Some Variations on Maxwell's Equations
Abstract
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier worka class of nonlinear Maxwell theories with welldefined Galilean limits (and correspondingly generalized YangMills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systemsone describing ordinary electromagnetism, and the other describing a universally attractive or repulsive longrange force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.
 Publication:

arXiv eprints
 Pub Date:
 October 2006
 DOI:
 10.48550/arXiv.physics/0610020
 arXiv:
 arXiv:physics/0610020
 Bibcode:
 2006physics..10020A
 Keywords:

 Physics  Classical Physics;
 Physics  General Physics
 EPrint:
 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equations