dorsal/arxiv
View SchemaSome Variations on Maxwell's Equations
| Authors | Giorgio A. Ascoli, Gerald A. Goldin |
|---|---|
| Categories | |
| ArXiv ID | physics/0610020 |
| URL | https://arxiv.org/abs/physics/0610020 |
Abstract
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills 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 systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range 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.
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"abstract": "In the first sections of this article, we discuss two variations on Maxwell\u0027s\nequations that have been introduced in earlier work--a class of nonlinear\nMaxwell theories with well-defined Galilean limits (and correspondingly\ngeneralized Yang-Mills equations), and a linear modification motivated by the\ncoupling of the electromagnetic potential with a certain nonlinear Schroedinger\nequation. In the final section, revisiting an old idea of Lorentz, we write\nMaxwell\u0027s equations for a theory in which the electrostatic force of repulsion\nbetween like charges differs fundamentally in magnitude from the electrostatic\nforce of attraction between unlike charges. We elaborate on Lorentz\u0027\ndescription by means of electric and magnetic field strengths, whose governing\nequations separate into two fully relativistic Maxwell systems--one describing\nordinary electromagnetism, and the other describing a universally attractive or\nrepulsive long-range force. If such a force cannot be ruled out {\\it a priori}\nby known physical principles, its magnitude should be determined or bounded\nexperimentally. Were it to exist, interesting possibilities go beyond Lorentz\u0027\nearly conjecture of a relation to (Newtonian) gravity.",
"arxiv_id": "physics/0610020",
"authors": [
"Giorgio A. Ascoli",
"Gerald A. Goldin"
],
"categories": [
"physics.class-ph",
"physics.gen-ph"
],
"title": "Some Variations on Maxwell\u0027s Equations",
"url": "https://arxiv.org/abs/physics/0610020"
},
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