A new theory of elementary matter part III: A self-consistent field theory of electrodynamics and correspondence with quantum mechanics

Abstract

This paper exploits the axioms and general mathematical structure of a new theory of elementary matter, thus far developed in two earlier papers (Sachs, 1971b, c). It is shown here, in an explicit fashion, how the exact form of this theory approaches that of quantum mechanics of a ‘many-particle’ system that interacts electromagnetically. The form of the mathematical expression of quantum mechanics of a many-particle system is found to be a linear approximation for the nonlinear (deterministic) field theory of this author's approach. The latter approximation is valid only when the components of the (asserted) closed system are sufficiently weakly coupled so that it appears as a many-particle system. The physical equivalent of the Pauli exclusion principle is derived in this paper as anexact feature of the theory, which is, in fact, sensitive to its closed and nonlinear features. It is then shown how the Fermi-Dirac statistics in particle physics follows from the present nonlinear theory only in a linear approximation.