Relativity and Cosmology

   

Charge-Dependent Equivalence Principle Violation from Kinetic Mixing of the Photon with a New Long-Range Vector Field

Authors: Renato Vieira dos Santos

The weak equivalence principle (WEP) has been tested with extraordinary precision over the past decades, but invariably with electrically neutral bodies. This leaves a fundamental blind spot: does gravity feel electric charge? A recent phenomenological analysis introduced a parameter $kappaphen$ to quantify this unexplored sector, but lacked a consistent field-theoretic origin. In this work we show that the simplest mechanism is kinetic mixing between the standard photon and a new massless vector field $X_mu$ that mediates a long-range fifth force coupled to the ordinary mass current. The single gauge-invariant dimension-four operator $frac{xi}{2}F_{muu}X^{muu}$ preserves causality and unitarity. By adopting the action in which both fields couple to their respective currents with the same sign convention, the two-body potential is fully symmetric and exactly satisfies Newton's third law, rendering the model free of any mathematical pathology.The fifth force between equal masses is repulsive, a known property of vector-mediated interactions, but its contribution to the neutral gravitational acceleration is absorbed into the measured Newtonian constant.For a static, spherically symmetric source, the mixing induces an electric field proportional to the Newtonian gravitational field, leading to a charge-dependent acceleration from which we identify $kappaphen = -ximu_0,G_X/G_N$, where $G_X$ is the fifth-force coupling strength.The symmetric cross term $propto q_1m_2+q_2m_1$ in the two-body potential gives rise to dipole radiation from compact binaries, providing a direct link to pulsar-timing constraints.We derive explicit constraints from the Cassini bound on the PPN parameter $gamma$, from lunar laser ranging on $alpha_1$, and from the Hulse--Taylor pulsar, showing that the model is compatible with all existing data while providing a clear roadmap for future experimental tests.

Comments: 11 Pages.

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[v1] 2026-07-11 13:55:19

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