dorsal/arxiv
View SchemaRelativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways
| Authors | Michael Ibison, Harold E. Puthoff |
|---|---|
| Categories | |
| ArXiv ID | physics/0102087 |
| URL | https://arxiv.org/abs/physics/0102087 |
| DOI | 10.1088/0305-4470/34/16/310 |
| Journal | J. Phys. A. vol. 34 pp. 3421-3428 (2001) |
Abstract
It is well known that the third-order Lorentz-Dirac equation admits runaway solutions wherein the energy of the particle grows without limit, even when there is no external force. These solutions can be denied simply on physical grounds, and on the basis of careful analysis of the correspondence between classical and quantum theory. Nonetheless, one would prefer an equation that did not admit unphysical behavior at the outset. Such an equation - an integro-differential version of the Lorentz-Dirac equation - is currently available either in 1 dimension only, or in 3 dimensions only in the non-relativistic limit. It is shown herein how the Lorentz-Dirac equation may be integrated without approximation, and is thereby converted to a second-order integro-differential equation in 3D satisfying the above requirement. I.E., as a result, no additional constraints on the solutions are required because runaway solutions are intrinsically absent. The derivation is placed within the historical context established by standard works on classical electrodynamics by Rohrlich, and by Jackson.
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"abstract": "It is well known that the third-order Lorentz-Dirac equation admits runaway\nsolutions wherein the energy of the particle grows without limit, even when\nthere is no external force. These solutions can be denied simply on physical\ngrounds, and on the basis of careful analysis of the correspondence between\nclassical and quantum theory. Nonetheless, one would prefer an equation that\ndid not admit unphysical behavior at the outset. Such an equation - an\nintegro-differential version of the Lorentz-Dirac equation - is currently\navailable either in 1 dimension only, or in 3 dimensions only in the\nnon-relativistic limit.\n It is shown herein how the Lorentz-Dirac equation may be integrated without\napproximation, and is thereby converted to a second-order integro-differential\nequation in 3D satisfying the above requirement. I.E., as a result, no\nadditional constraints on the solutions are required because runaway solutions\nare intrinsically absent. The derivation is placed within the historical\ncontext established by standard works on classical electrodynamics by Rohrlich,\nand by Jackson.",
"arxiv_id": "physics/0102087",
"authors": [
"Michael Ibison",
"Harold E. Puthoff"
],
"categories": [
"physics.gen-ph"
],
"doi": "10.1088/0305-4470/34/16/310",
"journal_ref": "J. Phys. A. vol. 34 pp. 3421-3428 (2001)",
"title": "Relativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways",
"url": "https://arxiv.org/abs/physics/0102087"
},
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