The electrodynamic 2-body problem and the origin of quantum mechanics

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.