Probability and Typicality in Deterministic Physics

Sheldon Goldstein

Daniele Sasso

In scientific literature the Esaki junction is considered a typical system of quantum physics and its behavior is explained with the theory of probability. In this article we prove that the functioning of the Esaki junction can be explained very well without making use of the theory of probability but only by means of deterministic physical reasonings. This research is the first step in order to show that it is possible to think on a theory of quantum physics which is able to leave probability aside for a complete and exhaustive understanding of physical phenomena which happen in the microphysical world.

Tim Maudlin

Abstract This chapter considers three ways in which probabilities may be derived from a physical theory without adverting to subjective considerations. The first derives from a fundamentally stochastic dynamics that implies transition chances at the level of natural law. The second is a Humean approach, in which probabilities are deployed as part of a compact system for conveying information about the structure of the Humean mosaic, i.e. the distribution of local physical quantities in space-time. The last employs either deterministic or stochastic dynamics together with a measure of typicality, i.e. a measure of sets of initial conditions that count as extremely large. Probabilities emerge in this setting as typical frequencies, that is, frequencies exhibited by most initial conditions.

Barry Loewer

Jeffrey Alan Barrett

Hugh Everett III's pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett's argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship between the predictions of pure wave mechanics and the standard quantum probabilities.

Lazar Mayants