Dual Lorentz force and free-fall atomic model

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Dual Lorentz force and free-fall atomic model

Postby Jarek » Sun Jan 24, 2016 7:23 am

Electric and magnetic parts of Maxwell's equations are kind of similar, so physical effects relating these properties have many 'dual' analogues - with exchanged places.
For example in Aharonov-Bohm effect, the phase of charged particle depends on side of magnetic flux tube it comes through, while in its 'dual' analogue: Aharonov-Casher, the particle has magnetic moment and tube contains line of charge (it was used e.g. for neutron or fluxon interference).
Another interesting 'dual' effect (hypothetical) can be found in magnetic monopole Wikipedia article - full expression for Lorenz force in such case would be:
where q_m is magnetic charge - the last term corresponds to magnetic monopole - electric field interaction.

The question is if we should expect similar term for not only magnetic monopoles, but also for much more common: magnetic dipoles like electron or neutron ?
So imagine classical electron traveling in proton's electric field - let's change reference frame such that electron stops (for infinitesimal time) and proton is moving in also magnetic field created by quite large electron's magnetic moment - because of 3rd Newton's law, resulting Lorentz force should also work on electron ...
Here is Lagrangian for such electron's movement:
where the last term would correspond to such eventual magnetic moment-electric field interaction.
Derivation: https://dl.dropboxusercontent.com/u/124 ... eefall.png

As many persons here don't like quantum description (which I see as an effective one), we would like to understand the trajectories of electrons in atoms/molecules.
The standard Bohr/Sommerfeld models assume circular or elliptic trajectories, and disagree with nature - the discussed dual Lorentz force might bring the answer.
So it says that electron falling on nucleus, due to own magnetic dipole moment, undergoes perpedicular Lorentz force - which bends the trajectory, preventing falling onto the nucleus - this is so called free-fall atomic model, which is claimed to give much better agreement: https://en.wikipedia.org/wiki/Free-fall_atomic_model
one-electron simulations in Mathematica: https://dl.dropboxusercontent.com/u/124 ... reefall.nb
slides: https://dl.dropboxusercontent.com/u/124 ... eefall.pdf

While this dual Lorentz force seems important: classical analogue of spin-orbit interaction, I couldn't find any serious materials about it - have you met it anywhere?
Where it might be important? Some experiments with electrons?
What other dual effects seem important ... forgotten?
Have you seen some good materials about this free-fall atomic model? What do you think about it?
Jarek
 
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