arXiv subjects

David C. Lush

Publications and source records attributed to David C. Lush.

8 recordsLinked to original sources

arXiv2024

Quantum Wave Mechanics as the Magnetic Interaction of Dirac Particles

It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic force between two classical point charges, each undergoing relativistic circulatory motion of small radius compared to the separation between their centers of circulation, and assuming a time-symmetric electromagnetic interaction, is modulated by a factor that behaves similarly to the Schrödinger wavefunction. The magnetic force between relativistically-circulating charges has been shown previously to have a radially-directed inverse-square part of similar strength to the Coulomb force, and sinusoidally modulated by the phase difference of the charges' circulatory motions. The magnetic force modulation in the case of relatively moving centers of charge circulation solves an equation formally identical to the time-dependent free-particle Schrödinger equation, apart from a factor of two on the partial time derivative term. Considering motion in a time-independent potential obtains that the modulation also satisfies an equation formally similar to the time-independent Schrodinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schrödinger equation is solved exactly by the resulting modulation function. The significance of the quantum mechanical wavefunction follows straightforwardly from these observations. After considering the modification of Wheeler-Feynman absorber theory required by the adoption of Minkowski-Osiak relativity, the model is extended to obtain the full complex Schrödinger wavefunction.

physics.gen-ph↗

arXiv2019

The Magnetic Force as a Kinematical Consequence of the Thomas Precession

The requirements imposed by relativistic covariance on the physical description of two interacting classical charged particles are investigated. Because rotational pseudo-forces 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. Other forces corresponding to the Euler and centrifugal rotational pseudo-forces 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 anti-centrifugal force of the Thomas precession is shown.

physics.class-ph↗

arXiv2019

Does Bohm's Quantum Force Have a Classical Origin?

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 {\em 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.

physics.class-ph↗

arXiv2010

Angular momentum nonconservation and conservation in quasiclassical Positronium

It is shown that due to Thomas precession, angular momentum is not generally a constant of the motion in a quasiclassical model of the Positronium atom consisting of circular-orbiting point charges with intrinsic spin and associated magnetic moment. Despite absence of externally-applied torque, angular momentum is a constant of the motion only if the electron and positron intrinsic angular momentum vector components perpendicular to the orbital angular momentum are antiparallel and of equal magnitude.

physics.class-ph↗

arXiv2010

On the influence of hidden momentum and hidden energy in the classical analysis of spin-orbit coupling in hydrogenlike atoms

In a recent article, Kholmetskii, Missevitch and Yarmin ["On the classical analysis of spin-orbit coupling in hydrogenlike atoms," Am. J. Phys. 78(4), April 2010 (428-432)] examine in detail the spin-orbit coupling in the semiclassical hydrogenic atom, and identify a need to account for non-Coulomb forces not included in the standard analysis. Kholmetskii, et al., showed that the experimentally-measured coupling continues to be obtained when the new forces are incorporated in the analysis. This requires that the change in orbital radius due to non-Coulomb forces is also properly accounted for. In response to a comment, Kholmetskii, et al., showed that the experimentally-measured coupling continues to be obtained when so-called "hidden momentum" forces are also included. However it has been postulated that when hidden momentum is nonvanishing, a corresponding hidden energy must also be present, that was not included in the total energy by Kholmetskii, et al. Hidden energy is postulated necessary to obtaining a relativistically covariant description. Inclusion of hidden energy leads to disagreement with the experimentally-determined spin-orbit coupling magnitude if the Bohr postulate, that orbital angular momentum is quantized in whole multiples of the reduced Planck constant, is assumed to apply to kinetic momentum alone. The empirical result may be recovered in the semiclassical picture and using the general approach developed by Kholmetskii, et al., if the Bohr postulate is reinterpreted to apply to orbital angular momentum that consists of hidden as well as kinetic momentum.

physics.class-ph↗

arXiv2010

Comment on "On the classical analysis of spin-orbit coupling in hydrogenlike atoms," [Am. J. Phys. 78 (4) 428-432, April 2010]

In their recent paper, Kholmetskii, Missevitch, and Yarman "reanalyze the usual classical derivation of spin-orbit coupling in hydrogenlike atoms" and find a result "in qualitative agreement with the solution of the Dirac-Coulomb equation for hydrogenlike atoms." However, the authors' result is based on an equation of translational motion of the electron that omits any contribution due to the existence of "hidden" momentum of the electron intrinsic magnetic dipole moment in the electric field of the nucleus. Accounting for hidden momentum is necessary to obtaining conservation of linear momentum in the interaction of a magnetic dipole with a point charge. If hidden momentum is omitted from the description, the force on the nucleus due to the electron will differ from the force on the electron due to the nucleus. Thus, omitting the hidden momentum contribution, the binding energy including the spin-orbit coupling cannot be consistently calculated, while including hidden momentum, the value obtained is in disagreement with experiment.

physics.class-ph↗

arXiv2010

Regarding Llewellyn Thomas's paper of 1927 and the "hidden momentum" of a magnetic dipole in an electric field

L. H. Thomas, in his 1927 paper, "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.

physics.gen-ph↗

arXiv2009

On the Bohr radius relationship to spin-orbit interaction, spin magnitude, and Thomas precession

The dynamics of the spin-orbit interaction in atomic hydrogen are studied in a classical electrodynamics-like setting. A Rutherfordian atomic model is used assuming a circular electron orbit, without the quantum principle as imposed arbitrarily in the Bohr model, but with an ad hoc incorporation in the electron of intrinsic spin and associated magnetic dipole moment. Analyzing the motions of the electron spin and orbital angular momenta, it is found that in the presence of Thomas precession, the total angular momentum averaged over the orbit is not generally a constant of the motion. It is noted this differs from the finding of Thomas in a similar assessment of 1927, and the reason for this difference is provided. It is found that although the total orbit-averaged angular momentum is not a constant of the motion, it precesses around a fixed axis similarly to the precession of the total angular momentum vector seen in spin-orbit coupling in quantum theory. The magnitude of the angular velocity of the total orbit-averaged angular momentum is seen to vanish only when the spin and orbital angular momenta are antiparallel and their mutual precession frequencies equate. It is then found, there is a unique radius where the mutual precession frequencies equate. Assuming the electron magnetic moment is the Bohr magneton, and an electron g-factor of two, this radius corresponds to where the orbital angular momentum is the reduced Planck's constant. The orbit radius for stationary total angular momentum for the circular orbit model with nonzero orbital angular momentum is thus the ground-state radius of the Bohr model.

physics.gen-ph↗