A Topological Study of Contextuality and Modality in Quantum Mechanics

Domenech, Graciela; Freytes, Héctor; Ronde, Christian de

doi:10.1007/s10773-007-9595-8

Cited by 14 publications

(19 citation statements)

References 18 publications

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“…For obvious reasons, we called it the Modal Kochen-Specker (MKS) theorem [14]. As in the case of actual propositions, the MKS theorem may be demonstrated with topological tools [15]. It is important to remark that our formalism also provides a formal meaning in an algebraic frame to the Born rule, something that has been discussed by Dieks in relation to the possible derivation of a preferred probability measure [10].…”

Section: Quantum Contextuality and Modalitymentioning

confidence: 99%

Interpreting the Modal Kochen–Specker theorem: Possibility and many worlds in quantum mechanics

Ronde

Freytes

Domenech

2014

Studies in History and Philosophy of Science Part B: Studies in

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In this paper we attempt to physically interpret the Modal Kochen-Specker (MKS) theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of "possibility" in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between actual and possible realms.

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Section: Quantum Contextuality and Modalitymentioning

confidence: 99%

Interpreting the Modal Kochen–Specker theorem: Possibility and many worlds in quantum mechanics

Ronde

Freytes

Domenech

2014

Studies in History and Philosophy of Science Part B: Studies in

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“…Some important remarks are at stake. The above discussion is related to a well-known fact: it is possible to define local classical valuations for maximal Boolean subalgebras of L(H), but the Kochen-Specker theorem forbids the existence of global ones (see sections II and III of [6]; for more discussion on the subject, see [59][60][61][62][63]). Another related fact is that of the non-existence of states whose range is equal to the set {0, 1} (also known as dispersion-free states in the foundations of quantum physics literature).…”

Section: The Kochen-specker Theorem and The Failure Of Truth Functionmentioning

confidence: 99%

Non-Deterministic Semantics for Quantum States

Jorge

Holik

2020

Entropy

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In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.

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“…Escaping the metaphysics of actuality and starting from the formalism, a good candidate to develop a mode of existence is of course quantum possibility. In several papers, together with Domenech and Freytes, we have analyzed how to understand possibility in the context of the orthodox formalism of QM [26,27,28,29]. From this investigation there are several conclusions which can be drawn.…”

Section: The Physical Representation Of Quantum Superpositionsmentioning

confidence: 99%

Modality, Potentiality, and Contradiction in Quantum Mechanics

Ronde

2015

Springer Proceedings in Mathematics &Amp; Statistics

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In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that -taking into account the square of opposition-quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In [17] we defended the Paraconsistent Approach to Quantum Superpositions (PAQS) and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings of modality, potentiality and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions (CAQS) proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider.

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A Topological Study of Contextuality and Modality in Quantum Mechanics

Cited by 14 publications

References 18 publications

Interpreting the Modal Kochen–Specker theorem: Possibility and many worlds in quantum mechanics

Interpreting the Modal Kochen–Specker theorem: Possibility and many worlds in quantum mechanics

Non-Deterministic Semantics for Quantum States

Modality, Potentiality, and Contradiction in Quantum Mechanics

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