The logic approach to axiomatic quantum mechanics via orthocomplemented partial ordered sets of yes–no measurements, which constitute the observing part of a concretely realizable experiment on microworld, has been criticized from the empirical point of view by Mielnik, which on the contrary privileges the convex scheme linked to the preparing part. In this work we do assume that a description of quantum phenomenology must take into account both these two parts in which every elementary experiment can be decomposed. According to this predecision, we develop an axiomatic approach based on indistinguishability principles of a quantum information system. The very general concept of yes–no measurement or ‘‘question’’ is accepted, and then the set of all questions is classified according to the behavior with respect to a phenomenological orthogonality relation. In particular, we single out the set F of fuzzy events or effects and the set E⊆F of exact events. The Mielnik critique is then refused since it regards the order structure of E using counterexamples which pertain to F/E. The notions of physical property and noperty are then introduced and an axiomatic foundation of quantum mechanics based on a pre‐Hilbert space is discussed.
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|Titolo:||Orthogonality and orthocomplementations in the axiomatic approach to quantum mechanics: Remarks about some critiques|
|Data di pubblicazione:||1984|
|Citazione:||Orthogonality and orthocomplementations in the axiomatic approach to quantum mechanics: Remarks about some critiques / Cattaneo, G; Nistico', Giuseppe Antonio. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 25(1984), pp. 513-531.|
|Appare nelle tipologie:||1.1 Articolo in rivista|