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arXiv:quant-ph/0209021

Quantum mechanics as electrodynamics of curvilinear waves

Alexander G. Kyriakos

Published Sep 2, 2002• 3 citations
arXivHTMLPDF

Abstract

The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory.
DOI
10.48550/arxiv.quant-ph/0209021

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In the first part of this work (http://www.arxiv.org/abs/quant-ph/0509044), it was shown that the Klein-Gordon-Maxwell electrodynamics in the unitary gauge allows natural elimination of the particle wave function and describes independent evolution of the electromagnetic field. Therefore, the electromagnetic field can be regarded as the guiding field in the Bohm interpretation of quantum mechanics. An extension of those results to the Dirac-Maxwell electrodynamics was less general, but represented at least an interesting toy model of quantum theory. Another model based on the Dirac-Maxwell electrodynamics is considered in this work. The model also typically allows elimination of the wave function and describes independent evolution of the electromagnetic field.
This article proposes an interpretation of quantum physics based on the theory of solitons. According to this interpretation, the elementary particle (in particular, the electron) is a soliton solution of the system of nonlinear equations, while the linear equations of quantum mechanics for the wave functions represent the boundary conditions for soliton solutions. The nonlinear equations for the quantum electron are hypothesized to be the usual Maxwell equations in which the charge and current densities are expressed through quadratic combinations of the electromagnetic field strength. The complex wave function describing the motion of the electron in this case is the usual electromagnetic wave, where the real part is the electric field strength, and the imaginary part is the magnetic field strength. Soliton equations, Maxwell equations and quantum equations are easily written using 3+1 Pauli matrices, which indicates that the 3+1 system of coordinates of space and time is a natural realization of the particle-wave soliton world. The proposed interpretation allows combining both the Copenhagen interpretation and Bohm's theory of "hidden" variables.