Quantum Mechanics as Bayesian Complex Probability Theory

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 R^d 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.