It's Hard to Learn How Gravity and Electromagnetism Couple

TL;DR

This paper systematically constructs the most general effective Lagrangian coupling gravity and electromagnetism up to dimension 6, identifying only two unique terms and analyzing their observational implications.

Contribution

It provides a complete enumeration of non-minimal gravity-electromagnetism couplings up to dimension 6, clarifying their physical origins and observational relevance.

Findings

Only two unique coupling terms exist after redefinitions.

One term arises from QED loop effects; the other is parity-violating.

Current tests do not effectively probe these couplings.

Abstract

We construct the most general effective Lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non-minimal coupling terms respecting both diffeomorphism and gauge invariance. In all, there are only two unique terms after field re-definitions; one is known to arise from loop effects in QED while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. We show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of General Relativity are useful probes of these terms. These non-minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future.