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NATO ASI series. Series B : Physics

Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems

Hans Primas

Published Jan 1, 1990• 75 citations
Publisher
DOI
10.1007/978-1-4684-8771-8_14

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Sixty-Two Years of Uncertainty : Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics

Arthur I. Miller

Opening Remarks.- Imagery, Probability and the Roots of Werner Heisenberg's Uncertainty Principle Paper.- Against An Exposition of Bell's Theorem.- Wave-Particle Duality: A Case Study.- Sein Kann Was Nicht Sein Darf, Or the Prehistory of the EPR, 1909-1935: Einstein's Early Worries About the Quantum Mechanics of Composite Systems.- to Two-Particle Interferometry.- A New View on the Uncertainty Principle.- Measurement Problems in Quantum Field Theory in the 1930's.- On the Collapse of the Wave Function.- Old and New Ideas in the Theory of Quantum Measurement.- Toward a Relativistic Theory of Statevector Reduction.- The Breakdown of the Superposition Principle.- Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems.- Induced Nonlinear Time Evolution of Open Quantum Objects.- Quantum Logic: A Summary of Some Issues.- Remarks on the Measurement of Discrete Physical Quantities.- Some Comments and Reflections.- Invited Lecturers.

•Jan 1, 1990•77 citations

Concepts and Methods in the Theory of Open Quantum Systems

Heinz‐Peter Breuer, Francesco Petruccione

arXiv:quant-ph/0302047•Lecture notes in physics•Jan 1, 2003•745 citations

Constraint Closure and the Quantum-to-Classical Transition: Decoherence, the Measurement Problem, and the Ontology of Macroscopic Determinacy

Paul D Prideaux

The quantum-to-classical transition — the disappearance of quantum superposition, interference, and entanglement at macroscopic scales — is standardly explained through decoherence: environmental entanglement suppresses interference terms, making macroscopic superpositions effectively unobservable. Decoherence is mathematically rigorous and empirically well-confirmed, but it faces a persistent philosophical limitation: it explains the appearance of classicality without fully accounting for its ontology. The measurement problem survives decoherence because decoherence does not explain why quantum systems produce definite outcomes, why the pointer basis is selected, or what it means for a macroscopic object to have a determinate state rather than merely appearing to have one. This paper argues that Constraint Theory (CT) — the thesis, established by transcendental argument, that constraint is the ontological primitive constitutive of determinate existence as such — provides the ontological grounding that decoherence theory presupposes but does not supply. On the CT account, quantum superposition is open constraint configuration: the genuine ontological openness of a possibility space that has not been closed by the system’s constraint profile or its environmental interactions. Macroscopic determinacy is closed constraint configuration: the progressive closure of macroscopic possibility spaces by the cumulative propagation of environmental constraint into the system’s profile at a rate that overwhelms quantum coherence. Decoherence is the process by which environmental constraint propagation closes possibility spaces; CT explains why this closure has the ontological consequences it does rather than merely the epistemic consequences that the standard account describes. The pointer basis selection problem receives a principled CT resolution: the pointer basis is the constraint-stable basis, the set of states whose constraint pro files are robust under the specific pattern of environmental constraint propagation. The measurement problem is reframed as the question of which branch of an open constraint configuration is closed by a measurement interaction, a question that CT narrows to its irreducible residual without dissolving prematurely. The mesoscopic regime — where quantum behaviour persists at scales larger than individual particles — is explained as the regime of partial constraint closure: systems whose environmental coupling is sufficient to close some but not all dimensions of their possibility space. The paper engages the principal interpretations of quantum mechanics and the philosophical literature on decoherence, situating the CT account as an ontological foundation compatible with multiple interpretive positions.

•Mar 21, 2026•0 citations

Conceptual and mathematical aspects of quantum mechanics

Mark W. Paschke

•Jan 1, 2009•1 citation

Comments

S. B. Treiman

This commentator format is quite unfamiliar to me, and somewhat uncomfortable. I don't know whether I'm supposed to flatter the speakers, criticize them, grade them, or merely parrot them. Or should I go off on my own? This latter is tempting. If unleashed I could provide you with true answers to all the questions before us, philosophical, historical, physical, mathematical, physical-mathematical, and so on. But I'll bite my tongue and try to stick to the commentator role. First, a few words on the topic of the opening session this afternoon - why are philosophers interested in quantum field theory? Quantum mechanics undoubtedly abounds in genuine, deep and still unresolved philosophical questions. These are usually posed, at least in popular accounts, in the context of finite systems of nonrelativistic point particles. In preparation for the conference, I asked myself: does relativistic QFT introduce any really distinctive philosophical problems? There are several possibilities, which I can only express in low-brow form. For one thing, a field is really a collection of infinitely many degrees of freedom, one for each point in space. I can well suppose that infinity raises interesting questions for philosophers. Certainly for physicists, especially in the field theory context, it has been a great preoccupation. As we'll hear later from Jackiw, infinity has its useful aspects. Next, for systems of relativistic particles in interaction, it is no longer so easily possible to speak of measurements of position and momentum of individual particles, except perhaps in asymptotic regions.

Cambridge University Press eBooks•Feb 18, 1999•0 citations

The Mathematics of Open Quantum Systems

Konstantin A. Makarov, Eduard Tsekanovskiı̆

WORLD SCIENTIFIC eBooks•May 26, 2021•10 citations
Opening Remarks.- Imagery, Probability and the Roots of Werner Heisenberg's Uncertainty Principle Paper.- Against An Exposition of Bell's Theorem.- Wave-Particle Duality: A Case Study.- Sein Kann Was Nicht Sein Darf, Or the Prehistory of the EPR, 1909-1935: Einstein's Early Worries About the Quantum Mechanics of Composite Systems.- to Two-Particle Interferometry.- A New View on the Uncertainty Principle.- Measurement Problems in Quantum Field Theory in the 1930's.- On the Collapse of the Wave Function.- Old and New Ideas in the Theory of Quantum Measurement.- Toward a Relativistic Theory of Statevector Reduction.- The Breakdown of the Superposition Principle.- Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems.- Induced Nonlinear Time Evolution of Open Quantum Objects.- Quantum Logic: A Summary of Some Issues.- Remarks on the Measurement of Discrete Physical Quantities.- Some Comments and Reflections.- Invited Lecturers.
The quantum-to-classical transition — the disappearance of quantum superposition, interference, and entanglement at macroscopic scales — is standardly explained through decoherence: environmental entanglement suppresses interference terms, making macroscopic superpositions effectively unobservable. Decoherence is mathematically rigorous and empirically well-confirmed, but it faces a persistent philosophical limitation: it explains the appearance of classicality without fully accounting for its ontology. The measurement problem survives decoherence because decoherence does not explain why quantum systems produce definite outcomes, why the pointer basis is selected, or what it means for a macroscopic object to have a determinate state rather than merely appearing to have one. This paper argues that Constraint Theory (CT) — the thesis, established by transcendental argument, that constraint is the ontological primitive constitutive of determinate existence as such — provides the ontological grounding that decoherence theory presupposes but does not supply. On the CT account, quantum superposition is open constraint configuration: the genuine ontological openness of a possibility space that has not been closed by the system’s constraint profile or its environmental interactions. Macroscopic determinacy is closed constraint configuration: the progressive closure of macroscopic possibility spaces by the cumulative propagation of environmental constraint into the system’s profile at a rate that overwhelms quantum coherence. Decoherence is the process by which environmental constraint propagation closes possibility spaces; CT explains why this closure has the ontological consequences it does rather than merely the epistemic consequences that the standard account describes. The pointer basis selection problem receives a principled CT resolution: the pointer basis is the constraint-stable basis, the set of states whose constraint pro files are robust under the specific pattern of environmental constraint propagation. The measurement problem is reframed as the question of which branch of an open constraint configuration is closed by a measurement interaction, a question that CT narrows to its irreducible residual without dissolving prematurely. The mesoscopic regime — where quantum behaviour persists at scales larger than individual particles — is explained as the regime of partial constraint closure: systems whose environmental coupling is sufficient to close some but not all dimensions of their possibility space. The paper engages the principal interpretations of quantum mechanics and the philosophical literature on decoherence, situating the CT account as an ontological foundation compatible with multiple interpretive positions.
This commentator format is quite unfamiliar to me, and somewhat uncomfortable. I don't know whether I'm supposed to flatter the speakers, criticize them, grade them, or merely parrot them. Or should I go off on my own? This latter is tempting. If unleashed I could provide you with true answers to all the questions before us, philosophical, historical, physical, mathematical, physical-mathematical, and so on. But I'll bite my tongue and try to stick to the commentator role. First, a few words on the topic of the opening session this afternoon - why are philosophers interested in quantum field theory? Quantum mechanics undoubtedly abounds in genuine, deep and still unresolved philosophical questions. These are usually posed, at least in popular accounts, in the context of finite systems of nonrelativistic point particles. In preparation for the conference, I asked myself: does relativistic QFT introduce any really distinctive philosophical problems? There are several possibilities, which I can only express in low-brow form. For one thing, a field is really a collection of infinitely many degrees of freedom, one for each point in space. I can well suppose that infinity raises interesting questions for philosophers. Certainly for physicists, especially in the field theory context, it has been a great preoccupation. As we'll hear later from Jackiw, infinity has its useful aspects. Next, for systems of relativistic particles in interaction, it is no longer so easily possible to speak of measurements of position and momentum of individual particles, except perhaps in asymptotic regions.