On the causality of electrodynamics and the Aharonov-Bohm effect

TL;DR

This paper introduces a non-instant field model for electrodynamics that provides a causal explanation for the Aharonov-Bohm effect and enables covariant quantization of Maxwell's equations, aligning classical and quantum perspectives.

Contribution

It proposes a novel non-instant field model satisfying a covariant averaging principle, allowing a causal interpretation of the Aharonov-Bohm effect and quantization of the field energy.

Findings

Causal explanation of the Aharonov-Bohm effect.

Covariant quantization of Maxwell equations.

Field energy is quantized.

Abstract

This paper presents a \emph{non-instant field model} for electrodynamics that permits a causal explanation of the \emph{Aharonov-Bohm effect} and a \emph{covariant quantization} of the respective Maxwell equations via the \emph{Gupta-Bleuler method}. Our model satisfies the following \emph{correspondence principle}: if $A^\mu$, $\vE$, $\vB$ denote the four potential, the electric field and the magnetic field of the non-instant field model, then the respective classical quantities are $\A[A^\mu]$, $\A[\vE]$, $\A[\vB]$, where $\A$ is a covariant time averaging operator. Here $\A[A^\mu]$ is interpreted as the best possible measurement of the four potential $A^\mu$. Although the Lorentz condition is not satisfied for $A^\mu$, it is satisfied for $\A[A^\mu]$. The latter fact means that the Lorentz condition does not hold for the quantized field but for its expectation value (cf. \emph{Gupta-Bleuler method} of quantization). Finally, we derive the energy conservation law of our field model and show that the field energy is quantized.