Quantum field theory and time machines

TL;DR

This paper critically examines the F-locality condition in quantum field theory on non-globally hyperbolic spacetimes, proposing a modification that allows for the existence of time machines without violating locality principles.

Contribution

It demonstrates that the F-locality condition can be modified to accommodate time machines, challenging previous theorems and offering a new consistent framework called the MF-locality condition.

Findings

The F-locality condition conflicts with the existence of time machines.

A modified MF-locality condition is proposed that is compatible with time machines.

The new condition retains desirable features like locality and consistency with quantum field theory.

Abstract

We analyze the "F-locality condition" (proposed by Kay to be a mathematical implementation of a philosophical bias related to the equivalence principle, we call it the "GH-equivalence principle"), which is often used to build a generalization of quantum field theory to non-globally hyperbolic spacetimes. In particular we argue that the theorem proved by Kay, Radzikowski, and Wald to the effect that time machines with compactly generated Cauchy horizons are incompatible with the F-locality condition actually does not support the "chronology protection conjecture", but rather testifies that the F-locality condition must be modified or abandoned. We also show that this condition imposes a severe 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 above mentioned philosophical bias. So, one need not sacrifice the GH-equivalence principle to "emend" the F-locality condition. 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 locality and the existence of time machines.