Historical research guide · 0753 · 2020
Stochastic Electrodynamics: Renormalized Noise in the Hydrogen Ground-State Problem
Theo M. Nieuwenhuizen
In one minute
Stochastic electrodynamics is the attempt to get quantum behaviour out of classical physics plus one extra ingredient: a real random electromagnetic field filling all of space — the zero-point field. An electron then orbits a nucleus like a planet, radiating energy away and absorbing energy back from the field, and the hydrogen ground state is supposed to be the balance point between the two. That is Puthoff’s 1987 picture, and Theo Nieuwenhuizen of the University of Amsterdam is testing whether the balance actually holds. His group’s earlier simulations found the atom drifts apart instead. Here he asks whether that failure was an artefact of how the random force is handled at very high frequencies, and works through several ways of smoothing it. His answer is that it was not: with the noise treated carefully, an orbit whose angular momentum falls below about 0.59 in atomic units still gains more from the field than it radiates. He concludes that a deeper reformulation of the theory is needed.
Connection
Chapter 3 rests on the zero-point field holding the atom together — Puthoff’s 1987 result that the hydrogen ground state is a balance between radiation loss and vacuum absorption. Nieuwenhuizen is the person checking that balance line by line, and his answer sharpens the question rather than closing it: the classical orbit picture needs something more, and he shows exactly what would fix it. His energy-gain calculation is also chapter 6’s subject in miniature — a charged particle drawing net energy out of the vacuum, with a precise threshold for when it happens.
From the source
Stochastic electrodynamics is a classical theory in which particles move in classical orbits and a real stochastic electromagnetic force filling the universe acts as an environment on charged particles, producing quantum behaviour at a statistical level; for the harmonic oscillator it gives reasonable agreement with quantum mechanics, though not in every detail.Section 1, Introduction
In stochastic electrodynamics the binding parameter of the Kepler orbit takes any value from loosely to strongly bound, and the ground state energy is meant to emerge as the time average of the orbital energy over the stationary distribution — the quantum ground state being the single value that classical mechanics would fix.Section 2, Kepler Orbits
In the limit of near-zero orbital energy the accounting is explicit: radiation loss per orbit goes as the square of the coupling divided by the fifth power of the angular momentum, while the average gain from the stochastic field gives a net change per orbit proportional to a critical angular momentum minus the actual one, with that critical value equal to 16 divided by 5π times the square root of 3, or 0.588057 — so orbits below it gain energy on average.Section 3.2, Equations 3.16 and 3.21
Several ways of renormalizing the stochastic force were tried — a short-time scheme built on the curvature matrix, an absolute-value variant, a broken-power variant and a third-root pair of stochastic fields. Some are well behaved and some induce long-time divergences from the high-frequency fix, but every well-defined scheme leaves a positive critical angular momentum, the smallest found being 0.33855.Sections 3.1 and 3.3, Equations 3.20, 3.26, 3.35 and 3.37
The instability is not in the Kepler orbits themselves but in the close approach to the nucleus, where a relatively large amount of energy is absorbed from the stochastic force: adding a repulsive term to the Newton potential raises the effective angular momentum and, for a coefficient of order six or more, yields a stable system with no self-ionization.Section 4, Discussion
Stability of orbits near zero energy can only be achieved in a scheme where the critical angular momentum vanishes; the author expects on physical grounds that this quantity can be proven positive but knows of no such proof, and concludes that a fundamental reformulation of stochastic electrodynamics is required.Section 4, Discussion
The way in
https://doi.org/10.3389/fphy.2020.00335How to cite it
Theo M. Nieuwenhuizen (2020) Stochastic Electrodynamics: Renormalized Noise in the Hydrogen Ground-State Problem doi:10.3389/fphy.2020.00335