A model of Piron's preparation-question structures in Ludwig's selection structures |
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Authors: | Gianpiero Cattaneo Giuseppe Nisticò |
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Affiliation: | (1) Dipartimento di Scienze dell'Informazione, Università di Milano, Milan, Italy;(2) Dipartimento di Matematica, Università della Calabria, Arcavacata, Italy |
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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 = or ()= 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. |
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