Simulation of the hydrogen ground state in stochastic electrodynamics
Theo M. Nieuwenhuizen · Matthew T. P. Liska
Abstract and summary · read the original at the source
In one page
Stochastic electrodynamics keeps the electron an ordinary classical particle and hands the quantum work to a real random electromagnetic field — the zero-point field, half a quantum of energy in every mode. Its central promise is Puthoff’s: hydrogen is stable because the orbiting electron absorbs from that field exactly as much as it radiates away. Theo Nieuwenhuizen and Matthew Liska of the University of Amsterdam put the promise on a computer. They integrate the electron’s equation of motion with damping and noise directly, build the random field from a sum of frequency components, and run it on graphics hardware, which lets them treat the full three-dimensional atom and reach far longer times than Cole and Zou managed in 2003. For short runs the orbit statistics drift toward the quantum ground-state distribution, which is what the theory hopes for. Run longer and every scheme they tried ends the same way: the electron gains more than it loses, the orbit stretches, and the atom ionises. They name the suspect energy term and ask what would cancel it.
Why it matters hereChapter 3 rests on the hydrogen ground state being a balance struck with the zero-point field rather than a postulate, and this is the first attempt to watch that balance hold or fail in three dimensions, for millions of orbits, on real hardware. It is also chapter 6 in miniature: the term the authors blame for the ionisation is a charged particle steadily drawing energy out of the vacuum field.
What it claims
01Stochastic electrodynamics assumes the physical vacuum consists of fluctuating classical electromagnetic fields carrying half a quantum of energy in each mode — the zero-point Planck spectrum — and asserts that the radiative energy an orbiting electron loses is statistically compensated by energy gained from those fields, which is what makes hydrogen, and matter generally, stable.Abstract; Section 1, Introduction, opening paragraph
Published and peer-reviewed02The hydrogen problem is solved by numerically integrating the Abraham–Lorentz equation in the dipole approximation, with the Gaussian stochastic field replaced by a one-dimensional sum over frequency components chosen to reproduce the same correlation function, and the dynamics parallelised in OpenCL on a graphics processor. This improves on Cole and Zou’s 2003 attempt by treating the full three-dimensional problem and reaching far longer simulation times.Abstract; Section 2, Eq. 1; Section 4 and Appendix
Published and peer-reviewed03The conjectured phase-space density for the ground state, written as a function of the conserved energy and angular momentum, reproduces the quantum-mechanical result exactly when integrated over momenta: the radial density comes out as the square of the 1s wavefunction times the spherical harmonic, correctly normalised.Section 3, Eqs. 42 to 46
Published and peer-reviewed04With a moving frequency cutoff at 2.5 times the orbital frequency the first runs looked stable, but instabilities grew on timescales of order ten million Bohr periods and ended in ionisation; higher harmonics ionised sooner still, and a fixed cutoff ionised within about ten thousand orbits, with the electron’s energy climbing toward zero and its orbital eccentricity increasing first.Sections 4.1.1 and 4.1.2
Published and peer-reviewed05The authors identify the suspect: the energy of the electron in the vector potential, which quantum mechanics absorbs as a renormalisation of the electron rest mass, acts in stochastic electrodynamics as a real dynamical energy transferred through the momentum-times-potential term of the Hamiltonian, on a scale of the fine-structure constant times the electron rest energy — far above the Rydberg energy. They ask whether a compensation mechanism for that transfer exists.Section 5, Summary and outlook, paragraph 3
What to watch06The named next measurements are to add the magnetic field, the weak spatial dependence of the electric field and spin-orbit coupling to the simulation. Relativistic corrections matter only when the electron comes close to the nucleus and are expected to enter as small mechanical corrections to the Kepler problem, so the authors do not expect them to change the finding.Section 5, final paragraph
What to watch
Read it · abstract
Abstract
Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy one half of the reduced Planck constant times the frequency in each mode, i.e., the zero-point Planck spectrum. While this classical theory explains many quantum phenomena related to harmonic oscillator problems, hard results on nonlinear systems are still lacking. In this work the hydrogen ground state is studied by numerically solving the Abraham–Lorentz equation in the dipole approximation. First the stochastic Gaussian field is represented by a sum over Gaussian frequency components, next the dynamics is solved numerically using OpenCL. The approach improves on work by Cole and Zou 2003 by treating the full 3d problem and reaching longer simulation times. The results are compared with a conjecture for the ground state phase space density. Though short time results suggest a trend towards confirmation, in all attempted modelings the atom ionises at longer times.
The way in
https://doi.org/10.1088/0031-8949/2015/t165/014006Published in Physica Scripta T165, 014006, in the topical issue on the foundations of quantum mechanics, by Theo M. Nieuwenhuizen of the Institute for Theoretical Physics at the University of Amsterdam and the International Institute of Physics at Natal, with Matthew T. P. Liska. The manuscript is free to read on arXiv as 1502.06856, but that posting carries arXiv’s non-exclusive distribution licence and the version of record carries IOP’s text-and-data-mining terms — neither is a Creative Commons licence — so this page holds the summary, the claims and the authors’ own abstract and sends the reader to the source. This is the simulation paper in Nieuwenhuizen’s hydrogen series: the 2019 harmonic-oscillator paper that fixes the method is at /library/stm-b98f6364e3, and the 2020 renormalised-noise paper that returns to hydrogen with the noise handled several different ways is at /library/stm-9ebf7acf49. Read this one for what the computer actually did.
How to cite it
Theo M. Nieuwenhuizen, Matthew T. P. Liska (2015) Simulation of the hydrogen ground state in stochastic electrodynamics. doi:10.1088/0031-8949/2015/t165/014006
Where it sits in the curriculum
Inertia and gravity from the vacuumWhat the vacuum isThe evidence ladderEnergy from the vacuum