Soliton Interpretation of Quantum Theory

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.