Roman ring

Abstract: 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.

Abstract: them, is probably of fourth-century date. The absence of detail regarding its original situation means that its function can only be guessed at. Although those tanks bearing the Chi-Rho or other Christian symbols were presumably in Christian ownership this cannot be assumed for the class as a whole. The ambiguity of the cross or wheel on the Oxborough tank increases the difficulty of assessing its function and ownership. Although those in Christian ownership may have had a liturgical function it is possible that all the tanks may have been nothing more than decorated water-containers. A fuller discussion of these objects and their possible uses has already been published in Britannia. The Oxborough tank is yet another example to come from East Anglia, although to the north of the main group (FIG. 3). This concentration suggests that there may have been a manufacturer somewhere in Cambridgeshire, but there are insufficient similarities between the tanks to prove this. Indeed, the lack of similarity implies that they were made individually and perhaps close to their findspots. The absence of a known findspot for this tank again prevents any conclusions being drawn. I would like to thank Tony Gregory of the Norfolk Archaeological Unit for providing me with the information on the tank and Elizabeth James of the Lynn Museum, Kings Lynn, for allowing me to publish this article. The tank was purchased for the Lynn Museum in 1985 with the help of a Victoria and Albert Museum grant. It is currently undergoing conservation by the Norfolk Museum Service conservation department at Norwich Castle before going on display at the Lynn Museum.