Testing non-linear vacuum electrodynamics with Michelson interferometry

TL;DR

This paper proposes using Michelson interferometry to test non-linear vacuum electrodynamics, predicting that light's phase velocity depends on background electromagnetic fields, with potential setups involving strong fields and large or tabletop interferometers.

Contribution

It introduces a novel experimental approach to test non-linear electrodynamics theories using Michelson interferometry, applicable to all Plebański class theories including Born-Infeld and Heisenberg-Euler.

Findings

Numerical estimates for Born, Born-Infeld, and Heisenberg-Euler theories.

Two experimental configurations for detecting phase velocity changes.

Theoretical foundation for future high-precision tests of non-linear electrodynamics.

Abstract

We discuss the theoretical foundations for testing non-linear vacuum electrodynamics with Michelson interferometry. Apart from some non-degeneracy conditions to be imposed, our discussion applies to all non-linear electrodynamical theories of the Pleba\'nski class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to non-linear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background field. There are two possible experimental set-ups for testing this prediction with Michelson interferometry. The first possibility is to apply a strong electromagnetic field to the beam in one arm of the interferometer and to compare the situation where the field is switched on with the situation where it is switched off. The second possibility is to place the whole interferometer in a strong electromagnetic field and to rotate it. If an electromagnetic field is placed in one arm, the interferometer could have the size of a gravitational wave detector, i.e., an arm-length of several hundred meters. If the whole interferometer is placed in an electromagnetic field, one would have to do the experiment with a table-top interferometer. [...] We specify the general results to some particular theories of the Pleba\'nski class; in particular, we give numerical estimates for Born, Born-Infeld and Heisenberg-Euler theories.