Although wormholes have been discussed in other areas of the site, the concepts behind them deserve a centralized and coherent explanation. A wormhole is any structure connecting two regions or areas otherwise distant or unrelated. They have long been discussed as a possible mode of interstellar travel and even of time travel. They are fairly well-popularized by science fiction, especially Star Trek: Deep Space Nine, which depicts a large traversible wormhole that allows the characters to travel from familiar regions of space to a distant and unrelated area on the other side of the galaxy.
Wormholes connect two otherwise unrelated regions to form what is called a multiply connected space. They present paths much quicker to travel than the paths presented by ordinary space. For example, travel from Point A to Point B in the image is greatly facilitated by the presence of the wormhole. Wormholes may be possible on microscopic distances as a result of the quantum foam which allows particle/antiparticle pairs to leap into existence momentarily, then subsequently disappear. Interestingly, wormholes allow travel between different times as well as different locations, so time travel may be theoretically possible. Wormholes are commonly postulated to exist at the centers of black holes or between parallel universes with no other connections. The image below is a representation of a wormhole connecting two parallel universes.
Georg Riemann, the mathematician who first formulated higher-dimensional geometry, was also one of the first to discuss wormholes. His wormholes, called Riemann cuts, are connections between spaces (multiply connected spaces) with zero length. For example, a bug, used to living on the gray surface in the image at right, might one day walk through a cut connecting his universe to the white surface, where everything seems out of place. He learns that he can re-enter the cut and thus return to his own world, but the strange connection remains. The connection is an example of a Riemann cut. Though Riemann himself did not view his cuts as modes of transportation between universes, the idea nevertheless arose and was used to great effect in Lewis Carroll's Alice in Wonderland.
The relativistic description of black holes requires wormholes at their centers. These wormholes, called Einstein-Rosen bridges after Einstein and his collaborator Nathan Rosen, seem to connect the center of a black hole with a mirror universe on the "other side" of spacetime. At first, the bridge was considered a mathematical oddity, but nothing more. It was essential for the internal consistency of the Schwarzschild solution to Einstein's equations, which was the first relativistic solution involving black holes. However, the wormhole could not be traversed because the center of a black hole is a singularity, a point of infinite spacetime curvature, where the gravity would also be infinite and all matter would be crushed to its most fundamental constituents. Additionally, travel through the wormhole would require motion faster than the speed of light, a physical impossibility. For these reasons, Einstein-Rosen bridges were quickly forgotten despite other later solutions that included them. They were assumed to be mathematical oddities that had no bearing on physical reality.
In 1963, Roy Kerr devised the famous Kerr solution to Einstein's equations, a more realistic description of black holes than the original Schwarzschild solution. Kerr assumed the star that would form the black hole to be rotating and found that it would not eventually collapse to a point, but rather to a ring. When approaching the ride from the side, gravity and spacetime curvature are both still infinite, so matter is again inevitably destroyed. However, traveling through the ring would result in large but finite gravity. An object that does so and avoids being crushed by the still-formidable gravity can enter the Einstein-Rosen bridge and gain access to the mirror universe.
In 1985, cosmologist Kip Thorne was asked by science popularizer Carl Sagan to devise a hypothetical traversible wormhole. Thorne and his collaborators then created what was a remarkably simple solution that would in theory connect two periods in time. The wormhole would not rip its occupants apart, would stay open for the duration of a trip through, would not freeze its occupants inside, and would not create time paradoxes. However, it would require a never-observed form of exotic matter whose total energy is negative.
Based on this solution, Thorne later made the first scientifically sound - though not technically feasible - proposal for the design of a machine for time travel. In one version of his time machine, a chamber containing two parallel metal plates is placed on a rocket ship and accelerated to near-light velocities. An identical chamber, with the time traveler inside, is placed on earth. The electrical field created by the plates (the Casimir effect) creates a tear in spacetime. Since the clocks in the two chambers are ticking at different rates due to relativistic effects, the traveler is hurtled into the past or the future.
Another possible time machine involves a cylinder made of the abovementioned exotic matter. A time traveler stands inside the cylinder as the matter forms a wormhole, then rides comfortably to a distant place and time.
The mathematical reasoning of these devices is quite sound; the difficulty is in locating and exploiting exotic matter (if it even exists). The key is a condition called averaged weak energy condition (AWEC), which must be violated for the wormhole to work. Additionally, Stephen Hawking has declared that the wormhole entrance will emit enough radiation to make it unstable or even close it permanently.
It is ironic that the principal criticism of Thorne's wormholes comes from Stephen Hawking, whose own theory proposes an infinite number of parallel universes connected by wormholes. Hawking and his collaborator Jim Hartle have two main components to their theory: imaginary time and the wave-function of the universe. They propose an imaginary time running at right angles to ordinary time and without beginning or end or any singularities. They plan to use imaginary time to calculate the wave-function of the universe, thus proving our universe stable and unique. They will start with an infinite number of universes with an infinite number of different characteristics, then calculate the wave-function to see if it is largest around our own. They have essentially resurrected the many-worlds theory with one important difference - tiny wormholes connect the universes, thus making this theory testable and providing a small but calculable chance of an object quantum-leaping into one of the parallel universes. The image below exemplifies many such bubble universes, some rich and some barren, some connected to many others, some virtually isolated.
Sidney Coleman, a famous and idiosyncratic physics professor at Harvard, has recently put forward the theory that wormholes eliminate excess contributions to the cosmological constant, a measure of the inherent energy of vacuum. In the 1970s, physicists studying symmetry breaking calculated a cosmological constant some 10100 times greater than the observed value, which is somewhere close to zero. When Coleman added the contributions of the infinite series of wormholes proposed by Hawking, he found that the universe's wave-function grows very large around a value of zero cosmological constant, rendering the possibility extremely likely, but quickly vanished when the constant is large, rendering that universe impossible.
Almost as soon as Coleman published his results, critics objected that he had failed to account for large wormholes - all his calculations had involved wormholes of about the Planck length. He promptly wrote another paper stating that large wormholes can be ignored. If his reasoning is correct, it will mean that wormholes are not mathematical oddities. In fact, it would imply that infinite universes connected by infinite wormholes are necessary to keep the cosmological constant very close to zero. If it was negative, the universe would wrap up into a tiny hypersphere, and if it were positive, the universe would virtually explode, so his correctness would imply that only tiny wormholes keep the universe in a stable condition.
This, like many other developments in theoretical physics, invokes distances of the Planck length and smaller - distances that our current particle accelerators cannot even approach. The final word on wormholes - and the cosmological constant - will wait until either we can access the Planck length or we develop a truly cohesive picture through string theory.