dorsal/arxiv
View SchemaThe electrodynamic 2-body problem and the origin of quantum mechanics
| Authors | C. K. Raju |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511235 |
| URL | https://arxiv.org/abs/quant-ph/0511235 |
| DOI | 10.1023/B:FOOP.0000034223.58332.d4 |
| Journal | Foundations of Physics 34 (2004) 937--62 |
Abstract
We numerically solve the functional differential equations (FDE's) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard-Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODE's). The ODE formulation is mathematically suspect since FDE's and ODE's are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a `delay' torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDE's naturally exhibit an_infinite_ spectrum of _discrete_ frequencies. The conclusion is that (a) the Coulomb force is_not_ a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics.
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"abstract": "We numerically solve the functional differential equations (FDE\u0027s) of\n2-particle electrodynamics, using the full electrodynamic force obtained from\nthe retarded Lienard-Wiechert potentials and the Lorentz force law. In\ncontrast, the usual formulation uses only the Coulomb force (scalar potential),\nreducing the electrodynamic 2-body problem to a system of ordinary differential\nequations (ODE\u0027s). The ODE formulation is mathematically suspect since FDE\u0027s\nand ODE\u0027s are known to be incompatible; however, the Coulomb approximation to\nthe full electrodynamic force has been believed to be adequate for physics. We\ncan now test this long-standing belief by comparing the FDE solution with the\nODE solution, in the historically interesting case of the classical hydrogen\natom. The solutions differ.\n A key qualitative difference is that the full force involves a `delay\u0027\ntorque. Our existing code is inadequate to calculate the detailed interaction\nof the delay torque with radiative damping. However, a symbolic calculation\nprovides conditions under which the delay torque approximately balances (3rd\norder) radiative damping. Thus, further investigations are required, and it was\nprematurely concluded that radiative damping makes the classical hydrogen atom\nunstable. Solutions of FDE\u0027s naturally exhibit an_infinite_ spectrum of\n_discrete_ frequencies. The conclusion is that (a) the Coulomb force is_not_ a\nvalid approximation to the full electrodynamic force, so that (b) the n-body\ninteraction needs to be reformulated in various current contexts such as\nmolecular dynamics.",
"arxiv_id": "quant-ph/0511235",
"authors": [
"C. K. Raju"
],
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"quant-ph"
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"doi": "10.1023/B:FOOP.0000034223.58332.d4",
"journal_ref": "Foundations of Physics 34 (2004) 937--62",
"title": "The electrodynamic 2-body problem and the origin of quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0511235"
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