Gauge-underdetermination and shades of locality in the Aharonov-Bohm effect

TL;DR

This paper critically examines the physical reality of electromagnetic potentials in the Aharonov-Bohm effect, highlighting gauge-underdetermination issues and proposing the Lorenz gauge potentials as a promising ontological framework.

Contribution

It offers a detailed philosophical and historical analysis of the potentials view, introduces the concept of gauge-underdetermination, and advocates for the Lorenz gauge as the basis for electrodynamics ontology.

Findings

Gauge equivalence classes encode different physical states.

Local explanations require narrower gauge equivalence classes.

Lorenz gauge potentials support signal locality and finite propagation speed.

Abstract

I address the view that the classical electromagnetic potentials are shown by the Aharonov-Bohm effect to be physically real (which I dub: 'the potentials view'). I give a historico-philosophical presentation of this view and assess its prospects, more precisely than has so far been done in the literature. Taking the potential as physically real runs prima facie into 'gauge-underdetermination': different gauge choices represent different physical states of affairs and hence different theories. I then illustrate this theme by what I take to be the basic insight of the AB effect for the potentials view, namely that the gauge equivalence class that directly corresponds to the electric and magnetic fields (which I call the Wide Equivalence Class) is too wide, i.e., the Narrow Equivalence Class encodes additional physical degrees of freedom: these only play a distinct role in a multiply-connected space. There is a trade-off between explanatory power and gauge symmetries. Although this narrower equivalence class gives a explanation in terms of `local interactions', locality is not satisfied in the sense of signal locality. It is therefore intellectually mandatory to seek desiderata that will distinguish even within these narrower equivalence classes, i.e. will prefer some elements of such an equivalence class over others. I consider various formulations of locality, such as Bell locality, local interaction Hamiltonians, and signal locality. I show that Bell locality can only be evaluated if one fixes the gauge freedom completely. Yet, an explanation in terms of signal locality can be accommodated by the Lorenz gauge: the potentials propagate in waves at finite speed. I therefore suggest the Lorenz gauge potentials theory -- an even narrower gauge equivalence relation -- as the ontology of electrodynamics.