Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory

TL;DR

This paper investigates the D-CTC condition within quantum field theory, showing it cannot be exactly fulfilled under certain conditions but can be approximated in theories with many uncorrelated states, challenging its interpretation as indicative of CTCs.

Contribution

It provides a rigorous analysis of the D-CTC condition in quantum field theory, demonstrating limitations and possibilities for its fulfillment, and questions its association with closed timelike curves.

Findings

D-CTC cannot be fulfilled in energy-analytic or Reeh-Schlieder states.

In theories with the split property, D-CTC can be approximated arbitrarily well.

Interpreting D-CTC as characteristic of CTCs may be misleading.

Abstract

The D-CTC condition is a condition originally proposed by David Deutsch as a condition on states of a quantum communication network that contains "backward time-steps" in some of its branches. It has been argued that this is an analogue for quantum processes in the presence of closed timelike curves (CTCs). The unusual properties of states of quantum communication networks that fulfill the D-CTC condition have been discussed extensively in recent literature. In this work, the D-CTC condition is investigated in the framework of quantum field theory in the local, operator-algebraic approach due to Haag and Kastler. It is shown that the D-CTC condition cannot be fulfilled in states which are analytic for the energy, or satisfy the Reeh-Schlieder property, for a certain class of processes and initial conditions. On the other hand, if a quantum field theory admits sufficiently many uncorrelated states across acausally related spacetime regions (as implied by the split property), then the D-CTC condition can always be fulfilled approximately to arbitrary precision. As this result pertains to quantum field theory on globally hyperbolic spacetimes where CTCs are absent, one may conclude that interpreting the D-CTC condition as characteristic for quantum processes in the presence of CTCs could be misleading, and should be regarded with caution. Furthermore, a construction of the quantized massless Klein-Gordon field on the Politzer spacetime, often viewed as spacetime analogue for quantum communication networks with backward time-steps, is proposed in this work.