Tests of Lorentz invariance: a 2013 update

TLDR

Lorentz invariance underpins modern physics, and its potential violations are examined within local effective field theories, with constraints on breaking parameters derived from dynamical frameworks and the von Ignatovski theorem. The authors update the review of Lorentz invariance tests in effective field theories across matter and gravity sectors. They review local EFT frameworks for Lorentz violation, discuss constraints on breaking parameters, and illustrate the approach with two examples—OPERA and Hořava–Lifshitz gravity. The OPERA case demonstrates how general techniques constrain observed Lorentz violation, while the Hořava–Lifshitz example shows that applying these techniques to quantum gravity yields far‑reaching implications beyond phenomenological EFTs.

Abstract

We present an updated review of Lorentz invariance tests in effective field theories (EFTs) in the matter as well as in the gravity sector. After a general discussion of the role of Lorentz invariance and a derivation of its transformations along the so-called von Ignatovski theorem, we present the dynamical frameworks developed within local EFT and the available constraints on the parameters governing the Lorentz breaking effects. In the end, we discuss two specific examples: the OPERA 'affaire' and the case of Hořava–Lifshitz gravity. The first case will serve as an example, and a caveat, of the practical application of the general techniques developed for constraining Lorentz invariance violation to a direct observation potentially showing these effects. The second case will show how the application of the same techniques to a specific quantum gravity scenario has far-reaching implications not foreseeable in a purely phenomenological EFT approach.