Objective Quantum Probabilities

Objective quantum probabilities represent the polar opposite to the Bayesian approach to quantum probabilities, which assumes probabilities to be subjective degrees of belief. In the objective theory, probabilities of quantum events are part of the physical world, and take their values independently of what human beings believe. The first objective theory was Karl Popper's propensity theory of probabilities, which identified propensities as the dispositional properties of particles to assume certain states under given conditions [1]. The propensity theory placed Popper squarely on the “particle” side of de Broglie's and Bohr's ► wave-particle duality. Propensities, however, suffered from the defect that Popper was unable to specify where in the physical world the values of his propensities lay. The present theory deals with this problem in locating precise quantum probability values in space-time structure.

Imagine that a spin-1/2 particle with direction of ► spin at an angle of 60° to the vertical is passed through an “HV apparatus”, a vertically-oriented Stern-Gerlach magnet with two exit channels which separates particles into a “spin-up” stream (direction of spin v or vertical) and a “spin-down” stream (direction of spin h or horizontal). The spin-60° particle has a probability of cos² 30° = 3/4 of emerging in the spin-up channel. In the objective theory, this value is encoded in space-time structure in the following way. Imagine that at the time the particle enters the apparatus the 4-dimensional manifold divides into non-mutually-accessible future branches, and that on 75% of these branches the particle is measured spin-up and that on 25% it is measured spin-down. Figure 1, part (i), depicts a simple instance of this branching in space-time.