Application-Oriented Relativistic Electrodynamics (2)
This article is a revised and upgraded edition of a previous one published in this journal, hence the label (2), see the General Remarks section below. Relativistic Electrodynamics, for many years a purely academic subject from the point of view of the applied physicist and electromagnetic radiation engineer, is nowadays recognized as pertinent to many practical applications. We therefore need to define a syllabus and explore the best methods for educating future generations of such users. Such
... an attempt is presented here, and is of course biased by personal preferences. What emerges as general guidelines are the facts that Relativistic Electrodynamics should be presented axiomatically, without trying to "explain the physical meaning" of Special Relativity, that four-vectors and their mathematical properties should be emphasized, and that the field tensors, an elegant formalism, albeit of limited practical use, should be avoided. Use of four-fold Fourier transforms not only greatly simplifies the relevant manipulations, it is also of paramount importance for discussion of dispersive media. This approach yields many concepts as mathematical results, e.g., the Relativistic Doppler effect, which therefore do not require a long phenomenological discussion with many "explanations". Introducing this approach as early as possible opens new vistas for the student and the educator, indeed some of the new results here do not appear in textbooks on Special Relativity. One of the main results shown here is the fact that the generalized Fermat principle states that the ray will propagate in such a manner that the proper time will be minimized (or extremized, in general). It also strips the mystique of this principle, showing that it is in fact equivalent to a modest mathematical condition on the smoothness of the phase function. The presentation is constructed in a way 108 Censor that allows the student to gradually overcome difficulties in assimilating new concepts and applying them. In that too it is different from many conventional presentations.