Is the relativity principle consistent with classical electrodynamics? Towards a logico-empiricist reconstruction of a physical theory

The transformation rules for the basic electrodynamical quantities are routinely derived from the hypothesis that the relativity principle (RP) applies for Maxwell's electrodynamics. These derivations leave open several questions: (1) Is the RP a true law of nature for electrodynamical phenomena? (2) Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? (3) Is the RP consistent with the laws of electrodynamics in one single inertial frame of reference? (4) Are, at least, the derived transformation rules consistent with the laws of electrodynamics in one single frame of reference? (1) and (2) are empirical questions; we will investigate problems (3) and (4). First we will develop a formalism of the RP. In the second part, we will deal with the operational definitions of the fundamental quantities. In the third part of the paper we will show that the proper transformation rules are indeed identical with the ones obtained by presuming the covariance, and that the covariance is indeed satisfied. Problem (3) raises conceptual problems to which there seems no satisfactory solution in electrodynamics; thus, contrary to the widespread views, the question we asked in the title has no obvious answer.