dorsal/arxiv
View SchemaLes structures fines de l'\'{e}lectromagn\'{e}tisme classique et de la relativit\'{e} restreinte (The fine structures of Classical Electromagnetism and Special Relativity)
| Authors | Yves Pierseaux, Germain Rousseaux |
|---|---|
| Categories | |
| ArXiv ID | physics/0601023 |
| URL | https://arxiv.org/abs/physics/0601023 |
Abstract
One of us (Y.P.) has shown the existence of a longitudinal component in the propagation of light waves on the basis of the kinematics underlying Poincar\'{e}'s ellipse. We show how this statement agrees with the electromagnetic theory. We recall that the second of us supports the existence of a "fine structure" of Electromagnetism that is, the co-existence of two theories, one based on the fields (Heaviside-Hertz) and the other on the potentials (Riemann-Lorenz). The existence of two different kinematics (the "fine structure" of Special Relativity : Einstein or Poincar\'{e}) corresponds to these two formulations of Classical Electromagnetism. With this goal in mind, we prove the relativistic covariance of the Helmholtz decomposition of the vector potential. This one translates into a generalized compensation for all directions of propagation, on the basis of the tangent to Poincar\'{e}'s ellipse, between the scalar potential and the longitudinal component of the vector potential. The adoption by Poincar\'{e} of the Lorenz gauge condition (with longitudinal and temporal components) is in contrast with the Einsteinian photon and the Einsteinian kinematics with only transversal components compatible with the choice of the "completed" Coulomb gauge condition (transverse gauge).
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"abstract": "One of us (Y.P.) has shown the existence of a longitudinal component in the\npropagation of light waves on the basis of the kinematics underlying\nPoincar\\\u0027{e}\u0027s ellipse. We show how this statement agrees with the\nelectromagnetic theory. We recall that the second of us supports the existence\nof a \"fine structure\" of Electromagnetism that is, the co-existence of two\ntheories, one based on the fields (Heaviside-Hertz) and the other on the\npotentials (Riemann-Lorenz). The existence of two different kinematics (the\n\"fine structure\" of Special Relativity : Einstein or Poincar\\\u0027{e}) corresponds\nto these two formulations of Classical Electromagnetism. With this goal in\nmind, we prove the relativistic covariance of the Helmholtz decomposition of\nthe vector potential. This one translates into a generalized compensation for\nall directions of propagation, on the basis of the tangent to Poincar\\\u0027{e}\u0027s\nellipse, between the scalar potential and the longitudinal component of the\nvector potential. The adoption by Poincar\\\u0027{e} of the Lorenz gauge condition\n(with longitudinal and temporal components) is in contrast with the Einsteinian\nphoton and the Einsteinian kinematics with only transversal components\ncompatible with the choice of the \"completed\" Coulomb gauge condition\n(transverse gauge).",
"arxiv_id": "physics/0601023",
"authors": [
"Yves Pierseaux",
"Germain Rousseaux"
],
"categories": [
"physics.hist-ph",
"physics.gen-ph"
],
"title": "Les structures fines de l\u0027\\\u0027{e}lectromagn\\\u0027{e}tisme classique et de la relativit\\\u0027{e} restreinte (The fine structures of Classical Electromagnetism and Special Relativity)",
"url": "https://arxiv.org/abs/physics/0601023"
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