Unitarity Restoration in the Presence of Closed Timelike Curves

TL;DR

This paper proposes a new, causal, and probability-preserving method for handling evolution in spacetimes with closed timelike curves, ensuring unitarity through a redefinition of the Hilbert space.

Contribution

It introduces a mathematically unambiguous, linear, and causal approach to restore unitarity in the presence of closed timelike curves by redefining the final Hilbert space.

Findings

Provides a consistent interpretation of nonunitary evolution

Ensures probability conservation in closed timelike curve scenarios

Offers a mathematically rigorous framework for evolution with CTCs

Abstract

A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations, this proposal is causal, linear in the initial density matrix and preserves probability. It provides a physically reasonable interpretation of invertible nonunitary evolution by redefining the final Hilbert space so that the evolution is unitary or equivalently by removing the nonunitary part of the evolution operator using a polar decomposition.