Abstract

Abstract

Quantum foundation and statistics.

A new foundation of quantum mechanics, a foundation largely based upon statistical concepts, is described. The basic notion is that of theoretical variables, which may be accessible or inaccessible to a researcher or a group of communicating researchers in a given situation. An important case is when the theoretical variables are statistical parameters, which are accessible when they can be estimated from the given data. Two mathematical theorems are formulated. The first theorem assumes the existence of two different maximal accessible parameters. Then there exists a Hilbert space describing the situation, and every accessible parameter has a self-adjoint operator associated with it. Consequences of this theorem are given. The second theorem gives conditions under which a conditional distribution of parameters may be described by quantum probabilities. Several statistical applications are under investigation.