Testing causality violation on spacetimes with closed timelike curves

TL;DR

This paper investigates how closed timelike curves (CTCs) in spacetime can cause acausal effects in quantum scattering experiments, leading to deviations in measurable cross-sections depending on the CTC configuration.

Contribution

It demonstrates that CTCs can influence scattering probabilities and cross-sections, revealing new effects of causality violation in quantum mechanics within specific spacetime models.

Findings

CTCs cause the transition probability to depend on their distribution.

Deviations in total cross-section are negligible if CTCs are small or sparse.

For pervasive CTCs, the total cross-section aligns with standard predictions due to cancellation.

Abstract

Generalized quantum mechanics is used to examine a simple two-particle scattering experiment in which there is a bounded region of closed timelike curves (CTCs) in the experiment's future. The transitional probability is shown to depend on the existence and distribution of the CTCs. The effect is therefore acausal, since the CTCs are in the experiment's causal future. The effect is due to the non-unitary evolution of the pre- and post-scattering particles as they pass through the region of CTCs. We use the time-machine spacetime developed by Politzer [1], in which CTCs are formed due to the identification of a single spatial region at one time with the same region at another time. For certain initial data, the total cross-section of a scattering experiment is shown to deviate from the standard value (the value predicted if no CTCs existed). It is shown that if the time machines are small, sparsely distributed, or far away, then the deviation in the total cross-section may be negligible as compared to the experimental error of even the most accurate measurements of cross-sections. For a spacetime with CTCs at all points, or one where microscopic time machines pervade the spacetime in the final moments before the big crunch, the total cross-section is shown to agree with the standard result (no CTCs) due to a cancellation effect.