Reply to Leiter's criticism of a new theory of elementary matter

Abstract

In a recent note, Leiter (1973) claimed to have found an error in my formulation of a new theory of elementary matter (Sachs, 1971, 1972a, b). This was in regard to its application to etectrodynamics in the quantum domain. He asserts that my formal structure cannot incorporate the Pauli exclusion principle and from this he concludes that the theory must be false. In this note, I will rebut Leiter's comments, indicating the set of technical errors that he makes in the criticism. The exact form of the mathematical structure of my theory is in terms of a set of coupled, relativistically covariant, nonlinear spinor field equations. Each of the coupled equations corresponds to a particle component of an assumed closed system. These are referred to as 'particle components' only because they have the asymptotic feature (according to the axiomatic basis of the theory) of approaching the particle solutions of the linear formalism of ordinary quantum mechanics, in the limit as the energy and momentum transfer between the components becomes arbitrarily weak. But it is an important feature of this theory that the exact limit is not contained in the structure of the theory (even though it can be approached arbitrarily closely). Another important feature is that all of the nonlinear field solutions are mapped in a single space-time-they are a set of field solutions that represent a closed system that is, in fact, without parts. Leiter's main error was to claim that an exact solution of my nonlinear formalism, for the Kth particle component of my assumed closed system, is the stationary state eigenfunction ~(K)(x, t) = x(K)(x) exp(--/E(K)t)