Abstract
We numerically solve the functional differential equations (FDEs) 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 (ODEs). The ODE formulation is mathematically suspect since FDEs and ODEs 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 FDEs 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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Preliminary versions of aspects of this paper have been circulating for some time, having been presented and discussed at various conferences and lectures over the past several years, e.g., "Simulating a tilt in the arrow of time: preliminary results," Seminar on Some Aspects of Theoretical Physics, Indian Statistical Institute, Calcutta, 14–15 May 1996, "The electrodynamic 2-body problem and the origin of quantum mechanics." Paper presented at the International Symposium on Uncertain Reality, New Delhi, 5–9 Jan 1998, "Relativity: history and history dependence." Paper presented at the On Time Seminar, British Society for History of Science, and Royal Society for History of Science, Liverpool, August 1999. "Time travel," invited talk at the International Seminar, Retrocausality Day, University of Groningen, September 1999, and in talks at the Universities of Southampton, Utrecht, Pittsburgh, etc.
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Raju, C.K. The Electrodynamic 2-Body Problem and the Origin of Quantum Mechanics. Foundations of Physics 34, 937–962 (2004). https://doi.org/10.1023/B:FOOP.0000034223.58332.d4
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DOI: https://doi.org/10.1023/B:FOOP.0000034223.58332.d4