arXiv:hep-th/9307019 · Modern Physics Letters A

QUANTUM MECHANICS AS BAYESIAN COMPLEX PROBABILITY THEORY

Saul Youssef

Published Sep 14, 1994• 57 citations

Abstract

As a possible alternative to conventional quantum mechanics, the Bayesian version of probability theory is extended to include complex probabilities. An additional assumption of realism restores a frequency interpretation while coexisting with Bell’s theorem. Such complex probabilities are shown to have a superposition principle, to include wave functions which are expansions in eigenfunctions of Hermitian operators, to have a path-integral representation and to describe both pure and mixed systems. A scalar particle in Rd is shown to obey the Schrödinger equation with mass, vector potential and metric appearing as moments of a fundamental probability. Illustrative examples are given. The quantum version of Bayesian inference is discussed.

DOI: 10.1142/s0217732394002422

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