Stochastic Electrodynamics: Renormalized Noise in the Hydrogen Ground-State Problem

Theo M Nieuwenhuizen

doi:10.3389/fphy.2020.00335

Abstract

The hydrogen ground state problem is a touchstone for the theory of Stochastic Electrodynamics. Recently, we have shown numerically and theoretically that the H-atom self-ionizes after a characteristic time. In another approach we reconsidered the harmonic oscillator and renormalized the stochastic force in order to suppress high-frequency tails so that all frequency integrals are dominated by the physical resonances. In the present work we consider the regularization of the noise in the hydrogen ground state problem. Several renormalization schemes are considered. Some are well behaved, while in other ones, the high frequency renormalization induces pathologies at low frequencies. In no situation we find a way to escape from the previously signaled self-ionization.

Highlights

Stochastic electrodynamics (SED) is a classical theory that aims to explain quantum phenomena
While the outcomes of various frequency integrals were routinely taken from their resonances, we have recently introduced a renormalization of the stochastic force such that high-frequency pathologies do not occur [10]
Which sets the boundary for self-ionizing orbits because (3.36) exceeds this for other x-values. Both analytical and numerical, have pointed out that the hydrogen problem in Stochastic Electrodynamics leads to a self-ionization of the electron

Summary

INTRODUCTION

Stochastic electrodynamics (SED) is a classical theory that aims to explain quantum phenomena. The two celebrated touchstones of quantum physics, the harmonic oscillator [3,4,5,6] and the hydrogen problem [7,8,9], have received much attention within SED. Liska employed video cards and a modern computer code, speeding up the simulations significantly They were carried out for the non-relativistic problem [16] and with the inclusion of relativistic corrections [17]. Renormalized Noise in SED Hydrogen line was that there was always self-ionization, suggesting that SED is not a basis for quantum mechanics. The question of whether a proper definition of SED can describe the hydrogen atom is of fundamental interest It is the purpose of the present work to reinspect stability in the hydrogen ground-state problem, inspired by our recent renormalization of the stochastic force for the harmonic oscillator.

KEPLER ORBITS

STOCHASTIC ELECTRODYNAMICS

Short-Time Regularization

Nearing the Self-Ionization

Other Renormalization Schemes

DISCUSSION