It could be that there simply is no extra inertia in a potential, but we are not willing to abandon our extra inertia hypothesis yet.
Classically, the acceleration of the electron would cause it to radiate, but that does not happen if the electron is on a stationary orbit. Could it be that the absence of extra inertia is related to this? Maybe the field is not "dynamic" when the electron is stationary?
On March 13, 2021 we were able to derive the Lamb shift, assuming that the electric field of the electron is elastic (= the rubber plate model). This is a dynamic behavior of the field.
We should find an explanation why certain dynamic behavior of the field happens and the other not.
There is not enough energy to "implement" the miniature energy flow in the combined field of the electron and the proton?
In a macroscopic system we may hypothesize that the Poynting vector describes an energy flow in space. Let the electron in a hydrogen atom be at a typical distance from the proton. Then its potential energy is -27.2 eV.
If we have a photon whose energy is 27.2 eV, its wavelength is 44 nanometers, or 420 times the diameter of the hydrogen atom. We cannot describe miniature energy flows within the atom with such photons. The spatial resolution is too poor.
Could it be that the energy flow does not exist because a photon is not able to resolve it?
When the electron is very close to the proton, at 10⁻¹⁵ m, the potential is ~ -511 keV, and the corresponding photon wavelength is 2.4 * 10⁻¹² m. Again, it is not possible to resolve the miniature energy flow with the photon of the given wavelength.
What is the nature of the energy flow which is described by the Poynting vector? It arises from changes in the electromagnetic field. It does not look like ordinary, oscillating photons.
The Lamb shift and the rubber plate model of the electron electric field
On March 13, 2021 we were able to explain the Lamb shift through the assumption that the electric field of the electron is elastic, and the far field does not have time to follow the electron in abrupt movements. The end result is that the effective mass of the electron is reduced.
In this case, the interaction between the far field and the electron are primarily forces which transfer momentum.
"Virtual photons" which transfer momentum are quite different things from photons which transfer energy. It might be that the resolution problem, which we described in the preceding section, does not exist for virtual photons.
Also, in this case the process is private to the electron plus its own field, while the Poynting vector process is collective with the proton.
It might be that the resolution problem does not appear here.
Radiation of a photon when an electron falls into a lower energy state
This phenomenon falls into the category of energy flow. The process is private for the electron plus its own field.
The resolution problem does not appear, because it is the far field of the electron which is lagging behind the electron motion, and "produces" the photon. The photon is "born" in a large volume.
Conclusions
In this blog post we touched a fundamental problem: what classical phenomena with charges also appear in the miniature world of the hydrogen atom?
It sounds quite natural that the Poynting vector energy flow cannot be reproduced in the miniature world. The resolution is not good enough.
The production of an electromagnetic wave is a process which is private to the electron and its own field. We know that the classical process does happen in the miniature world, too.
We have explained the Lamb shift with the elasticity of the electric field of the electron. The process is somewhat like the production of an electromagnetic wave, but in this case no photon escapes. The process is private to the electron and its own field.
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