In defense of operational quantum logic

Smets, Sonja

doi:10.12775/llp.2003.010

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…The generalized axiomatic operational quantum formalism in which we performed this investigation on separated physical entities is the one currently referred to as the Geneva-Brussels School on quantum theory (Piron, 1964, 1976, 1989, 1990; Aerts, 1982a, 1983a,b, 1986, 1999a,b, 2009c; Cattaneo and Nistico, 1991, 1993; Aerts et al, 1999; Aerts and Van Steirteghem, 2000; Coeck et al, 2000; Smets, 2003; Engesser et al, 2007; Sassoli de Bianchi, 2010, 2011, 2013). …”

Section: Quantum Axiomatics and Separationmentioning

confidence: 99%

“…In this respect, we specifically want to put forward and analyze a result we obtained ourselves quite some time ago when investigating the situation of ‘separated physical entities’ within such a generalized axiomatic and operational quantum theory, because of its relevance for the main question considered in the present article. The generalized axiomatic operational quantum formalism in which we performed this investigation on separated physical entities is the one currently referred to as the Geneva-Brussels School on quantum theory (Piron, 1964 , 1976 , 1989 , 1990 ; Aerts, 1982a , 1983a , b , 1986 , 1999a , b , 2009c ; Cattaneo and Nistico, 1991 , 1993 ; Aerts et al, 1999 ; Aerts and Van Steirteghem, 2000 ; Coeck et al, 2000 ; Smets, 2003 ; Engesser et al, 2007 ; Sassoli de Bianchi, 2010 , 2011 , 2013 ).…”

Section: Quantum Axiomatics and Separationmentioning

confidence: 99%

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Quantum theory and human perception of the macro-world

Aerts¹

2014

Front. Psychol.

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We investigate the question of ‘why customary macroscopic entities appear to us humans as they do, i.e., as bounded entities occupying space and persisting through time’, starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new ‘conceptual quantum interpretation’, including a highly detailed reformulation of the question to confront the new insights and views that arise with the foregoing analysis. At the end of the final section, a nuanced answer is given that can be summarized as follows. The specific and very classical perception of human seeing—light as a geometric theory—and human touching—only ruled by Pauli's exclusion principle—plays a role in our perception of macroscopic entities as ontologically stable entities in space. To ascertain quantum behavior in such macroscopic entities, we will need measuring apparatuses capable of its detection. Future experimental research will have to show if sharp quantum effects—as they occur in smaller entities—appear to be ontological aspects of customary macroscopic entities. It remains a possibility that standard quantum theory is an incomplete theory, and hence incapable of coping ultimately with separated entities, meaning that a more general theory will be needed.

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Section: Quantum Axiomatics and Separationmentioning

confidence: 99%

Section: Quantum Axiomatics and Separationmentioning

confidence: 99%

Quantum theory and human perception of the macro-world

Aerts¹

2014

Front. Psychol.

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“…One of the most basic and very often misunderstood ingredients (see e.g. Smets, 2003) of the Jauch-Piron approach is the construction of the conjunction or meet of properties via product questions, i.e. non-deterministic choice of "questions" (which is most often viewed as a form of disjunction or join).…”

Section: Introductionmentioning

confidence: 99%

Complete Axiomatizations for Quantum Actions

Baltag

Smets

2005

Int J Theor Phys

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We present two equivalent axiomatizations for a logic of quantum actions: one in terms of quantum transition systems, and the other in terms of quantum dynamic algebras. The main contribution of the paper is conceptual, offering a new view of quantum structures in terms of their underlying logical dynamics. We also prove Representation Theorems, showing these axiomatizations to be complete with respect to the natural Hilbert-space semantics. The advantages of this setting are many: (1) it provides a clear and intuitive dynamic-operational meaning to key postulates (e.g. Orthomodularity, Covering Law);(2) it reduces the complexity of the Solèr-Mayet axiomatization by replacing some of their key higher-order concepts (e.g. "automorphisms of the ortholattice") by first-order objects ("actions") in our structure; (3) it provides a link between traditional quantum logic and the needs of quantum computation.

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The modes of physical properties in the logical foundations of physics

Smets¹

2005

LLP

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In defense of operational quantum logic

Cited by 3 publications

References 21 publications

Quantum theory and human perception of the macro-world

Quantum theory and human perception of the macro-world

Complete Axiomatizations for Quantum Actions

The modes of physical properties in the logical foundations of physics

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