Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics

TL;DR

This paper compares approaches to resolving quantum paradoxes with closed timelike curves, highlighting how unitarity preservation and the many worlds interpretation address these issues, with implications for macroscopic object interactions.

Contribution

It analyzes two methods—path integrals and many worlds—for avoiding quantum paradoxes with CTCs, revealing their limitations and conditions for viability.

Findings

Preserving unitarity prevents paradoxes by altering time evolution.

Many worlds interpretation avoids paradoxes if detection resolution time is considered.

Macroscopic objects must fragment to interact with wormholes without paradoxes.

Abstract

We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves (CTCs). In a model similar to Politzer's, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events bewcome certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the "many worlds interpretation". We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments.