Wormhole Construction: Proceed with Caution
Spaceships on Star Trek: Deep Space 9 regularly take a shortcut between distant parts of the Universe by traveling through a wormhole, a kind of spacetime tunnel. Although Einstein’s General Relativity theory allows wormholes to exist, physicists have been trying for decades to construct them mathematically without breaking any other laws of physics. Most researchers agree that wormholes require “exotic matter”–stuff that is repelled by gravity, rather than attracted–but some have claimed ways around that problem. Now a report in the 27 July PRL shows that all wormholes, no matter how cleverly constructed, require exotic matter–a condition that many in the field are already working to satisfy.
According to Matt Visser of Washington University in St. Louis, “The good news about Lorentzian wormholes is that after about ten years of hard work we cannot prove that they don’t exist.” But a publication five years ago  showed that a large class of wormholes require exotic matter to keep them open. Researchers haven’t given up, however, because exotic matter–which has less energy than a pure vacuum–does exist, at least in small amounts, thanks to the ghostly virtual particles in certain quantum physics experiments.
On the other hand, no one knows if enough of this weird stuff can exist in one place at one time to create a decent-sized wormhole. To avoid the problem, a number of theorists have claimed to construct special wormholes that do not require exotic matter. In their PRL paper, Visser and David Hochberg, of the Laboratory for Space Astrophysics and Fundamental Physics in Madrid, Spain, show that all wormholes–even time-dependent and asymmetric ones–require exotic matter, which in turn requires quantum mechanical effects. “You cannot just get away with normal classical physics,” says Visser. The authors blame many of the contrary claims on confusion about the precise definition of a wormhole and the concept of “passing through” it.
Their approach was to rigorously define a wormhole “throat” (the narrowest point) and show that because light rays spread out as they emerge from it, there must be a kind of “antigravity”–the hallmark of exotic matter. In the process they found that time-dependent wormholes actually have two throats, one for each direction of traffic, and they say that was one source of the confusion: A theoretical traveler could paradoxically pass the middle of the wormhole without actually reaching the throat for her direction. Part of the problem is the lack of a good physical picture for a dynamic wormhole, which is a complicated four-dimensional object; the usual image (see figure) is legitmate only for one that doesn’t change in time.
The requirement of exotic matter has been “pretty well understood in the community,” says Eanna Flanagan, of Cornell University, despite the number of contrary papers and the lack of an air-tight proof. But the new work does a good job of showing that requirement in a new and interesting way that supplements previous work, while also clarifying errors in other research, he says.
- J.L. Friedmann, K. Schleich, and D.M. Witt, Phys. Rev. Lett. 71, 1486 (1993)
Later work by Visser showed that the amount of exotic energy can be arbitrarily small: M. Visser, S. Kar, and N. Dadhich, “Traversable Wormholes with Arbitrarily Small Energy Condition Violations,” Phys. Rev. Lett. 90, 201102 (2003)