GaugeUnderdetermination and Shades of Locality in the AharonovBohm Effect
Abstract
I address the view that the classical electromagnetic potentials are shown by the AharonovBohm effect to be physically real (which I dub: `the potentials view'). I give a historicophilosophical 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 `gaugeunderdetermination': different gauge choices represent different physical states of affairs and hence different theories. This fact is usually not acknowledged in the literature (or in classrooms), neither by proponents nor by opponents of the potentials view. 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 multiplyconnected space. There is a tradeoff between explanatory power and gauge symmetries. On the one hand, this narrower equivalence class gives a local explanation of the AB effect in the sense that the phase is incrementally picked up along the path of the electron. On the other hand, locality is not satisfied in the sense of signal locality, viz. the finite speed of propagation exhibited by electric and magnetic fields. 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.
 Publication:

Foundations of Physics
 Pub Date:
 April 2021
 DOI:
 10.1007/s10701021004469
 arXiv:
 arXiv:2103.02684
 Bibcode:
 2021FoPh...51...48M
 Keywords:

 Quantum Physics;
 Physics  History and Philosophy of Physics
 EPrint:
 Preprint (accepted for Foundations of Physics (Springer))