Operational understanding of the covariance of classical electrodynamics

TL;DR

This paper investigates whether the transformation laws of electrodynamic quantities derived from covariance assumptions match empirical laws, using a theoretical approach based on Lorentzian pedagogy to clarify foundational issues.

Contribution

It provides a theoretical validation that the transformation laws obtained from covariance assumptions are indeed the true empirical laws of electrodynamics.

Findings

Transformation laws match empirical observations

Covariance of electrodynamics equations is confirmed

Operational definitions of quantities are clarified

Abstract

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamic quantities are derived from the pre-assumption that the equations of electrodynamics are covariant against these---unknown---transformation rules. There are several problems to be raised concerning these derivations. This is, however, not our main concern in this paper. Even if these derivations are regarded as unquestionable, they leave open the following fundamental question: Are the so-obtained transformation rules indeed identical with the true transformation laws of the empirically ascertained electrodynamic quantities? This is of course an empirical question. In this paper, we will answer this question in a purely theoretical framework by applying what J. S. Bell calls "Lorentzian pedagogy"---according to which the laws of physics in any one reference frame account for all physical phenomena, including what a moving observer must see when performs measurement operations with moving measuring devices. We will show that the real transformation laws are indeed identical with the ones obtained by presuming the covariance of the equations of electrodynamics, and that the covariance is indeed satisfied. Beforehand, however, we need to clarify the operational definitions of the fundamental electrodynamic quantities. As we will see, these semantic issues are not as trivial as one might think.