Speed addition and closed time cycle in Lorentz-non-invariant theories

TL;DR

The paper demonstrates that in Lorentz-non-invariant theories involving external tensors, the relativistic addition rule for signal speed still applies, enabling closed time cycles and causality violations if superluminal signals exist.

Contribution

It shows that the relativistic speed addition rule remains valid in Lorentz-violating theories with external tensors, allowing causality violations through closed time cycles.

Findings

Relativistic addition rule applies in Lorentz-non-invariant theories.

Superluminal signals can create closed time cycles.

Optical anisotropy arises in moving media from Lorentz violation.

Abstract

In theories, whose Lorentz invariance is violated by involvement of an external any-rank tensor, we show that the standard relativistic rule still holds true for summing the signal speed, understood as the group velocity of a wave, with the speed of the reference frame. Provided a superluminal signal is available, this observation enables one to arrange a closed time cycle and hence causality violation, notwithstanding the Lorentz noninvariance. Also an optical anisotropy of a moving medium, isotropic at rest, is revealed.