A model of Piron's preparation-question structures in Ludwig's selection structures

Abstract

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of “preparation-question structure” (with four basic axioms and without axioms C, P, A), in terms of Ludwig's “selection structure”; in the latter structure the primitive notion of “individual sample” of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of “question” in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as “performable together questions”; moreover, results such as “α∼∼=α” or “(αδΒ)∼=α∼▽Β∼” can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.