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Zenith Grant Awardee

Ken Olum

Tufts University


Project Title

Does general relativity permit time travel?

Project Summary

Is time travel possible? In general relativity, matter and energy curve spacetime. Perhaps the right matter and energy would curve spacetime back on itself so that an object could return to the same place in space at an earlier time than it left. But is there any matter and energy that would produce such curvature? It would have to have negative energy density. That is unlike nearly every kind of matter and energy that we know, but quantum mechanics can give rise to negative energy densities, for example between parallel plates in the "Casimir effect". But it is not enough just to have negative energy density in a few places. Rather, the energy density added up along the complete path of a light ray must be negative. Previous work showed that that would be impossible in flat spacetime. But of course flat spacetime is not curved into a time machine. What matters is whether there is a spacetime curved in a way to allow time travel which simultaneously allows the right distribution of negative of energy to produce the curvature of that spacetime self-consistently. The goal of this project is to determine whether or not this is possible.

Technical Abstract

Does semiclassical gravity permit the construction of time machines or other exotic phenomena? Given any spacetime, Einstein's equations tell you what source is necessary to produce it. Exotic spacetimes require sources that violate the averaged null energy condition (ANEC), which requires that the total energy seen by an observer traveling on a null geodesic be nonnegative. In free field theory in flat space, ANEC is obeyed, but quantum fields in curved backgrounds can easily violate it. The goal of this project is to determine whether such violations can be self consistent, i.e., whether their curvature can be generated by a stress-energy tensor produced with that very same spacetime as the background. If not, exotic phenomena would be impossible. The best possibility seems to be to start with an ANEC-obeying curved background and produce ANEC violation by a quantum field on that background. Since we must be far from the Planck scale to be in the regime of semiclassical gravity, the quantum field effects are small compared to the background, so corrections at the next order can be ignored. But if the background gives zero contribution to ANEC, even a small correction could produce a violation.

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