Quantum locality and time machines
Serguei Krasnikov · arXiv (Cornell University) · 1998
We analyze the “F-locality condition”, which was taken by Kay to be a mathematical implementation of the philosophical bias (we call it the “Locality principle”) that in a sufficiently small region of an arbitrary spacetime the laws must coincide with that usual in the Minkowski space. In a succession of papers the F-locality condition was used to build a generalization of semiclassical gravity to non-globally hyperbolic spacetimes. In particular, a theorem was proved by Kay, Radzikowski and Wald showing that existence of a time machine with a compactly generated Cauchy horizon is inconsistent with the F-locality condition. We argue that this result is against the F-locality condition rather than against the time machine. We also show that this condition imposes a sever restriction on the geometry of the world (it is just this restriction that comes into conflict with the existence of a time machine), which does not follow from the abovementioned philosophical bias. So, the F-locality condition can be abandoned or modified without sacrificing the Locality principle. As an example we consider a particular modification, the “MF-locality condition”. The theory obtained by replacing the F-locality condition with the MF-locality condition possesses a few attractive features. One of them is that it is consistent with both the Locality principle and existence of time machines. 1