The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations
Christian de Ronde,César Massri +1 more
Reads0
Chats0
TLDR
In this article, the authors present a new categorical approach which attempts to provide an original understanding of QM by considering the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about.Abstract:
In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about --rather than as problems that need to be bypassed in order to allow a restoration of a classical "common sense" understanding of what there is. In particular, we discuss a solution to Kochen-Specker contextuality through the generalization of the meaning of global valuation. This idea has been already addressed by the so called topos approach to QM --originally proposed by Isham, Butterfield and Doring-- in terms of sieve-valued valuations. The logos approach to QM presents a different solution in terms of the notion of intensive valuation. This new solution stresses an ontological (rather than epistemic) reading of the quantum formalism and the need to restore an objective (rather than classical) conceptual representation and understanding of quantum physical reality.read more
Citations
More filters
Posted Content
Against Collapses, Purity and Separability Within the Definition of Quantum Entanglement
Christian de Ronde,César Massri +1 more
TL;DR: In this article, the authors argue against the orthodox definition of quantum entanglement which has been implicitly grounded on several widespread (metaphysical) presuppositions which have no relation whatsoever to the formalism of QM.
Posted Content
Taking Mermin's Relational Interpretation of QM Beyond Cabello's and Seevinck's No-Go Theorems
TL;DR: In this article, the Logos Categorical Approach to Quantum Relationalism (LCAQM) is proposed to escape Cabello's and Seevinck's no-go theorems.
Kochen-Specker Theorem, Physical Invariance and Quantum Individuality
Christian de Ronde,César Massri +1 more
TL;DR: In this paper, a Corollary to Kochen-specker's theorem is derived, which states that a vector in Hilbert space cannot be interpreted coherently as an object possessing (objective) physical properties.
Posted Content
The Dilemma of Quantum Individuality Beyond Particle Metaphysics
TL;DR: In this article, the authors address the metaphysics presuppositions involved within Arenhart's dilemma which ground the question of individuality in QM on a strong presupposition regarding the existence of quantum objects.
Posted Content
Against the Tyranny of Pure States in Quantum Theory
Christian de Ronde,César Massri +1 more
Abstract: We argue that the notion of pure sate within Standard Quantum Mechanics is presently applied within the specialized literature in relation to two mutually inconsistent definitions. While the first (operational purity) provides a basis-dependent definition which makes reference to the certain prediction of measurement outcomes, the latter (trace-invariant purity) provides a purely abstract invariant definition which lacks operational content. In this work we derive a theorem which exposes the serious inconsistencies existent within these two incompatible definitions of purity.
References
More filters
Journal ArticleDOI
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
TL;DR: Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.
Book
Categories for the Working Mathematician
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
Book
Graph Theory
TL;DR: Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.
Journal ArticleDOI
Speakable and Unspeakable in Quatum Mechanics
J. S. Bell,N. David Mermin +1 more
TL;DR: Koestler's book The Sleepwalkers as discussed by the authors is an account of the Copernican revolution, with Copernicus, Kepler, and Galilei as heroes, and he concluded that they were not really aware of what they were doing.
Journal ArticleDOI
On the Problem of Hidden Variables in Quantum Mechanics
TL;DR: The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered in this article, and it is shown that their essential axioms are unreasonable.