dorsal/arxiv
View SchemaStability of the hydrogen atom of classical electrodynamics
| Authors | Jayme De Luca |
|---|---|
| Categories | |
| ArXiv ID | physics/0412022 |
| URL | https://arxiv.org/abs/physics/0412022 |
Abstract
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the interparticle distance performs bounded oscillations about a metastable orbit. The stability mechanism is established by the existence of a quartic resonant constant generated by the stiff eigenvalues of the linear stability problem. This constant bounds the particles together during the radiative recoil. The condition of resonant dissipation predicts angular momenta for the metastable orbits in reasonable agreement with the Bohr atom. The principal result is that the emission lines agree with the predictions of quantum electrodynamics (QED) with 1 percent average error even up to the $40^{th}$ line. Our angular momenta depend logarithmically on the mass of the heavy body, such that the deuterium and the muonium atoms have essentially the same angular momenta, in agreement with QED. Analogously to QED, our stability analysis naturally uses the eigenvalues of an infinite-dimensional linear operator; the infinite-dimensionality is brought in by the delay of the electromagnetic interaction.
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"abstract": "We study the stability of the circular orbits of the electromagnetic two-body\nproblem of classical electrodynamics. We introduce the concept of resonant\ndissipation, i.e. a motion that radiates the center-of-mass energy while the\ninterparticle distance performs bounded oscillations about a metastable orbit.\nThe stability mechanism is established by the existence of a quartic resonant\nconstant generated by the stiff eigenvalues of the linear stability problem.\nThis constant bounds the particles together during the radiative recoil. The\ncondition of resonant dissipation predicts angular momenta for the metastable\norbits in reasonable agreement with the Bohr atom. The principal result is that\nthe emission lines agree with the predictions of quantum electrodynamics (QED)\nwith 1 percent average error even up to the $40^{th}$ line. Our angular momenta\ndepend logarithmically on the mass of the heavy body, such that the deuterium\nand the muonium atoms have essentially the same angular momenta, in agreement\nwith QED. Analogously to QED, our stability analysis naturally uses the\neigenvalues of an infinite-dimensional linear operator; the\ninfinite-dimensionality is brought in by the delay of the electromagnetic\ninteraction.",
"arxiv_id": "physics/0412022",
"authors": [
"Jayme De Luca"
],
"categories": [
"physics.atom-ph"
],
"title": "Stability of the hydrogen atom of classical electrodynamics",
"url": "https://arxiv.org/abs/physics/0412022"
},
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