Comment on "Causality-violating Higgs singlets at the LHC"

TL;DR

This paper discusses the causality-violating properties of a simple flat Minkowski spacetime with a compactified timelike dimension, examining its theoretical implications and consistency with observational constraints relevant to LHC phenomenology.

Contribution

It clarifies the nature of causality violations in a simple Minkowski spacetime with a compactified time dimension and assesses its physical consistency.

Findings

The spacetime admits closed timelike curves only if the compact dimension is timelike.

It trivially satisfies all standard energy conditions.

The relevance to LHC phenomenology depends on observational gravity constraints.

Abstract

The spacetime of Ho and Weiler [Phys. Rev. D {\bf 87}, 045004 (2013)] supposedly admitting closed timelike curves (CTCs) is flat Minkowski spacetime with a compactified coordinate and can only contain CTCs if the compact direction is chosen to be timelike. This case of a "periodic time" is probably the simplest example of a causality-violating spacetime; it trivially satisfies all energy conditions usually assumed in general relativity, and its geodesics are just straight lines. Its relevance for phenomenology of the LHC, on the other hand, depends on consistency with observational constraints on gravity, as is mentioned in general but not discussed in any detail by Ho and Weiler. We verify a basic consistency check for stationary sources.