[論文レビュー] Does Gravity Care About Electric Charge? A Minimalist Model and Experimental Test

Renato Vieira dos Santos|arXiv (Cornell University)|Jan 22, 2026

Cosmology and Gravitation Theories被引用数 0

ひとこと要約

The paper presents a minimal complex-conservation model unifying charge and mass, deriving a one-parameter coupling that predicts a charge-to-mass dependent violation of the weak equivalence principle, and proposes a modified torsion-balance experiment to test it.

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.

研究の動機と目的

• Introduce a minimal complex charge-mass conservation principle that unifies electromagnetism and linearized gravity.
• Derive a one-parameter coupling predicting a measurable Δa/g ∝ (q/m) difference between test bodies.
• Identify an experimental regime (varying q/m) previously avoided in precision gravity tests as a clean test bed.
• Propose a practical experimental pathway, notably a modified torsion balance, to probe EM-gravity mixing.

提案手法

• Postulate local conservation of a complex current J^μ = J_V^μ + i J_W^μ with Q = q + i λ m.
• Introduce a complex four-potential A^μ = φ_V + i φ_W and field tensor F^μν = ∂^μ A^ν − ∂^ν A^μ.
• Derive real observable fields as a real mixing of the complex fields via a matrix M = [[1, κ], [κ, -1]] that encodes EM-gravity mixing.
• Obtain unified 3+1 field equations that couple electric and gravitational sectors through the single parameter κ.
• Show static point-source solutions where E_V and E_W contain cross terms proportional to κ q and κ m.
• Demonstrate a test-particle acceleration a = −g + κ (q/m) g, leading to Δa/g = κ[(q/m)_1 − (q/m)_2].

実験結果

リサーチクエスチョン

• RQ1 Does a nonzero κ lead to measurable cross-coupling between electric charge and gravity in the weak-field limit?
• RQ2 Is the differential acceleration between test bodies with different q/m ratios detectable, i.e., does Δa/g scale as κ(q/m) as predicted?
• RQ3 Can a torsion-balance setup be adapted to treat q/m as a controlled variable rather than a background nuisance?
• RQ4 What experimental regime is opened by varying q/m to test EM-gravity mixing beyond neutral-matter WEP tests?

主な発見

• A complex-conservation framework yields a minimal EM-gravity coupling characterized by a single parameter κ.
• Cross-terms in the fields imply electric charge can source gravity and mass can source electric fields, with identical κ strength.
• The predicted violation of the weak equivalence principle is Δa/g = κ[(q/m)_1 − (q/m)_2], vanishing for neutral matter.
• The model recovers standard physics when κ → 0, with a renormalization factor (1 + κ^2)^{-1} in the fields.
• Existing precision WEP tests are insensitive to this effect because they minimize q/m, leaving a new experimental regime unexplored.
• A modified torsion-balance experiment that varies q/m could directly test the predicted linear dependence on q/m.