Statistical Ensemble Technique in Application to Description of the Electron

Abstract

A dynamic systems SP and SD described by the Pauli equation and the Dirac equation are investigated merely as a distributed dynamic systems. No quantum principles are used. The system SP is shown to be a statistical ensemble of non-relativistic stochastic pointlike particles. The electron spin is shown to have a classical analog which is a collective (statistical) property of the ensemble (not a property of a single electron). Magnetic moment of the electron is a quantum property which has no classical analog. The magnetic moment is parallel to the spin only in the stationary state. In the arbitrary state the magnetic moment is not connected with the spin direction. The dynamic system SD described by the Dirac equation is shown to be non-relativistic, because after transforming to hydrodynamic variables and eliminating gamma-matrices, a constant timelike vector f appears. This vector describes a split of the space-time into space and time.