Electrodynamics of Moving Media

Abstract

A. RESEARCH OBJECTIVESFinding the force of electromagnetic origin in a continuous medium is an old problem that has not been solved except in rather special cases. (An exception is the work of Meixner and his associates. -4) It involves the unification of two physical theoriescontinuum mechanics and electromagnetism.Since nonrelativistic mechanics is not, in general, compatible with electromagnetism, relativistic mechanics must be used.The relativistic theory of continuum mechanics (without electromagnetic fields) is fairly well understood, at least insofar as its basic equations are concerned. Electromagnetism in stationary bodies is also fairly well understood.To unite the two theories, the effect of each upon the other must be calculated. The study of the effect of mechanical motion and deformation upon electromagnetism is known as "electromagnetism of moving media," and there are several theories that 5 are formally different but lead to the same physical predictions.The inverse problem, finding the effects of the electromagnetic fields upon the mechanical equations, has never been solved adequately, and it is this problem that we wish to discuss now.The fundamental equations of relativistic continuum mechanics are: (1) Newton's Law, which, in its simplest form, is expressed aswhere n is the number of particles per unit volume, m the relativistic mass per particle, V the velocity, and fmech the force density, now of entirely mechanical origin; and (2) a specification of the way in which fmech is related to n, the strain, the strain rate or other kinematic variables. That is, the fundamental equations are Newton's Law, and the mechanical (and thermodynamic) constitutive relations of the material.The fundamental equations of electromagnetism of stationary bodies are Maxwell's equations, and relations among the field quantities, that is, electromagnetic constitutive relations of the material.It is instructive to consider how mechanical motion affects electromagnetism because the inverse problem, broadly speaking, is similar. Fundamentally, mechanical motion can affect electromagnetism in two ways. First, additional terms may enter, as source terms, into Maxwell's equations. Second, the constitutive relations may be altered in form.There is essentially only one theory of electromagnetism in free space, but, if materials are present, there are several, including (among others) the Minkowski QPR No. 70

Charge Coupled Device Camera–Scintillator System for Two Dimensional Proton Dose Measurements

“…As explained by Penfield and Haus [7] the correct fluid formation variables must be momentum, energy, etc., in the volume assigned per particle. It should also be noted that microscopic drift or guiding center reasoning do not generally allow for the correct handling neither of charge neutrality nor of inertial effects.…”

Tenseurs d'impulsion–énergie asymétriques et moment angulaire à six composantes dans le problème des deux impulsions du photon et celui de l'effet magnétodynamique

“…circuit AmpCrien plong6 dans un champ Clectrique En utilisant le postulat d'tquivalence entre un feuillet magnttique et un circuit Amptrien d'intensitts i l'on (Penfield et Haus 1965, 1968Costa de Beauregard 1967bShockley et James 1967;Coleman et Van Vleck 1968) transforrne I'expression Coulombienne de l'impulsion potentielle en son expression Amptrienne (invariante de jauge)…”

“…Par ailleurs, l'argument initial de de Broglie et Brillouin ressurgit sous une forme Cltgante, mais dissimulte, dans la thtorie de 'l'impulsion cachte dans les aimants 'de Coleman et Van Vleck (Penfield et Haus 1965, 1968Costa de Beauregard 1967bShockley et James 1967;Coleman et Van Vleck 1968).…”

“…Notre thtorie est prtsentte comme un scheme gtntral, essentiellement covariant relativiste, pour rtsoudre ce probleme et d'autres analogues, dont nous donnons deux exemples: les deux impulsions du photon, d'Abraham et de Minkowski, au sein de I'onde Cvanescente de Fresnel, en relation avec les dtcalages de Goos-Hanchen et dYImbert en rtflexion totale (Costa de Beauregard et al 1971 ; Costa de Beauregard 1973); et 'I'impulsion cachte' dans un circuit Amptrien plongt dans un champ tlectrique, qui a t t t tres ttudite il y a peu d'anntes (Penfield et Haus 1965, 1968Costa de Beauregard 19676, 1969;Shockley et James 1967;Coleman et Van Vleck 1968).…”

“…IV), mais aussi au probltme des deux impulsions du photon dans l'onde Cvanescente de Fresnel (Costa de Beauregard et al 1971 ; Costa de Beauregard 1973) ou le tenseur asymttrique impliqut est le de de Broglie-GChCniau (de Broglie 1940, 1957Gthtniau 1939) (Sect. V), puis au probltme de 'l'impulsion cachte' dans un circuit AmpCrien (Penfield et Haus 1965, 1968Costa de Beauregard 1967aShockley et James 1967;Coleman et Van Vleck 1968), oh le tenseur asymktrique est le proposC par nous (Costa de Beauregard 1946Beauregard , 1966b …”