V. F. Mikhailov. Influence of an electrostatic potential on the inertial
electron mass. Annales de la Fondation Louis de Broglie, 26:33–38, 2001.
V. F. Mikhailov observed a change in the oscillation frequency of electrons in a Barkhausen-Kurz oscillator which is placed inside a charged spherical shell. But subsequent experiments have not confirmed his result.
https://www.researchgate.net/publication/316716539_Experimental_Investigation_of_the_Influence_of_Spatially_Distributed_Charges_on_the_Inertial_Mass_of_Moving_Electrons_as_Predicted_by_Weber's_Electrodynamics
Our thought experiments, on the other hand, suggest that the inertial mass has to change. If not, the center of mass of the system would not be conserved.
Mikhailov and others have thought they are testing Wilhelm Weber's electrodynamic hypothesis from 1848. We did not know of Weber when we designed our thought experiments. The thought experiments use just the basic electrodynamics, Newton's law, and Einstein's mass-energy equivalence.
1. Very basic electrodynamics claims that since the electron in the charged sphere sees a zero electric and zero magnetic field, there are no forces on it. This does not yet determine what is the inertia of the electron, but people seem to think the inertia is the same as for a free electron.
2. Poynting's vector, on the other hand, claims that the movement of the electron causes energy flow in the electric field surrounding the sphere. That energy flow should exert inertia on the movement of the electron.
3. The Aharonov-Bohm effect says that also a constant potential affects electron behavior. There is no need for the field strength vector to be non-zero at the electron.
Why were several experimenters unable to measure the change in the inertial mass? The obvious suspect is the influence of the electron on the charge distribution of the metal sphere surrounding it.
The metal sphere tries to keep its electric field uniform and normal to the surface. If we move an electron slowly inside the shell, then the electric field outside the shell does not change at all. There is no flow of energy in the electric field outside the shell, and thus no extra inertia from the electric potential of the shell.
The charge distribution in the shell polarizes to cancel any change in the outside electric field. We may model the polarization with a "mirror electron" which moves to the opposite direction from the test electron. The effective inertial mass of the test electron should thus be constant, twice the inertial mass of a free electron.
There is an electric current in the shell. That will cause resistive energy loss. In the oscillator, there is energy loss from electromagnetic radiation. Can we discern these losses? Did the experimenters calculate these?
At high frequencies of 1 GHz or more, the field of the oscillator will "mostly" be electromagnetic radiation. How does that affect the model?
The electron in the hydrogen atom has a frequency of some 10^18 Hz. Hydrogen does not show a distorted spectrum inside a metal shell. Maybe the electric neutrality of the atom cancels the effects on the inertial mass of the electron in the atom. This is probably a quantum effect. The mirror electron model would make the inertial mass double.
The shell should be made of an insulator. Even in that case, can we be sure that there is no current or significant polarization in the insulator?
There are several metal parts around the oscillating electrons inside the shell. The electron will polarize charges in these, and the influence tends to reduce the temporal change of the electron's electric field. Did the experimenters calculate these?
Polarization of air and non-metallic parts will shield some of the changes of the electric field.
We need to check the articles of the experiments.
Mikhailov and others have thought they are testing Wilhelm Weber's electrodynamic hypothesis from 1848. We did not know of Weber when we designed our thought experiments. The thought experiments use just the basic electrodynamics, Newton's law, and Einstein's mass-energy equivalence.
1. Very basic electrodynamics claims that since the electron in the charged sphere sees a zero electric and zero magnetic field, there are no forces on it. This does not yet determine what is the inertia of the electron, but people seem to think the inertia is the same as for a free electron.
2. Poynting's vector, on the other hand, claims that the movement of the electron causes energy flow in the electric field surrounding the sphere. That energy flow should exert inertia on the movement of the electron.
3. The Aharonov-Bohm effect says that also a constant potential affects electron behavior. There is no need for the field strength vector to be non-zero at the electron.
Sources of error in the experiments
Why were several experimenters unable to measure the change in the inertial mass? The obvious suspect is the influence of the electron on the charge distribution of the metal sphere surrounding it.
The metal sphere tries to keep its electric field uniform and normal to the surface. If we move an electron slowly inside the shell, then the electric field outside the shell does not change at all. There is no flow of energy in the electric field outside the shell, and thus no extra inertia from the electric potential of the shell.
The charge distribution in the shell polarizes to cancel any change in the outside electric field. We may model the polarization with a "mirror electron" which moves to the opposite direction from the test electron. The effective inertial mass of the test electron should thus be constant, twice the inertial mass of a free electron.
There is an electric current in the shell. That will cause resistive energy loss. In the oscillator, there is energy loss from electromagnetic radiation. Can we discern these losses? Did the experimenters calculate these?
At high frequencies of 1 GHz or more, the field of the oscillator will "mostly" be electromagnetic radiation. How does that affect the model?
The electron in the hydrogen atom has a frequency of some 10^18 Hz. Hydrogen does not show a distorted spectrum inside a metal shell. Maybe the electric neutrality of the atom cancels the effects on the inertial mass of the electron in the atom. This is probably a quantum effect. The mirror electron model would make the inertial mass double.
The shell should be made of an insulator. Even in that case, can we be sure that there is no current or significant polarization in the insulator?
There are several metal parts around the oscillating electrons inside the shell. The electron will polarize charges in these, and the influence tends to reduce the temporal change of the electron's electric field. Did the experimenters calculate these?
Polarization of air and non-metallic parts will shield some of the changes of the electric field.
We need to check the articles of the experiments.
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