does not, in fact, lead to such violations. The reason is that light also travels in spacetime, and is carried along just as the spaceship is. The light beam is still traveling at the speed of light, relative to the spaceship, which itself is not accelerating relative to the spacetime in its immediate vicinity. Although Alcubierre's warp drive does not engender any causal paradoxes, one might still be concerned for a space traveler's welfare. To get to a distant star and back in only moments, the traveler would have to be accelerated at a very large rate, effectively turning him into soup. Or at least this would be true, if not for the fact that accelerations are relative in general relativity.

Although the acceleration of the spaceship as seen by someone on Earth would be enormous, the acceleration experienced by the space traveler would be zero! The space traveler would be weightless, just as astronauts are in orbit around the Earth. Finally, Alcubierre also shows that a traveler using his warp drive would experience no time dilation. One of the predictions of Einstein's special theory of relativity is that time flows at different rates (Keely said that 'Time is Gravity') for observers moving relative to one another. Consider two space travelers, John W. and Campbell Jr., who decide to visit the great galaxy of Andromeda, which is about 2 million light-years away. John travels in a spaceship that advertises "one Earth gravity all the way." Campbell spends most of the trip traveling near the speed of light. Because of time dilation, Campbell is able to survive the trip, aging only 60 years in the process. However, because the galaxy is 2 million light years away, about 4 million years pass on Earth before Campbell gets home. In contrast, John is able to make the journey to the galaxy and be back in time for supper on Earth!

Of course, there is no such thing as a free lunch (or supper). The key to Alcubierre's warp drive is something called exotic matter. Exotic matter has the curious property of having a negative energy density, unlike normal matter (the stuff that makes up people, planets and stars), which has a positive energy density. Two bits of matter that have the same energy density are attracted to each other by gravity. In contrast, bits of positive and negative energy matter would be repelled by gravity. It is the negative energy density of exotic matter that powers the warp drive. A negative energy density is not the nonsensical thing it appears to be. Indeed, in 1948 the Dutch physicist Hendrik Casimir first predicted that one could observe the effects of negative energy densities. He reasoned that if negative energy densities existed, two closely spaced parallel conducting plates in a vacuum would be attracted to one another. This phenomenon, now called the Casimir effect, was measured in 1958 by M. Sparnaay, and is usually taken to be a confirmation that negative energy densities are possible. Exotic matter of a slightly different type is also invoked in the modern theory of cosmology known as inflation. According to the theory of inflation, exotic matter in the early universe (moments after the big bang) had a positive energy density, but a very large negative pressure. The negative pressure was so large that it counteracted the effects of the positive energy density. The result was an expansion of spacetime so rapid that two observers originally very close to each other would be carried apart faster than the speed of light.

This paradigm of spacetime expansion provided the motivation for Alcubierre's warp drive. There are, of course, 'technical details' to be worked out before the aerospace firms can start building starships. Foremost among these is the production of exotic matter. Alcubierre has not given that aspect of the problem much thought. Although he is an avid reader of science fiction, he does not intend to pursue the subject much further. Currently, he spends most of his time working on other problems with general relativity. The warp-drive scenario, he says, is a very simple thing that he came up with in his spare time. Perhaps the problem will be taken up by some future physicists in their 'spare time'. The rewards could be astronomical.