Toward Charge-Dependent Tests of the Equivalence Principle: A Phenomenological Parameter and an Unexplored Frontier

TL;DR

This paper introduces a new parameter to test for charge-dependent violations of the equivalence principle, estimates current experimental sensitivity, and discusses future experimental strategies to explore electromagnetic couplings in gravity.

Contribution

It defines the phenomenological parameter κ for charge-gravity coupling, estimates current bounds, and connects it to existing frameworks, highlighting an unexplored empirical frontier.

Findings

Current bounds on κ are less than 2.1×10⁻⁴ at 95% confidence.

Electromagnetic coupling violations are eleven orders of magnitude less constrained than composition-dependent ones.

Future experiments could probe physics beyond minimal gravitational EFT via charge-to-mass ratio differences.

Abstract

We introduce and define the phenomenological parameter $\kappa$, defined by $\Delta a/g = \kappa \, \Delta(q/m)$, to quantify potential linear coupling between electric charge and gravitational acceleration. A synthesis of existing precision equivalence principle experiments yields the first quantitative estimate of the effective sensitivity to this coupling: $|\kappa| < 2.1 \times 10^{-4}~\si{\kilo\gram\per\coulomb}$ at 95\% confidence level. This constraint is approximately eleven orders of magnitude less stringent than corresponding bounds on composition-dependent violations, revealing that the electromagnetic axis remains a largely underexplored frontier in empirical gravity. We connect $\kappa$ to established frameworks -- the Standard-Model Extension and the $TH\epsilon\mu$ formalism -- showing that it occupies a region of parameter space untouched by existing high-precision tests. An effective field theory analysis shows that dimension-six operators that couple curvature directly to the electromagnetic field strength are suppressed by the minuscule terrestrial spacetime curvature ($G_N \rho_\oplus \sim 10^{-55}~\text{GeV}^2$) and are therefore phenomenologically irrelevant. Consequently, a future measurement of $\kappa$ at an accessible level would not probe minimal geometric couplings but would signal physics beyond minimal gravitational EFT, such as mediation by light scalar fields as in Einstein-Maxwell-Dilaton theory. We examine the Schiff-Barnhill effect, the primary systematic background for any such measurement, and show how it can be separated from a genuine signal. We outline the necessary experimental strategy, focused on maximizing charge-to-mass ratio differences, to transform this overlooked axis into a targeted probe for new physics.