For the purposes of science fiction, it is usually assumed that a wormhole in space-time represents a shortcut--that by traveling a small distance through the wormhole tunnel, you might end up at a destination which could be light-years away through conventional space. In terms of the theoretical physics of wormholes, however, there is no particular reason why the distance must be shorter; the wormhole might actually be the longer route (analogous to a long, complicated, twisting hole that a worm might leave in an apple, where the entrance and exit mouths might be quite close to each other on the surface).
Wormholes can exist within the classical black hole solutions of the Einstein equations. These wormholes are useless for travel, however, as they collapse before any spaceship (or even a ray of light) could pass through them. In addition, the black holes formed by a collapsing star have no associated wormhole at all.
"Traversable" wormholes exist in wormhole space-times in which the wormhole is held open at least long enough for a signal or object (spaceship) to pass through. Interest in such wormhole solutions in general relativity was stimulated when Michael Morris and Kip Thorne of the California Institute of Technology examined the general properties necessary for a wormhole to remain open. They found that if a wormhole is static and unchanging in time, then it must contain "exotic" matter. Such matter has negative energy density and a large negative pressure (or tension)--larger in magnitude than the energy density. Such matter is called "exotic" because it so little resembles all forms of known matter.
All the forms of matter familiar to physicists and chemists have positive energy density (or, equivalently, positive mass), and pressures or tensions that are always less than the energy density in magnitude. In a stretched rubber band, for example, the density is 1014, or 100 million million times, greater than the tension. The one possible source of "exotic" matter known to theoretical physics lies in the behavior of certain vacuum states in quantum field theory. This possibility is the focus of most current theoretical research involving wormholes.
Such research has shown that it appears difficult to use quantum effects to open a wormhole much larger than the characteristic length associated with quantum gravity, known as the Planck length (about 10-33 centimeter). If the wormhole were not much larger than this, then not only would it be useless for transporting spaceships, but quantum gravity would be needed to describe the hole.
Analyses of the behavior of quantized fields in wormhole space-times by L.H. Ford and T.A. Roman, Brett E. Taylor, William A. Hiscock and Paul R. Anderson and others have shown that it is unlikely that quantum field effects could hold open a macroscopic wormhole. On the other hand, David Hochberg, A.D. Popov and Sergey V. Sushkov have found a wormhole solution using approximate expressions for a quantized scalar field, but had to make a number of assumptions concerning the (unknown) parameters of quantum gravity in their work.
While at present it appears unlikely that nature allows the existence of macroscopic wormholes, there is still sufficient uncertainty in the arguments to allow theoretical physicists to continue studying this odd and intriguing aspect of space-time.
And another reply comes from Matt Visser, an assistant professor of physics at Washington University in St. Louis:
Wormholes are hypothetical entities that show up in theoretical analyses of Einstein's theory of gravity (general relativity). Nobody has yet seen a wormhole, nor are we certain that they exist, but they seem to show up so easily when we do calculations that many physicists suspect that they might actually be out there in the real universe.
There are two main types of wormhole of interest to physicists: Lorentzian wormholes (general relativity) and Euclidean wormholes (particle physics).