Historical research guide · 0909 · 2016
On the Stability of Classical Orbits of the Hydrogen Ground State in Stochastic Electrodynamics
Theodorus M. Nieuwenhuizen
In one minute
Stochastic electrodynamics takes the zero-point field literally: real classical electromagnetic modes fill the vacuum, each carrying half a quantum of energy, and the atom holds its ground state by absorbing exactly as much from that field as it radiates away. Luis de la Peña and Harold Puthoff proved the balance works for circular orbits. Theodorus Nieuwenhuizen extends their argument to elliptical ones and finds a gap: for very stretched orbits with energy near zero, each revolution takes in more than it gives back, and the electron eventually leaves — which is what his group's three-dimensional simulations kept doing. He locates the boundary precisely, at an angular momentum of 0.588 in units of Planck's constant over two pi, with the closest approach at about a sixth of a Bohr radius. He then adds a second, dipole-like term to the potential, keeps the problem exactly solvable, and shows that when that term is repulsive enough a stable ground state is predicted after all. Positronium behaves the same way.
Connection
Chapter 3 rests on the idea that the atom's ground state is a balance struck with the zero-point field rather than a postulate, and this is the sharpest published test of that balance. It also tells chapter 1 what a decisive result looks like here: the calculation names the exact orbit, the exact angular momentum, and the exact modification that would change the answer.
From the source
In stochastic electrodynamics the vacuum is treated as a real physical field of classical electromagnetic modes each carrying half of Planck’s reduced constant times the mode frequency, and on that basis the theory already accounts for van der Waals forces, the logarithm of the Lamb shift between the hydrogen 1s and 2p states, the Casimir effect and the Unruh effect.Section 1, paragraphs 1 and 2
For circular orbits the averaged energy gained from the stochastic field and lost to radiation balance in the way de la Peña and Puthoff first derived: at large negative energy the net change is positive, preventing collapse onto the nucleus, and at small negative energy it is negative, preventing self-ionisation.Section 2.3, the explicit result at zero eccentricity
Extending the same gain-and-loss calculation to elliptical orbits gives a gain function that runs from one half at zero eccentricity to 0.588084 in the limit of maximum eccentricity, and a net energy gain of a fixed amount per revolution once the energy approaches zero.Section 2.3, the gain function and its two limiting values
The instability therefore has a sharp threshold: orbits that reach near-zero energy with angular momentum below 0.588 in units of the reduced Planck constant self-ionise, the corresponding closest approach being 0.173 Bohr radii, and the numerical distribution of angular momentum from the author’s own simulations carries hardly any weight below that value.Section 2.3, critical values; Figure 1 caption; Section 4, second paragraph
The maximum orbital speed at that perihelion is 0.024 of the speed of light, so relativistic corrections are unlikely to be the cause, which the author states was verified numerically.Section 4, second paragraph
Adding a radially directed dipolar potential falling as one over the square of the distance keeps the problem exactly solvable, leaves circular-orbit stability intact, and in the repulsive case is predicted to give a stable ground state above a finite threshold in the coupling — a regime the author names as the interesting test for the numerical approach.Sections 3.4 and 3.5; Section 3.7 closing sentence; Section 4, third paragraph
The way in
https://doi.org/10.3390/e18040135How to cite it
Theodorus M. Nieuwenhuizen (2016) On the Stability of Classical Orbits of the Hydrogen Ground State in Stochastic Electrodynamics doi:10.3390/e18040135