On Decoupling Probability from Kinematics in Quantum Mechanics

Abstract

A means for separating subjective and objective aspects of the electron wave function is suggested, based on a reformulation of the Dirac Theory in terms of Spacetime Algebra. The reformulation admits a separation of the Dirac wave function into a two parameter probability factor and a six parameter kinematical factor. The complex valuedness of the wave function as well as its bilinearity in observables have perfect kinematical interpretations independent of any probabilistic considerations. Indeed, the explicit unit imaginary in the Dirac equation is automatically identified with the electron spin in the reformulation. Moreover, the canonical momentum is seen to be derived entirely from the rotational velocity of the kinematical factor, and this provides a geometrical interpretation of energy quantization. Exact solutions of the Dirac equation exhibit circular zitterbewegung in exact agreement with the classical Wessenhoff model of a particle with spin. Thus, the most peculiar features of quantum mechanical wave functions have kinematical explanations, so the use of probability theory in quantum mechanics should not differ in any essential way from its use in classical mechanics.