Advanced computational methods for simulating the classical hydrogen atom in stochastic electrodynamics
Abstract
Stochastic electrodynamics (SED) is a theory of nature seeking to derive key aspects of quantum mechanics and quantum electrodynamics from a purely classical physics perspective. While SED has been successful in many areas, it has had mixed success when addressing the classical hydrogen atom bathed in classical electromagnetic zero-point radiation. Because analytical approaches are largely intractable, advanced numerical simulation methods are required. To address this, we develop a pseudo-wave formulation that integrates the solid angle in k-space utilizing symmetry, resulting in a significantly reduced memory footprint and lower computational overhead for generating the zero-point radiation spectrum. This optimization is paired with a logarithmic frequency grid, a sliding window tracking the instantaneous Keplerian frequency, and a Tukey smoothing function to eliminate discrete force discontinuities. Integrated via an adaptive RK4 algorithm with step-doubling across highly dense grids of up to 100-million bins, these techniques demonstrate the asymptotic convergence of ensemble stability. We show that increasing grid resolution in the high-frequency domain systematically mitigates artificial electron decay, yielding a simulated probability density function that closely aligns with the quantum mechanical ground state P(r). Crucially, the simulations exhibit stable, low-eccentricity orbits without any observed atomic ionization events.
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BibTeX
@misc{cole2026advanced,
title = {{Advanced computational methods for simulating the classical hydrogen atom in stochastic electrodynamics}},
author = {Daniel C. Cole},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22393},
eprint = {2610.22393},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22393},
}
RIS
TY - UNPB
TI - Advanced computational methods for simulating the classical hydrogen atom in stochastic electrodynamics
AU - Daniel C. Cole
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.22393
UR - https://arxiv.org/abs/2610.22393
AB - Stochastic electrodynamics (SED) is a theory of nature seeking to derive key aspects of quantum mechanics and quantum electrodynamics from a purely classical physics perspective. While SED has been successful in many areas, it has had mixed success when addressing the classical hydrogen atom bathed in classical electromagnetic zero-point radiation. Because analytical approaches are largely intractable, advanced numerical simulation methods are required. To address this, we develop a pseudo-wave formulation that integrates the solid angle in k-space utilizing symmetry, resulting in a significantly reduced memory footprint and lower computational overhead for generating the zero-point radiation spectrum. This optimization is paired with a logarithmic frequency grid, a sliding window tracking the instantaneous Keplerian frequency, and a Tukey smoothing function to eliminate discrete force discontinuities. Integrated via an adaptive RK4 algorithm with step-doubling across highly dense grids of up to 100-million bins, these techniques demonstrate the asymptotic convergence of ensemble stability. We show that increasing grid resolution in the high-frequency domain systematically mitigates artificial electron decay, yielding a simulated probability density function that closely aligns with the quantum mechanical ground state P(r). Crucially, the simulations exhibit stable, low-eccentricity orbits without any observed atomic ionization events.
ER -