A constructive approach to the foundations of quantum mechanics

An axiomatic theory is formulated which describes a class of yes-no experiments, involving a fixed basic source, a fixed basic detector, and various filters. It is assumed that all filters considered can be constructed from a setP of primitive filters by composition and stochastic selection. Two physically plausible axioms are formulated which allow us to define the concept of asystem in the present context (cf. Definition2.4). To each system we can attach anorder unit module () (cf. Definition5.1) whereby () is acomplete, separable order unit space. Two additional axioms are proposed which have the effect that the space () becomes isomorphic to the order unit space underlying a JB-algebra, at least in the case where isfinite dimensional (cf. Corollary7.9).