Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2304.11051 · European Journal for Philosophy of Science

On the categoricity of quantum mechanics

Iulian D. Toader

Published Dec 17, 2020• 3 citations
arXivHTMLPDF

Abstract

Abstract The paper offers an argument against an intuitive reading of the Stone-von Neumann theorem as a categoricity result, thereby pointing out that, against what is usually taken to be the case, this theorem does not entail any model-theoretical difference between the theories that validate it and those that don’t.
DOI
10.1007/s13194-020-00328-3

Related papers

QUANTUM GROUPS AND VON NEUMANN THEOREM

Alfredo Iorio, Giuseppe Vitiello

We discuss the q-deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in quantum mechanics. We show that the q-deformation parameter labels the Weyl systems in quantum mechanics and the unitarily inequivalent representations of the canonical commutation relations in quantum field theory.

arXiv:math-ph/0009035•Modern Physics Letters B•Feb 20, 1994•17 citations

Bohr and von Neumann on the universality of quantum mechanics: materials for the history of the quantum measurement process

Federico Laudisa

Abstract The Bohr and von Neumann views on the measurement process in quantum mechanics have been interpreted for a long time in somewhat controversial terms, often leading to misconceptions. On the basis of some textual analysis, I would like to show that—contrary to a widespread opinion—their views should be taken less inconsistent, and much closer to each other, than usually thought. As a consequence, I claim that Bohr and von Neumann are conceptually on the same side on the issue of the universality of quantum mechanics: hopefully, this might contribute to a more accurate history of the measurement problem in quantum mechanics.

arXiv:2405.08722•The European Physical Journal H•Sep 11, 2024•3 citations

A Note Concerning Propositions in Quantum Mechanics

Joachim Schröter

Abstract It is shown that the interpretation of quantum mechanics as a theory describing systems for which their propositions are always valid or not leads to a contradiction within the theory. The proof does not depend on any specific property of measurements, but only the usual description of ensembles of quantum objects by statistical operators is used.

Annalen der Physik•Jan 1, 1970•1 citation

Beyond the Stone–von Neumann Theorem

Laura Ruetsche

This chapter catalogs circumstances under which the reassuring uniqueness results presented in Chapter 2 break down. The Stone-von Neumann theorem presupposes a continuity condition; with that presupposition suspended, it becomes possible to equip the quantum theory of a single mechanical system with exact position eigenstates. The Stone-von Neumann theorem presupposes the classical theory to be quantized to be set in Euclidean space; when systems such as a bead on a circle are quantized, the theorem breaks down and unitarily inequivalent representations of the physics ensue. Finally, the Stone-von Neumann and Jordan-Wigner theorems presuppose finitely many degrees of freedom. They therefore fail to apply to quantum field theories (because a field, assigning a value to each point of space[time] has infinitely many degrees of freedom), or theories at the thermodynamic (infinite volume) limit of quantum statistical mechanics. The chapter presents simple examples of infinite systems and their unitarily inequivalent quantizations: the free Klein-Gordon field and the infinite spin chain.

Oxford University Press eBooks•Jun 2, 2011•0 citations

Why John von Neumann did not Like the Hilbert Space formalism of quantum mechanics (and what he liked instead)

Miklós Rédei

Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics•Dec 1, 1996•133 citations

Von Neumann's information engine without the spectral theorem

Shintaro Minagawa, Hayato Arai, Francesco Buscemi

Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles. Despite being operational for the most part, von Neumann's argument departs from an operational narrative in its use of the spectral theorem. In this work, we show that the role of the spectral theorem in von Neumann's argument can be taken over by the operational assumptions of repeatability and reversibility, and, using these, we are able to explore the consequences of the second law also in theories that do not possess a unique spectral decomposition. As a byproduct, we obtain the Groenewold-Ozawa information gain as a natural monotone for a suitable ordering of instruments, providing it with an operational interpretation valid in quantum theory and beyond.

arXiv:2203.05258•Physical Review Research•Aug 1, 2022•6 citations
Abstract The Bohr and von Neumann views on the measurement process in quantum mechanics have been interpreted for a long time in somewhat controversial terms, often leading to misconceptions. On the basis of some textual analysis, I would like to show that—contrary to a widespread opinion—their views should be taken less inconsistent, and much closer to each other, than usually thought. As a consequence, I claim that Bohr and von Neumann are conceptually on the same side on the issue of the universality of quantum mechanics: hopefully, this might contribute to a more accurate history of the measurement problem in quantum mechanics.
This chapter catalogs circumstances under which the reassuring uniqueness results presented in Chapter 2 break down. The Stone-von Neumann theorem presupposes a continuity condition; with that presupposition suspended, it becomes possible to equip the quantum theory of a single mechanical system with exact position eigenstates. The Stone-von Neumann theorem presupposes the classical theory to be quantized to be set in Euclidean space; when systems such as a bead on a circle are quantized, the theorem breaks down and unitarily inequivalent representations of the physics ensue. Finally, the Stone-von Neumann and Jordan-Wigner theorems presuppose finitely many degrees of freedom. They therefore fail to apply to quantum field theories (because a field, assigning a value to each point of space[time] has infinitely many degrees of freedom), or theories at the thermodynamic (infinite volume) limit of quantum statistical mechanics. The chapter presents simple examples of infinite systems and their unitarily inequivalent quantizations: the free Klein-Gordon field and the infinite spin chain.
Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles. Despite being operational for the most part, von Neumann's argument departs from an operational narrative in its use of the spectral theorem. In this work, we show that the role of the spectral theorem in von Neumann's argument can be taken over by the operational assumptions of repeatability and reversibility, and, using these, we are able to explore the consequences of the second law also in theories that do not possess a unique spectral decomposition. As a byproduct, we obtain the Groenewold-Ozawa information gain as a natural monotone for a suitable ordering of instruments, providing it with an operational interpretation valid in quantum theory and beyond.