Does Gravity Care About Electric Charge? A Minimalist Model and Experimental Test

TL;DR

This paper asks whether gravity cares about electric charge by testing the weak equivalence principle in a regime where $q/m$ is varied rather than minimized. It proposes a minimalist, one-parameter framework based on a complex charge–mass conservation, yielding a linear prediction $\Delta a/g = \kappa(q/m)$ that activates only when charge is nonzero. The authors develop a complex-field formalism with a complex four-potential and a mixing matrix that produces cross-couplings between electric and gravitational fields, and they derive explicit field equations, 3+1 decompositions, and static-source solutions. An experimental pathway using torsion-balance setups (and complementary methods) is outlined to test a nonzero $\kappa$, offering a sharp target for laboratory gravity tests in uncharted parameter space. A nonzero result would imply a minimal EM–gravity unification via a single complex charge, while a null result would place new empirical constraints on linear charge–mass mixing with broad implications for fundamental interactions.

Abstract

Does gravity care about electric charge? Precision tests of the weak equivalence principle achieve remarkable sensitivity but deliberately minimize electric charge on test masses, leaving this fundamental question experimentally open. We present a minimalist framework coupling electromagnetism to linearized gravity through conservation of a complex charge-mass current, predicting charge-dependent violations $Δa/g = κ(q/m)$. Remarkably, this prediction occupies unexplored experimental territory precisely because precision gravity tests avoid charge variation. We identify this as a significant gap and propose a modified torsion balance experiment where $q/m$ is treated as a controlled variable. Such an experiment could test whether gravitational acceleration depends on electric charge, probing physics in genuinely new parameter space. This work exemplifies how theoretical minimalism can reveal overlooked opportunities in fundamental physics.