Fine-structure constant variability, equivalence principle and cosmology

TL;DR

This paper demonstrates that variations in the fine-structure constant do not necessarily violate the weak equivalence principle, and explains how magnetic energy, not Coulomb energy, drives cosmological alpha changes consistent with observations.

Contribution

It clarifies the relationship between alpha variability and the equivalence principle within Bekenstein's framework, highlighting the role of magnetic energy over Coulomb energy in cosmological evolution.

Findings

Violations of the weak equivalence principle are not implied by alpha variability.

Coulomb energy cancels out as a source of scalar field dynamics.

Magnetic energy drives the observed increase in alpha over cosmological time.

Abstract

It has been widely believed that variability of the fine-structure constant alpha would imply detectable violations of the weak equivalence principle. This belief is not justified in general. It is put to rest here in the context of the general framework for alpha variability [J. D. Bekenstein, Phys. Rev. D 25, 1527 (1982)] in which the exponent of a scalar field plays the role of the permittivity and inverse permeability of the vacuum. The coupling of particles to the scalar field is necessarily such that the anomalous force acting on a charged particle by virtue of its mass's dependence on the scalar field is cancelled by terms modifying the usual Coulomb force. As a consequence a particle's acceleration in external fields depends only on its charge to mass ratio, in accordance with the principle. And the center of mass acceleration of a composite object can be proved to be independent of the object's internal constitution, as the weak equivalence principle requires. Likewise the widely employed assumption that the Coulomb energy of matter is the principal source of the scalar field proves wrong; Coulomb energy effectively cancels out in the continuum description of the scalar field's dynamics. This cancellation resolves a cosmological conundrum: with Coulomb energy as source of the scalar field, the framework would predict a decrease of alpha with cosmological expansion, whereas an increase is claimed to be observed. Because of the said cancellation, magnetic energy of cosmological baryonic matter is the main source of the scalar field. Consequently the expansion is accompanied by an increase in alpha; for reasonable values of the framework's sole parameter, this occurs at a rate consistent with the observers' claims.