Classical Coulomb Resonator Spectra:\\ Stability, Non-Inertial Energy Balance, and\\ Model-Specific Stationary Radiation Scales

Version 9. A purely classical system consisting of a proton and an electron is considered as a Coulomb resonator. Due to the Coulomb interaction, the electron "falls" toward the proton but "misses" it, resulting in one of two possible scenarios: circular motion or oscillations passing nearly through the center. Such a system is unstable due to radiation and the electron's energy loss, calculated using the Larmor formula. However, when accounting for the fact that all real reference frames are stochastically non-inertial, the energy pumped by stochastic non-inertial forces is re-emitted as electromagnetic radiation. Equating energy input and output while requiring the classical system's stability yields an ensemble of classical resonators. Consequently, the Coulomb resonator's spectrum is formed not only by the probabilistic hopping of the electron from one resonator to another but is also supplemented by the spectrum resulting from non-inertial pumping and Larmor re-emission associated with the first stationary resonator (0.35725 1/cm, 10.71 GHz, 28.0 mm, etc., for subsequent stationary cases).