Download On the Frame Indifferent Formulation of the Governing Equations of

On the Frame Indifferent Formulation of the Governing Equations of the Electromagnetic Field
C. I. Christov,
Dept. of Mathematics, University of Louisiana at Lafayette
By observing that the notion of a field is intimately related to the concept of a mechanical continuum, we consider the electromagnetic field as an elastic fluid. We show that Maxwell's equations can be rigorously derived as corollaries from the linearized governing equations of an elastic fluid, provided that the electric field is identified as the stress vector, while the magnetic field is understood as the vorticity. An advantage of the new formulation is that when the full nonlinear equations are considered, the well known Oersted­Ampere, Biot­Savart and Lorentz­
force laws are also recovered as corollaries. Thus, a unified description is achieved in which all fundamental laws of electromagnetism are explained away by the continuum mechanics of the elastic fluid. The magnetic permeability and electric permittivity are shown to be the density of the fluid and the inverse of the elastic shear modulus. In its virtue of being the linear limit of the new system, the Maxwell system is merely Lorentz invariant: it is invariant only with respect to changes to coordinate systems which move rectilinearly with no acceleration and/or deformation. The new formulation is frame­indifferent, i.e., it is covariant with respect to changes to non­uniformly moving and even deforming coordinate systems, which establishes the true general covariance of electrodynamics.