Tufts University

Project Title

Does General Relativity Permit Exotic Phenomena?

Project Summary

Is it possible to create a stable wormhole, or to travel faster than light or backward in time? In general relativity, matter and energy curve space-time. If the space-time were curved enough and in the right way, such exotic things would be possible. 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 does sometimes 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. We already showed that this is impossible in flat space-time, even when there are boundaries, as in the Casimir system. The present project intends to show that even in curved space-time it is impossible to have the required negative energy, and thus that one cannot construct a wormhole or a time machine, or travel faster than light.

Technical Abstract

Does semiclassical gravity permit stable wormholes, faster-than-light travel, or the construction of time machines? To rule out such exotic phenomena requires energy conditions: restrictions on possible stress-energy tensors that can act as sources for gravity. The averaged null energy condition (ANEC) requires that the total energy seen by an observer traveling on a null geodesic be nonnegative. It would be sufficient to rule out the exotic phenomena above, but it is not universally obeyed in quantum field theory. In previous work, we discussed the "self-consistent achronal averaged null energy condition". It requires that ANEC hold only on achronal geodesics and only considers space-times, which are self-consistently generated by their stress-energy tensors. The self-consistent achronal ANEC is sufficient to rule out exotic phenomena, so we will attempt to show that this condition (or a similarly powerful one) holds for quantum field theory in curved space-time. The main obstacle to be overcome is the presence of the scale anomaly, which introduces extra, potentially ANEC-violating terms, when a system is rescaled. It is this anomaly, which necessitates the selfconsistency condition.

Hide Technical Abstract

Does semiclassical gravity permit stable wormholes, faster-than-light travel, or the construction of time machines? To rule out such exotic phenomena requires energy conditions: restrictions on possible stress-energy tensors that can act as sources for gravity. The averaged null energy condition (ANEC) requires that the total energy seen by an observer traveling on a null geodesic be nonnegative. It would be sufficient to rule out the exotic phenomena above, but it is not universally obeyed in quantum field theory. In previous work, we discussed the "self-consistent achronal averaged null energy condition". It requires that ANEC hold only on achronal geodesics and only considers space-times, which are self-consistently generated by their stress-energy tensors. The self-consistent achronal ANEC is sufficient to rule out exotic phenomena, so we will attempt to show that this condition (or a similarly powerful one) holds for quantum field theory in curved space-time. The main obstacle to be overcome is the presence of the scale anomaly, which introduces extra, potentially ANEC-violating terms, when a system is rescaled. It is this anomaly, which necessitates the selfconsistency condition.

Hide Technical Abstract

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