In Bohmian mechanics there is a quantum potential, and from its gradient

can be obtained a "quantum force." A few days ago I calculated the quantum force for the ground state of hydrogen and got that it's equal and opposite the Coulomb force between two charges. This is consistent with what I remembered about Bohmian mechanics, that in the s states the electron is stationary. This seemed far-fetched to me. However, it is not entirely unlike my recent finding regarding the magnetic force between two spinning charged particles where their spin is a consequence of circulatory motion of the charges at the speed of light.

In any case, if we have two particles that are going around in little circles at the speed of light (what I called zitter particles in my new paper, but Rivas refers to in the electron case as a Dirac electron, if I understand him correctly) then it's easy to have that the magnetic force between them exactly cancels the Coulomb force expected if the were static charges, if the circular motion centers stay fixed. The phase relationship between the two particles' positions in their circulatory motions however must be evaluated accounting for the propagation delay. This means that the phase relationship including retardation changes with separation, modulating the inverse square law magnetic force radially-acting part. The modulation wavelength is the Compton wavelength.

It's not obvious to me how this might correspond precisely to the quantum force of Bohmian mechanics but it's at least reminiscent of it. Of course, a classical force corresponding to the quantum force cannot cancel the Coulomb force precisely everywhere.

Manchester

2 hours ago

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