On Decoupling Probability from Kinematics in Quantum Mechanics

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. Introduction I believe that quantum mechanics, as generally understood and practiced today, intermixes subjective and objective components of human knowledge, and furthermore, that we will not understand the subject fully until those components can be cleanly separated. The main purpose of this article is to propose a means by which that separation might be effected. As will be seen, my proposal has many specific and surprising consequences as well as possibilities for further development. I regard the Dirac electron theory as the fundamental core of current quantum mechanics. It is from the Dirac theory that the most precise and surprising consequences of quantum mechanics have been derived. Some would claim that quantum field theory is more fundamental, but one can argue that field theory is merely a formal device for imposing boundary conditions of the single particle theory to accommodate particle creation and annihilation along with the Pauli principle [1]. For these reasons, it is to the Dirac theory that I look to understand the role of probability in quantum mechanics. We shall see that the Dirac theory supplies insights into the significance of quantum mechanical wave functions that could not possibly be derived from the Schrödinger theory. To separate subjective and objective components of the Dirac Theory I suggest that we need two powerful conceptual tools. The first tool is the Universal Probability Calculus which has been synthesized and expounded so clearly by Ed Jaynes and amply justified by