Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves

TL;DR

This paper compares two quantum mechanics formulations involving closed timelike curves, highlighting how nonlinearities affect unitarity and causality, and introduces new approaches to information flow that challenge existing views.

Contribution

It demonstrates alternative methods for handling information flow in quantum systems with closed timelike curves, expanding beyond Deutsch's density matrix approach.

Findings

Quantum field nonlinearities cause breakdown of unitarity and causality.

Deutsch's approach preserves causality but destroys coherence.

New prescriptions for information flow have implications for quantum systems with closed timelike curves.

Abstract

Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and superposition using a path integral. Deutsch's density matrix approach is causal but typically destroys coherence. For each of these formulations I demonstrate that there are yet further alternatives in prescribing the handling of information flow (inequivalent to previous analyses) that have implications for any system in which unitarity or coherence are not preserved.