An axiomatic deduction of the pauli spinor theory

Philip L. Bowers

Daniel C. Galehouse

Pertti Lounesto

Emily Adlam, Jacob A. Barandes

Any viable interpretation of quantum theory needs to account for the Born rule, from which the theory gets its probabilistic empirical predictions. In this paper, we give an overview of possible approaches to this problem in the context of the Many Worlds interpretation. We argue that, for structural reasons, none of them can possibly succeed. More precisely, we argue that the Many Worlds interpretation must obtain the Born rule by proceeding either axiomatically, deductively, or inductively, and that all three of these approaches run into general, fundamental obstructions.

Werner Karl Heisenberg

Thomas G. Blomberg

A deductive physical theory should in principle be a pure mathematical theory together with an identification of certain quantities/concepts (“observables”) in the theory and corresponding observable entities in the real world. This identification – the “interpretation” of the theory – should be unproblematic, both for the theoretician and the experimentalist. A general basis for a deductive physical theory, comprising both classical and quantum physics in a unified way, is proposed. The theory is based on successive confidence estimates on quantum-mechanical wave functions corresponding to space-localizations of particles. This allows a direct and simple way of describing both macroscopic and microscopic phenomena by means of the same basic concepts. Central in the axiomatics of the outlined theory is a concept called equiangular sequences of projection operators. It describes a successive sequence of “collapses of the wave function”. The proposed theory gives a basis for a general theory of irreversible processes based directly on quantum mechanics. It gives an alternative definition of entropy and an alternative derivation of entropy increase in irreversible processes.