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I. Introduction

Nothing can be said about Electrodynamics that has not already been said in a way or another. Most of the times the controversies, if they really occur, are conducted in terms of reasonable experimental possibilities or mathematical technicalities, thereby taking for granted a certain convenient position, lately not quite so often questioned, of the principles. Here we intend to move the discussion to the very level of these principles. As the official point of view seems to grant apriori a Space-Time description to Electrodynamics, and as we do not intend to go into relativistic considerations but rather stick with the geometrical side of the problem, we borrow the classical presentation of van Dantzig (van Dantzig, 1934), but in a modern form. Van Dantzig sets out to put in order the geometrical nature of electric and magnetic quantities, so that he writes the fundamental axioms of Electrodynamics as based on what we nowadays call differential forms. Since that time the formalism has been updated, and we use it here according to the newest style as presented by Hehl and Obukhov (Hehl, Obukhov, 2000). This last work, like van Dantzig’s, excels not only by simplicity and clarity regarding the basic necessary axioms, but also by a subtle difference from some other presentations. This difference, described by us in due time, occasioned the present essay. We thus refer everything, including the basic notations, to the work of Hehl and Obukhov – they have even a short but comprehensive Appendix introducing the exterior calculus – with a little exception: the vectors are here marked with an arrow, no matter if covariant or contravariant by their nature.

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