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Functional differential equations. 2: The classical hydrogen atom
C. K. Raju
AlBukhary International University, Alor Setar, Malaysia
The previous part closed with a doubt: textbook electrodynamics mentions only ordinary and partial differential equations (ODEs and PDEs), never any functional differential equations (FDEs). So are FDEs or past data really needed? In fact, to solve Maxwell's PDEs we need Cauchy data on fields, which is equivalent to past data on particle motions. Electrodynamics actually involves a textit{coupled} system of ODEs and PDEs, equivalent to FDEs which are currently the best way to solve such a coupled system. The full electrodynamic force is commonly approximated by the Coulomb force, but this approximates FDEs by ODEs, and is error prone. Specifically, circular or central orbits are not valid solutions of the electrodynamic 2-body problem, in the textit{absence} of radiation damping. We can see this heuristically, for the classical hydrogen atom, where the full electrodynamic force involves a delay torque. Hence, the century-old argument that classical electrodynamics is inadequate is based on erroneous reasoning (irrespective of whether the conclusion is valid)