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In this essay, I develop order-theoretic notions of determinism and contextuality on domains and topoi. In the process, I develop a method for quantifying contextuality and show that the order-theoretic sense of contextuality is analogous…

Quantum Physics · Physics 2014-09-30 Ian T. Durham

A realist interpretation of quantum mechanics is proposed - Contextual Quantum Realism (CQR) - according to which there exists a categorical distinction between the ideal (theory, observation instrument) and the real (quantum physical…

Quantum Physics · Physics 2025-10-13 Francois-Igor Pris

Recent years have seen new general notions of contextuality emerge. Most of these employ context-independent symbols to represent random variables in different contexts. As an example, the operational theory of Spekkens [1] treats an…

Quantum Physics · Physics 2020-11-16 Mojtaba Aliakbarzadeh , Kirsty Kitto

Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality…

Quantum Physics · Physics 2015-12-21 Barbara Amaral , Marcelo Terra Cunha , Adán Cabello

The distinctive features of quantum mechanics, which set it apart from other physical theories, challenge our notions of realism. Recovering realism from purely philosophical grounds, a quantitative and operational criterion was proposed in…

Quantum Physics · Physics 2024-04-15 D. M. Fucci , R. M. Angelo

The quantum realms of nonlocality and contextuality are delineated by Bell's theorem and the Kochen-Specker theorem, respectively, embodying phenomena that surpass the explanatory capacities of classical theories. These realms hold…

Quantum Physics · Physics 2024-03-27 Min-Gang Zhou , Hua-Lei Yin , Zeng-Bing Chen

Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…

Quantum Physics · Physics 2018-08-07 Andrei Khrennikov

Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different…

Artificial Intelligence · Computer Science 2026-05-26 Song-Ju Kim

The two previous papers developed quantum mechanical formalism from classical mechanics and two additional postulates. In the first paper it was also shown that the uncertainty relations possess no ontological validity and only reflect the…

Quantum Physics · Physics 2008-02-03 L. S. F. Olavo

It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We show that such a claim can be justified…

Quantum Physics · Physics 2007-05-23 Andrei Khrennikov , Igor Volovich

In this paper we investigate the history of relationalism and its present use in some interpretations of quantum mechanics. In the first part of this article we will provide a conceptual analysis of the relation between substantivalism,…

History and Philosophy of Physics · Physics 2017-12-21 Christian de Ronde , Raimundo Fernandez Moujan

After about a century since the first attempts by Bohr, the interpretation of quantum theory is still a field with many open questions. In this article a new interpretation of quantum theory is suggested, motivated by philosophical…

Quantum Physics · Physics 2022-08-25 Martin Korth

The Kochen-Specker (KS) theorem is a corner-stone result in the foundations of quantum mechanics describing the fundamental difference between quantum theory and classical non-contextual theories. Recently specific substructures termed…

Quantum Physics · Physics 2023-07-11 Yuan Liu , Ravishankar Ramanathan , Karol Horodecki , Monika Rosicka , Paweł Horodecki

At present, quantum theory leaves unsettled which quantities ontologically, physically exist in a quantum system. Do observables such as energy and position have meaningful values only at the precise moment of measurement, as in the…

Quantum Physics · Physics 2018-11-26 Brendan Marsh

The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…

General Relativity and Quantum Cosmology · Physics 2009-10-22 Rafael D. Sorkin

Bell nonlocality and Kochen-Specker contextuality are among the main topics of foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems…

A new quantum ontology of quantum mechanics has been proposed recently. This ontology is based on impossible to realize measurements which need to be performed repeatedly on the same single physical system or on the same pair of physical…

Quantum Physics · Physics 2016-02-11 Marian Kupczynski

Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the…

Quantum Physics · Physics 2010-12-01 Thomas Filk , Albrecht von Mueller

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…

Quantum Physics · Physics 2012-04-17 Borivoje Dakic , Caslav Brukner

General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…

General Relativity and Quantum Cosmology · Physics 2026-04-22 Tristan Hübsch , Djordje Minic
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