The Motion of a Lorentz Electron as a Wave Phenomenon

Young‐Sea Huang

Zhiyong Wang, Cai-Dong Xiong

C. S. Unnikrishnan

I show that the claim of the observation of matter wave beat phenomena in the classical macrodomain by Varma et al. [Phys. Rev. E 65, 026503 (2002)] is based on a mistaken interpretation of effects arising from multiple focusing of an electron beam in an axial magnetic field. I present the basic physical facts that mimic wavelike phenomena and suggest a classical explanation of modulations reported by Varma et al. Realization that the macroscopic "de Broglie wavelength" used by Varma et al. is the same as the focusing distance of a monoenergetic electron beam in the uniform magnetic field leads to a full classical explanation of all the effects reported by Varma et al. The reported observations are not evidence for any quantumlike phenomenon in the macrodomain, and their results do not indicate any violation of the Lorentz equation of motion.

Michael Tsamparlis

Earle H. Kennard

Walter Wessel, Stanley J. Czyzak

The independence of momentum and velocity in Dirac's theory of the electron may be understood classically as a consequence of the radiation reaction force. In earlier work one of the authors has tried to interpret the whole spin phenomenon on this basis, considering the new degrees of freedom as representatives of the higher time derivatives in the equation of motion of a particle extended in space. A consequent treatment of this question by Bopp on the basis of his linear electrodynamics revealed that this program is possible only for integral spin; also, it seemed to be necessary to ignore the non-conservative part of the radiation reaction force. We show here that without alteration of the new formalism the spin may be introduced as an intrinsic feature of the particles, as in older theories, so that half-integral values are included. The Poisson brackets are derived in full generality without reference to a specific model by extension of an idea of Anderson. It is then shown by a contact transformation first discovered in quantum mechanics that the motion under the (third order) radiation reaction force is contained as a particular integral in the (fourth order) equations of motion, which we have in common with Bopp. This holds exactly in absence of the Lorentz force and suggests a simple scheme for the interpretation in quantum mechanics of the radiation reaction. In order to maintain nearly the particular motion in presence of the Lorentz force, a slight alteration of the Hamiltonian is necessary, which has empirical support from the evaluation of the corresponding wave equation.