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Vacuum polarization at the chronology horizon of the Roman spacetime.

Hawking has speculated that his chronology protection conjecture is always enforced, i.e., closed timelike curves (CTC's) are always prevented from forming, by a divergent vacuum polarization of quantum fields at any chronology horizon where the CTC's try to form. In this paper, this enforcement mechanism is explored in a spacetime that has been carefully designed to make the mechanism very weak, and therefore very ineffective. The chosen spacetime (due to Roman) is one in which two wormholes move at high speed past each other. Each wormhole has time hooked up synchronously in its own rest frame, so every CTC must traverse both wormholes at least once before returning to its starting point. It is shown that by choosing the wormholes' impact parameter to be arbitrarily large compared to their throat radii, the divergence of the vacuum polarization can be arbitrarily weak. This weakness might (as Kim and Thorne have argued) enable quantum gravity to cut off the divergence, thereby permitting the CTC's to form. Alternatively (as Thorne has subsequently suggested), the quantum-gravity cutoff might be delayed by the same mechanism that weakens the vacuum polarization, thereby enabling the polarization always to grow strong enough to enforce chronology protection.