Constraining a possible dependence of Newton's constant on the Earth's magnetic field

TL;DR

This paper critically evaluates a model proposing that Earth's magnetic field influences Newton's constant via scalar fields, finding it incompatible with experimental tests and thus unlikely to explain measurement discrepancies.

Contribution

It provides a detailed assessment of a gravielectric coupling model, demonstrating its incompatibility with experimental constraints and offering a method applicable to similar theories.

Findings

Violations of the weak equivalence principle are four orders of magnitude beyond current limits.

The model cannot account for discrepancies in Newton's constant measurements.

The method can be applied to other theories with gravielectric coupling.

Abstract

Some time ago Mbelek and Lachieze-Rey proposed that the discrepancy between the results of the various measurements of Newton's constant could be explained by introducing a gravielectric coupling between the Earth's gravitational and magnetic fields mediated by two scalar fields. A critical assessment of this model is performed. By calculating the static field configuration of the relevant scalar around a nucleus in the linearised theory and then folding this result with the mass density of the nucleus its effective gravitational mass is determined. Considering test bodies of different materials one finds violations of the weak equivalence principle for torsion-balance experiments which are four orders of magnitude beyond the current experimental limit, thus rendering the model non-viable. The method presented can be applied to generic theories with gravielectric coupling and seems to rule out in general the explanation of the discrepant measurements of Newton's constant by such couplings.