Quantum Mechanics and Closed Timelike Curves

TL;DR

This paper investigates the compatibility of quantum mechanics with spacetimes containing closed timelike curves, concluding that such solutions are unphysical if quantum mechanics adheres to the correspondence principle.

Contribution

It demonstrates that generalizations of quantum mechanics on acausal manifolds are non-renormalizable, implying time travel solutions are unphysical under the correspondence principle.

Findings

Quantum mechanics cannot be consistently defined on acausal manifolds.

Solutions with closed timelike curves are unphysical if quantum mechanics is renormalizable.

Time travel solutions violate the correspondence principle.

Abstract

General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.