Application-Oriented Relativistic Electrodynamics (2)

Abstract

Abstract-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

Non-Relativistic Scattering by Time-Varying Bodies and Media

“…It has been observed previously, see for example [6,7], that the role of spatiotemporally-dependent velocity needs special considerations, and in fact leads to a breakdown of the perfect axiomatic structure of relativistic electrodynamics. This is a well-known problem in physics: In his book [8] (see p. 162 ff.…”

“…Einstein's Special-Relativity [4][5][6] In (1) r is the position vector, and v is the velocity of the primed frame, as observed from the unprimed one. It is sometimes claimed that for low velocities the second equation (1) becomes t = t, reducing (1) to the Galilean transformation.…”

Relativistic Electrodynamics: Various Postulate and Ratiocination Frameworks

“…In this section we examine an approach based on (11). Let us start with Einstein's principle of relativity, i.e., the stipulation of form-invariance in (1), (5). As long as the Lorentz transformation (6) is not included, we do not have (8) to work with, hence (10), (11) cannot be derived, let alone the comparison of observations in various inertial frames of reference, as suggested by (12), is not available.…”

“…The topsy-turvy model has been devised mainly for didactic reasons, in order to facilitate a straight-forward and compact analysis [5,7] for an application-oriented audience. Accordingly the Lorentz transformation (6) has been taken as a postulate, replacing the kinematical postulate of the constancy of c.…”

“…The present compact notation was used before in [5]. The macroscopic Maxwell Equations for the electromagnetic field (in the "unprimed" frame of reference denoted by Γ) are given by…”