Unitarity of Quantum Theory and Closed Time-Like Curves

Abstract

Interacting quantum fields on spacetimes containing regions of closed timelike curves (CTCs) are subject to a non-unitary evolution $X$. Recently, a prescription has been proposed, which restores unitarity of the evolution by modifying the inner product on the final Hilbert space. We give a rigorous description of this proposal and note an operational problem which arises when one considers the composition of two or more non-unitary evolutions. We propose an alternative method by which unitarity of the evolution may be regained, by extending $X$ to a unitary evolution on a larger (possibly indefinite) inner product space. The proposal removes the ambiguity noted by Jacobson in assigning expectation values to observables localised in regions spacelike separated from the CTC region. We comment on the physical significance of the possible indefiniteness of the inner product introduced in our proposal.

13 pages, LaTeX. Final revised paper to be published in Phys Rev D. Some changes are made to expand our discussion of Anderson's Proposal for restoring unitarity

References in corpus (7)

• Quantum Field Theory in Spaces with Closed Time-Like Curves
• Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes
• Simple Quantum Systems in Spacetimes with Closed Timelike Curves
• Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves
• Unitarity Restoration in the Presence of Closed Timelike Curves
• The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine
• Generalised Point Interactions for the Radial Schrodinger Equation via Unitary Dilations

Cited by in corpus (11)

• The quantum mechanics of time travel through post-selected teleportation
• Attractor scenarios and superluminal signals in k-essence cosmology
• Treating Time Travel Quantum Mechanically
• Nonlinearity in Quantum Theory and Closed Timelike Curves
• Topological censorship and chronology protection
• Divergences in the Effective Action for Acausal Spacetimes
• Classical and Quantum Initial Value Problems for Models of Chronology Violation
• Quantum Field Theory on Certain Non-Globally Hyperbolic Spacetimes
• Discontinuous quantum evolutions in the presence of closed timelike curves
• Reality, Causality, and Quantum Theory
• Quantum Mechanics and Closed Timelike Curves