On the logical foundations of the Jauch-Piron approach to quantum physics

Cattaneo, Gianpiero; Pozza, Carlo Dalla; Garola, Claudio; Nisticò, Giuseppe

doi:10.1007/bf00671312

Cited by 14 publications

(1 citation statement)

References 15 publications

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“…For sake of completeness we mention other work that has contributed to advances in the approach that is less directly of importance for what we do in this paper, but shows how the approach is developing into other directions as well [52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81].…”

Section: How We Will Proceedmentioning

confidence: 99%

Being and Change: Foundations of a Realistic Operational Formalism

Aerts¹

2002

Probing the Structure of Quantum Mechanics

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The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultural artifact, or the mind of a person, etc..., which means that we aim at very general description. The effect that a context has on the state of the entity plays a fundamental role, which means that our approach is intrinsically contextual. The approach is inspired by the mathematical formalisms that have been developed in axiomatic quantum mechanics, where a specific type of quantum contextuality is modelled. However, because in general states also influence contextwhich is not the case in quantum mechanics -we need a more general setting than the one used there. Our focus on context as a fundamental concept makes it possible to unify 'dynamical change' and 'change under influence of measurement', which makes our approach also more general and more powerful than the traditional quantum axiomatic approaches. For this reason an experiment (or measurement) is introduced as a specific kind of context. Mathematically we introduce a state context property system as the structure to describe an entity by means of its states, contexts and properties. We also strive from the start to a categorical setting and derive the morphisms between * Published as: D. Aerts, "Being and change: foundations of a realistic operational formalism", in Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation and Axiomatics, eds. D. Aerts, M. Czachor and T. Durt, World Scientific, Singapore (2002). 1 state context property systems from a merological covariance principle. We introduce the category SCOP with as elements the state context property systems and as morphisms the ones that we derived from this merological covariance principle. We introduce property completeness and state completeness and study the operational foundation of the formalism.

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