In the de Broglie -Bohm formulation of quantum mechanics, the electron is stationary in the ground state of the hydrogen atom, because the quantum force exactly cancels the Coulomb attraction of the electron to the proton. In this paper it is shown that classical electrodynamics similarly predicts the Coulomb force can be effectively canceled by part of the magnetic force that occurs between two similar particles each consisting of a point charge moving with circulatory motion at the speed of light. Supposition of such motion is the basis of the Zitterbewegung interpretation of quantum mechanics. The magnetic force between two luminally-circulating charges for separation large compared to their circulatory motions contains a radial inverse square law part with magnitude equal to the Coulomb force, sinusoidally modulated by the phase difference between the circulatory motions. When the particles have equal mass and their circulatory motions are aligned but out of phase, part of the magnetic force is equal but opposite the Coulomb force. This raises a possibility that the quantum force of Bohmian mechanics may be attributable to the magnetic force of classical electrodynamics. It is further shown that non-relativistic relative motion between the particles leads to modulation of the magnetic force with spatial period equal to the de Broglie wavelength.
The Kinematics of an Electron with an Axis", explained the then-anomalous factor of one-half in atomic spin-orbit coupling as due to a relativistic precession of the electron spin axis. Thomas's explanation required also that the total of the orbit-averaged, or "secular", orbital and spin angular momenta of the electron be a conserved quantity, as he found to be the case for either of two possible equations of translational motion of the magnetic electron. Thomas's finding is seen in the present work to require the "hidden momentum" of the electron intrinsic magnetic moment in the Coulomb field of the proton be omitted from its equation of translational motion. Omission of the hidden momentum is contrary to the position of standard modern electrodynamics texts, and leads to violation of Newton's law of action and reaction, negating Thomas's result. Including the hidden momentum results in linear momentum conservation, but in the presence of Thomas precession, the total angular momentum is not generally conserved. The total angular momentum precesses for non-aligned spin and orbit, even in the absence of externally-applied magnetic field. As Thomas observes that secular angular momentum conservation is a necessary condition for a consistent simultaneous description of spin-orbit coupling and the anomalous Zeeman effect, such is not possible within classical electrodynamics in its absence.
The requirements imposed by relativistic covariance on the physical description of two interacting classical charged particles are investigated. Because rotational pseudoforces cannot be caused by Thomas precession, kinematical considerations demand the presence of compensatory forces when Thomas precession of an inertial reference frame is observed. The magnetic force on a moving charge is apparently one such force, where Thomas precession of the laboratory frame is seen by an observer co-moving with the charge. Thus, no acceleration of the field source charge is required to cause the necessary Thomas precession, consistent with the known properties of the magnetic interaction. However, when the field source charge is accelerating, an additional magnetic-like force is expected. Other forces corresponding to the Euler and centrifugal rotational pseudoforces are also predicted by this line of reasoning. The plausibility that an anti-centrifugal force of the Thomas precession may account for the binding of quarks into nucleons is investigated. The similarity of the magnetic force on a relativistically-moving charge in the radiative magnetic field of a nearby Coulomb-accelerating charge to the predicted anticentrifugal force of the Thomas precession is shown.
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