Probability in Orthodox Quantum Mechanics: Probability as a Postulate Versus Probability as an Emergent Phenomenon

The role of probability in quantummechanics is reviewed, with a discussion of the “orthodox” versus the statistical interpretative frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum mechanics, a survey is given of attempts either to give a new interpretive framework assuming quantum mechanics is exact, or to modify quantum mechanics assuming it is a very accurate approximation to a more fundamental theory. This survey focuses particularly on the issue of whether probabilites in quantum mechanics are postulated or emergent. 1 Orthodox Quantum Mechanics and Issues it Raises Quantum mechanics (QM) is our most successful physical theory, encompassing phenomena as diverse as chemical bonding, the band structure of solids, and the standard model of particle physics. But the probabilistic aspect of quantum mechanics has been a source of unease from the outset. As surveyed by Home [1], the Founding Fathers were divided over this aspect of the theory that they had created: Bohr, Born, and Heisenberg were comfortable with the probabilistic structure of quantum theory, whereas Einstein and Schrödinger had profound reservations. This unease, and division, have continued to the present. 1.1 Postulates of Quantum Mechanics Let us begin with a review of the postulates of QM, in the arena of a complex Hilbert space, following for the larger part the presentation of Ballentine [2]. • Observables are associated with self-adjoint operators. Thus we have