The Many Classical Faces of Quantum Structures

Heunen, Chris

doi:10.3390/e19040144

Cited by 12 publications

(11 citation statements)

References 111 publications

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“…1.9 empirical relating to phenomena collectively entangled state superposition of composite system pure states; implies statistical balance in collective outcomes, among ensembles for measurements of differing observables on different subsystems; see Sect. 3.6 ensemble statistical ensemble epistemic refers to the ways in which humans acquire knowledge and process information [25, p. 57] [233] ergodicity the coincidence of time and ensemble averages in empirical data [337,338] event several meanings are possible [174, § 2]; this review will take event to mean the instantiation of one or more properties within some region of spacetime field specification of properties smoothly across spacetime [25, p. 57] formalism one of several mathematical structures, in which analysis in quantum mechanics can be carried out; examples include Hilbert spaces, Fock spaces [560], quasi-sets [560], Dirac brackets [277, § 5], Feynman path amplitudes [128, § 1], multiple trajectories [191,535] and algebraic theories [561] such as category theory [536] and topos theory [79,109][188, § 2, § 5].…”

Section: Glossary: Intended Meanings For Some Non-mathematical Termsmentioning

confidence: 99%

Understanding quantum mechanics: a review and synthesis in precise language

Drummond¹

2019

Open Physics

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This review, of the understanding of quantum mechanics, is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject. To enhance clarity, the main findings are presented in the form of a coherent synthesis of the reviewed sources. The review highlights core characteristics of quantum mechanics. One is statistical balance in the collective response of an ensemble of identically prepared systems, to differing measurement types. Another is that states are mathematical terms prescribing probability aspects of future events, relating to an ensemble of systems, in various situations. These characteristics then yield helpful insights on entanglement, measurement, and widely-discussed experiments and analyses. The review concludes by considering how these insights are supported, illustrated and developed by some specific approaches to understanding quantum mechanics. The review uses non-mathematical language precisely (terms defined) and rigorously (consistent meanings), and uses only such language. A theory more descriptive of independent reality than is quantum mechanics may yet be possible. One step in the pursuit of such a theory is to reach greater consensus on how to understand quantum mechanics. This review aims to contribute to achieving that greater consensus, and so to that pursuit.

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Section: Glossary: Intended Meanings For Some Non-mathematical Termsmentioning

confidence: 99%

Understanding quantum mechanics: a review and synthesis in precise language

Drummond¹

2019

Open Physics

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“…Then commeasurable subalgebras of a partial algebra can be seen as "classical contexts" in which a measurement may be performed on the corresponding quantum system [26, p. 48]. For more detail on this perspective, we refer readers to the recent survey [25].…”

Section: Partial Algebraic Structures and Kochen-specker Coloringsmentioning

confidence: 99%

A Kochen–Specker theorem for integer matrices and noncommutative spectrum functors

Ben-Zvi

Reyes

et al. 2017

Journal of Algebra

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Abstract. We investigate the possibility of constructing Kochen-Specker uncolorable sets of idempotent matrices whose entries lie in various rings, including the rational numbers, the integers, and finite fields. Most notably, we show that there is no Kochen-Specker coloring of the n × n idempotent integer matrices for n ≥ 3, thereby illustrating that Kochen-Specker contextuality is an inherent feature of pure matrix algebra. We apply this to generalize recent no-go results on noncommutative spectrum functors, showing that any contravariant functor from rings to sets (respectively, topological spaces or locales) that restricts to the Zariski prime spectrum functor for commutative rings must assign the empty set (respectively, empty space or locale) to the matrix ring M n (R) for any integer n ≥ 3 and any ring R.An appendix by Alexandru Chirvasitu shows that Kochen-Specker colorings of idempotents in partial subalgebras of M 3 (F ) for a perfect field F can be extended to partial algebra morphisms into the algebraic closure of F .

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“…Recent work by Hamhalter [9], Heunen and others, see [12,15,18] investigate to what extent the abelian *-subalgebras of a C*-algebra determine its structure. Also a number of interesting new results on AW*-algebras have been discovered; for example Hamhalter [8]; Heunen and Reyes [13] and [14].…”

Section: Aw*-algebrasmentioning

confidence: 99%