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Traversable Wormholes

Professor Kip Thorne, of the California Institute of Technology, was stimulated, in the summer of 1985, to search for alternate wormhole solutions that would allow safe passage for interstellar travelers. His motivation was a request for help from his friend and colleague, Carl Sagan. Professor Sagan was writing a science fiction story (The novel was entitled Contact which has been made into a motion picture staring Jodi Foster as the heroine) in which his heroine needed to cross a great interstellar distance in a very short time, namely the distance between Earth and the star Vega (see figure 3). Professor Thorne was only too happy to oblige. He found a solution which was so simple that he was surprised no one had found it before. The solution has the following metric equation.

                                  

Where b(r) determines the spatial shape of the wormhole, and Phi(r) determines the gravitational redshift. This solution has the property of having no horizons or excessive tidal forces to deal with which makes it safe for humans to travel through. But it does have one unfortunate drawback. In order to hold the throat open there has to be a negative energy density inside. There is no no known material that has this property. Though electro-magnetic vacuum fluctuations are sometimes measured to have negative energy densities and are correspondingly called ``exotic''. In order to keep the wormhole open it needs to be threaded with exotic matter that will create a tension to push the walls apart. This exotic matter would have the curious effect of defocusing light as it passed through (see figure 4).

                                   

Figure 4: A traversable Wormhole threaded with Exotic Matter. Light rays passing through the Wormhole are defocused.

Assuming that this exotic matter can be discovered or manufactured how would one go about constructing such a wormhole? Certainly objects such as these do not occur naturally. The answer may lie in quantum mechanics. On a sufficiently small scale the universe is probabilistic. Refer to figure 5 to see possible geometries at the quantum level.

                 

Figure 5: Embedding diagrams of the The Quantum Foam. The geometry of spacetime on a Planck scale is probabilistic. The probability for (a) is 0.1% , (b) is 0.4%, and (c) is 0.02%

This network of wormholes and black holes is known as the quantum foam. There are certain probabilities that wormholes will pop in and out of existence at this level. If we assume that we, or some other society, are sufficiently advanced that we can observe this quantum foam and manufacture exotic matter, then it might be possible to reach into this microscopic universe and capture a wormhole. By pouring exotic matter into it we might be able to blow it up to a macroscopic size. We would then be poised to embark on the greatest journey imaginable. [ Time Machine ]

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