Can a region of space contain less than nothing? Common sense would say no; the most one could do is remove all matter and radiation and be left with vacuum. But quantum physics has a proven ability to confound intuition, and this case is no exception. A region of space, it turns out, can contain less than nothing. Its energy per unit volume–the energy density–can be less than zero.

Needless to say, the implications are bizarre. According to Einstein's theory of gravity, general relativity, the presence of matter and energy warps the geometric fabric of space and time. What we perceive as gravity is the space-time distortion produced by normal, positive energy or mass. But when negative energy or mass–so-called exotic matter–bends space-time, all sorts of amazing phenomena might become possible: traversable wormholes, which could act as tunnels to otherwise distant parts of the universe; warp drive, which would allow for faster-than-light travel; and time machines, which might permit journeys into the past. Negative energy could even be used to make perpetual-motion machines or to destroy black holes. A Star Trek episode could not ask for more.

For physicists, these ramifications set off alarm bells. The potential paradoxes of backward time travel–such as killing your grandfather before your father is conceived–have long been explored in science fiction, and the other consequences of exotic matter are also problematic. They raise a question of fundamental importance: Do the laws of physics that permit negative energy place any limits on its behavior? We and others have discovered that nature imposes stringent constraints on the magnitude and duration of negative energy, which (unfortunately, some would say) appear to render the construction of wormholes and warp drives very unlikely.


Double Negative

Before proceeding further, we should draw the reader's attention to what negative energy is not. It should not be confused with antimatter, which has positive energy. When an electron and its antiparticle, a positron, collide, they annihilate. The end products are gamma rays, which carry positive energy. If antiparticles were composed of negative energy, such an interaction would result in a final energy of zero. One should also not confuse negative energy with the energy associated with the cosmological constant, postulated in inflationary models of the universe [see "Cosmological Antigravity, by Lawrence M. Krauss; SCIENTIFIC AMERICAN, January 1999]. Such a constant represents negative pressure but positive energy. (Some authors call this exotic matter; we reserve the term for negative energy densities.)

The concept of negative energy is not pure fantasy; some 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 fluctuate randomly. Even when the energy density is zero on average, as in a vacuum, it fluctuates. Thus, the quantum vacuum can never remain empty in the classical sense of the term; it is a roiling sea of "virtual" particles spontaneously popping in and out of existence [see "Exploiting Zero-Point Energy," by Philip Yam; SCIENTIFIC AMERICAN, December 1997]. In quantum theory, the usual notion of zero energy corresponds to the vacuum with all these fluctuations. So if one can somehow contrive to dampen the undulations, the vacuum will have less energy than it normally does–that is, less than zero energy.

As an example, researchers in quantum optics have created special states of fields in which destructive quantum interference suppresses the vacuum fluctuations. These so-called squeezed vacuum states involve negative energy. More precisely, they are associated with regions of alternating positive and negative energy. The total energy averaged over all space remains positive; squeezing the vacuum creates negative energy in one place at the price of extra positive energy elsewhere. A typical experiment involves laser beams passing through nonlinear optical materials [see "Squeezed Light," by Richart E. Slusher and Bernard Yurke; SCIENTIFIC AMERICAN, May 1988]. The intense laser light induces the material to create pairs of light quanta, photons. These photons alternately enhance and suppress the vacuum fluctuations, leading to regions of positive and negative energy, respectively.

Another method for producing negative energy introduces geometric boundaries into a space. In 1948 Dutch physicist Hendrik B. G. Casimir showed that two uncharged parallel metal plates alter the vacuum fluctuations in such a way as to attract each other. The energy density between the plates was later calculated to be negative. In effect, the plates reduce the fluctuations in the gap between them; this creates negative energy and pressure, which pulls the plates together. The narrower the gap, the more negative the energy and pressure, and the stronger is the attractive force. The Casimir effect has recently been measured by Steve K. Lamoreaux of Los Alamos National Laboratory and by Umar Mohideen of the University of California at Riverside and his colleague Anushree Roy. Similarly, in the 1970s Paul C. W. Davies and Stephen A. Fulling, then at King's College at the University of London, predicted that a moving boundary, such as a moving mirror, could produce a flux of negative energy.

For both the Casimir effect and squeezed states, researchers have measured only the indirect effects of negative energy. Direct detection is more difficult but might be possible using atomic spins, as Peter G. Grove, then at the British Home Office, Adrian C. Ottewill, then at the University of Oxford, and one of us (Ford) suggested in 1992.


Gravity and Levity

The concept of negative energy arises in several areas of modern physics. It has an intimate link with black holes, those mysterious objects whose gravitational field is so strong that nothing can escape from within their boundary, the event horizon. In 1974 Stephen W. Hawking of the University of Cambridge made his famous prediction that black holes evaporate by emitting radiation [see "The Quantum Mechanics of Black Holes," by Stephen W. Hawking; SCIENTIFIC AMERICAN, January 1977]. A black hole radiates energy at a rate inversely proportional to the square of its mass. Although the evaporation rate is large only for subatomic size black holes, it provides a crucial link between the laws of black holes and the laws of thermodynamics. The Hawking radiation allows black holes to come into thermal equilibrium with their environment.

At first glance, evaporation leads to a contradiction. The horizon is a one-way street; energy can only flow inward. So how can a black hole radiate energy outward? Because energy must be conserved, the production of positive energy - which distant observers see as the Hawking radiation–is accompanied by a flow of negative energy into the hole. Here the negative energy is produced by the extreme space-time curvature near the hole, which disturbs the vacuum fluctuations. In this way, negative energy is required for the consistency of the unification of black hole physics with thermodynamics.

The black hole is not the only curved region of space-time where negative energy seems to play a role. Another is the worm hole - a hypothesized type of tunnel that connects one region of space and time to another. 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 and Matt Visser of Washington University - 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 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 defocus - in other words, they must go from converging to diverging somewhere in between [see illustration below]. This defocusing requires negative energy. 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.