Non-Inertial Coulomb--Resonator Response Frequencies and Spectral Shifts in Hydrogen

Abstract

Version 7. Revised version focused on the non-inertialCoulomb-resonator interpretation and THz/GHz response-frequency signatures. We model the classical electron--proton system as a Coulomb resonatorwith stationary resonant modes in a weakly non-inertial referenceframe. The intrinsic Coulomb time and the non-inertial response timedefine a small parameter that orders the jerk--snap truncation. Thecentral physical picture is that a stationary mode of the Coulombresonator can resonantly re-emit energy supplied by a broadbandnon-inertial background while remaining in that mode. The leadingjerk contribution determines the energy scale of the fundamental mode,$9.10\,\mathrm{meV}$, and parameter-free characteristic wavelengthshifts for hydrogen-like reference intervals. In addition to the usualtransition frequencies corresponding to energy differences betweenselected stationary states, the model predicts weak internalnon-inertial response frequencies of individual resonator modes. Thesefrequencies scale as $n^{-5}$ and shift from the terahertz range forthe first mode into the microwave and radio-frequency ranges for highermodes. The spectrum of the described classical Coulomb resonator showsorder-of-magnitude agreement when compared with the hydrogen spectrum.There is nothing of quantum mechanics or QED in the present model; itconsiders exclusively the spectroscopic consequences of thenon-inertial Coulomb resonator and compares them with the observedhydrogen spectrum.