Beyond the Lorenz Gauge: Probing a Stueckelberg Scalar in the Electric Aharonov-Bohm Effect

TL;DR

This paper proposes an experimental test of the electric Aharonov-Bohm effect to investigate the physical reality of the Stueckelberg scalar field beyond the Lorenz gauge, using single-electron interferometry.

Contribution

It introduces a novel measurement protocol to detect the Stueckelberg scalar's potential effects in the electric Aharonov-Bohm experiment, challenging the conventional gauge choice.

Findings

The proposed experiment can distinguish scalar contributions via their unique phase signature.

It demonstrates the feasibility of testing fundamental gauge assumptions with current technology.

The work opens a new avenue for exploring scalar fields in electromagnetism.

Abstract

The electric Aharonov-Bohm effect -- a time-dependent scalar potential imparting a measurable phase shift on electrons in a region free of electromagnetic fields -- has never been experimentally tested in its original formulation with shielded, time-dependent potentials. This unexplored regime offers a rare opportunity: the Lorenz condition $\partial_\mu A^\mu = 0$, a choice that eliminates a scalar degree of freedom from the electromagnetic potential, may not be the last word. If the Stueckelberg scalar $B = \partial_\mu A^\mu$ survives as a physical field and couples to matter, it would produce a phase shift with a distinctive $1-\cos(\omega T)$ signature -- orthogonal to the standard $\sin(\omega T)$ and separable by a frequency sweep even if both contributions coexist. We propose a measurement protocol based on single-electron interferometry with picosecond time resolution, within reach of current technology. The experiment asks a question that has lingered since 1959: is the Lorenz gauge a matter of convenience, or a matter of principle?