exoticspaces A WORMHOLE WOULD APPEAR as a spherical opening to a distant part of the cosmos. In this doctored photograph of Times Square, the wormhole allows New Yorkers to walk to the Sahara with a single step. Although such a wormhole does not break any known laws of physics, it would require unrealistic amounts of negative energy. NEGATIVE WORMHOLES The construction of wormholes and warp drive But the same laws of physics that allow this 84 SCIENTIFIC AMERICAN Updated from the January 2000 issue COPYRIGHT 2003 SCIENTIFIC AMERICAN, INC. By Lawrence H. Ford ENERGY, and Thomas A. Roman and WARP DRIVE would require a very unusual form of energy. “negative energy” also appear to limit its behavior www.sciam.com THE EDGE OF PHYSICS 85 COPYRIGHT 2003 SCIENTIFIC AMERICAN, INC. Can a region of space contain less than nothing? Common sense would say no; the most one could do is remove potential paradoxes of backward time travel—such as killing all matter and radiation and be left with a vacuum. But quan- your grandfather before your father is conceived—have long tum physics has a proven ability to confound intuition, and this been explored in science fiction, and the other consequences case is no exception. A region of space, it turns out, can contain of exotic matter are also problematic. They raise a question of less than nothing. Its energy per unit volume—the energy den- fundamental importance: Do the laws of physics that permit sity—can be less than zero. negative energy place any limits on its behavior? We and oth- Needless to say, the implications are bizarre. According to ers have discovered that nature imposes stringent constraints general relativity, Einstein’s theory of gravity, the presence of on the magnitude and duration of negative energy, which (un- matter and energy warps the geometric fabric of space and time. fortunately, some would say) appear to render the construction What we perceive as gravity is the spacetime distortion pro- of wormholes and warp drives very unlikely. duced by normal, positive energy or mass. But when negative energy or mass—so-called exotic matter—bends spacetime, all Double Negative sorts of amazing phenomena might become possible: travers- BEFORE PROCEEDING, we should draw attention to what able wormholes, which could act as tunnels to otherwise dis- negative energy is not. It should not be confused with antimat- tant parts of the universe; warp drive, which would allow for ter, which has positive energy. When an electron and its an- faster-than-light travel; and time machines, which might per- tiparticle, a positron, collide, they annihilate. The end products mit journeys into the past. Negative energy could even be used are gamma rays, which carry positive energy. If antiparticles to make perpetual-motion machines or to destroy black holes. were composed of negative energy, such an interaction would For physicists, these ramifications set off alarm bells. The result in a final energy of zero. One should also not confuse neg- ) ative energy with the energy associated with the cosmological Energy ORDINARY LIGHT constant, postulated in inflationary models of the universe. In this page density the latter case, there is negative pressure but positive energy. (Some authors call this exotic matter; we reserve that term for negative energy densities.) The concept of negative energy is not pure fantasy; some ); LISA BURNETT ( of its effects have even been produced in the laboratory. They arise from Heisenberg’s uncertainty principle, which requires that the energy density of any electric, magnetic or other field preceding pages fluctuate randomly. Even when the energy density is zero on av- ) ( 0 Position erage, as in a vacuum, it fluctuates. Thus, the quantum vacuum Sahara can never remain empty in the classical sense of the term; it is ( Energy SQUEEZED STATE density a roiling sea of “virtual” particles spontaneously popping in and out of existence. In quantum theory, the usual notion of Corbis zero energy corresponds to the vacuum with all these fluctua- LAWRENCE H. FORD and THOMAS A. ROMAN have collaborated on negative energy issues for more than a decade. Ford received his ); JULIA WATERLOW Ph.D. from Princeton University in 1974 under John Wheeler, one of the founders of black hole physics. He is now professor of Position 0 physics at Tufts University and works on problems in both gener- Times Square al relativity and quantum theory, with a special interest in quan- THE AUTHORS tum fluctuations. Roman received his Ph.D. in 1981 from Syracuse University under Peter Bergmann, who collaborated with Albert Ein- WAVES OF LIGHT ordinarily have a positive or zero energy density at different stein on unified field theory. He is currently professor of physics points in space (top). But in a so-called squeezed state, the energy density at a particular instant in time can become negative at some locations at Central Connecticut State University. His interests include the (bottom). To compensate, the peak positive density must increase. implications of negative energy for a quantum theory of gravity. SLIM FILMS; DAN WAGNER ( 86 SCIENTIFIC AMERICAN THE EDGE OF PHYSICS COPYRIGHT 2003 SCIENTIFIC AMERICAN, INC. tions. So if one can somehow contrive to dampen the undula- SPACE OUTSIDE OF WORMHOLE tions, the vacuum will have less energy than it normally does— that is, less than zero energy. MOUTH A As an example, researchers in quantum optics have creat- LIGHT RAY ed special states of fields in which destructive quantum inter- ference suppresses the vacuum fluctuations. These so-called NEGATIVE ENERGY squeezed vacuum states involve negative energy. More pre- THROAT cisely, they are associated with regions of alternating positive and negative energy. The total energy averaged over all space B remains positive; squeezing the vacuum creates negative ener- gy in one place at the price of extra positive energy elsewhere. A typical experiment involves laser beams passing through non- linear optical materials. The intense laser light induces the ma- terial to create pairs of light quanta, photons. These photons alternately enhance and suppress the vacuum fluctuations, lead- ing to regions of positive and negative energy, respectively. WORMHOLE ACTS AS A TUNNEL between two different locations in space. Light rays traveling from A to B can enter one mouth of the wormhole, pass Another method for producing negative energy introduces through the throat and exit the other mouth—a journey that would take geometric boundaries into a space. In 1948 Dutch physicist Hen- much longer if they had to go the long way around. At the throat must be drik B. G. Casimir showed that two uncharged parallel metal negative energy (blue), the gravitational field of which allows converging plates alter the vacuum fluctuations in such a way as to attract light rays to begin diverging. (This diagram is a two-dimensional each other. The energy density between the plates was later cal- representation of three-dimensional space. The mouths and throat of the wormhole are actually spheres.) A wormhole could also connect two culated to be negative. In effect, the plates reduce the fluctuations different points in time (not shown here). in the gap between them; this creates negative energy and pres- sure, which pulls the plates together. The narrower the gap, the black hole’s horizon is a one-way street; energy can only flow more negative the energy and pressure, and the stronger the at- inward. So how can a black hole radiate energy outward? Be- tractive force. The Casimir effect has been measured by Steve K. cause energy must be conserved, the production of positive en- Lamoreaux of Los Alamos National Laboratory and by Umar ergy—which distant observers see as the Hawking radiation— Mohideen of the University of California at Riverside and his col- is accompanied by a flow of negative energy into the hole. Here league Anushree Roy. Other groups have recently confirmed the negative energy is produced by the extreme spacetime cur- these experiments and have even begun to explore the role of the vature near the hole, which disturbs the vacuum fluctuations. effect in nanotechnology. Similarly, in the 1970s Paul C. W. In this way, negative energy is required for the consistency of Davies and Stephen A. Fulling, then at King’s College at the Uni- the unification of black hole physics with thermodynamics. versity of London, predicted that a moving boundary, such as a The black hole is not the sole curved region of spacetime moving mirror, could produce a flux of negative energy. where negative energy seems to play a role. Another is the For both the Casimir effect and squeezed states, researchers wormhole—a hypothesized type of tunnel that connects one re- have measured only the indirect effects of negative energy. Di- gion of space and time to another. Physicists used to think that rect detection is more difficult but might be possible using atom- wormholes exist only on the very finest scales, bubbling in and ic spins, as Peter G. Grove, then at the British Home Office, out of existence like virtual particles. Adrian C. Ottewill, then at the University of Oxford, and one But in the late 1980s various researchers—notably Michael of us (Ford) suggested in 1992. S. Morris and Kip S. Thorne, both of the California Institute of Technology, and Matt Visser of Washington University—found Gravity and Levity that certain wormholes could in fact be made large enough for THE CONCEPT OF NEGATIVE ENERGY arises in several ar- a person or spaceship. Someone might enter the mouth of a eas of modern physics. It has an intimate link with black holes. wormhole stationed on Earth, walk a short distance inside the In 1974 Stephen W.