Friday, October 31, 2014

Is the Quantum Hamilton-Jacobi Equation just the Classical Hamilton-Jacobi Equation Properly accounting for Magnetic Interactions?

Wikipedia has a nice description of the quantum potential of Bohmian Mechanics, and the more I read it, the more I think it can fit in with the idea that quantum behavior is just the classical electrodynamical consequences of elementary particles being charges circulating at the speed of light.   In the quantum potential article, it is already discussed that the quantum potential can be equated to the internal energy of the zitterbewegung.  What better way for this to influence the motion than via magnetic interactions?

However, de Broglie-Bohm theory is, like quantum mechanics generally, a non-local theory.  Classical electrodynamics is of course Einstein-local, but it's also widely recognized that time-symmetric electrodynamics, while remaining Einstein local, has a substantial similarity to non-locality. Wheeler and Feynman famously used time-symmetric interactions with the rest of the universe to explain radiation reaction. So, the classical time-symmetric Hamilton-Jacobi equation accounting for magnetic zitterbewegung interactions may lead to a theory that has the apparent non-locality of quantum mechanics.

So far I've been focusing on just one small part of the total magnetic interaction; the part that's radially-directed and has a non-vanishing average and falls off inverse-squarely at long distance.  There are many other terms that would also need to be taken into account, particularly at distances where the separation is not large compared to the Compton radii of the interacting particles.  On the other hand, those that fall off less than inverse squarely will have a longer-range character, and when treated time-symmetrically, can plausibly interact significantly and seemingly non-locally with, say, slits in an obstructing plane.

A couple of days ago I got my paper returned from Physics Letters A.  Here is what the editor said:

Ms. Ref. No.:  PLA-D-14-02082
Title: Radially Acting, Relative Spin Phase and Polarization Modulated, Inverse Square Law Magnetic Force Between Spinning Charged Particles
Physics Letters A

Dear Mr. Lush,

Thank you for submitting your work to our journal.
I have read your manuscript with interest.
I regret that it is not suitable for publication in Physics Letters A since it does not satisfy our criteria of urgency and timeliness.
Please consider submitting your work to a journal which has a more pedagogical bias.

Yours sincerely,

{name removed)

I think I will take the kind editor's advice and submit it to a different journal, but first I'm going to add some speculation about the quantum force and the quantum Hamilton-Jacobi equation.

Thursday, October 30, 2014

Is the Quantum Force of Bohmian Mechanics the Magnetic Force Between Spinning Dirac Particles?

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.