Between classical and quantum

Abstract

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit of a large system, and through decoherence and consistent histores. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain "classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are "einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. We make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it.

100 pages, to appear in Elsevier's Handbook of the Philosophy of Physics

References in corpus (37)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Coherent Quantum Dynamics of a Superconducting Flux Qubit
• Classical Equations for Quantum Systems
• Environment-independent decoherence rate in classically chaotic systems
• On the Consistent Histories Approach to Quantum Mechanics
• Matter-wave interferometer for large molecules
• Quantization Methods: A Guide for Physicists and Analysts
• Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information
• Quantum Probes of Spacetime Singularities
• Against Many-Worlds Interpretations
• Quantum temporal logic and decoherence functionals in the histories approach to generalised quantum theory
• Superconducting Qubits: A Short Review
• Linear and Nonlinear Theory of Eigenfunction Scars
• Continuous Histories and the History Group in Generalised Quantum Theory
• Consistent Sets Yield Contrary Inferences in Quantum Theory
• Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets
• Complementarity of representations in quantum mechanics
• Recent Developments in the Theory of Scarring
• A simple example of "Quantum Darwinism": Redundant information storage in many-spin environments
• A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition
• Decoherent Histories and Hydrodynamic Equations
• Obstruction Results in Quantization Theory
• Obstructions to Quantization
• Weak Quantum Ergodicity
• Classical Dynamics of the Quantum Harmonic Chain
• A Categorical Approach to Imprimitivity Theorems for C*-Dynamical Systems
• General Theorems on Decoherence in the Thermodynamic Limit
• Quantum Histories
• How the Quantum Universe Became Classical
• Some Worlds of Quantum Theory
• Maximal Beable Subalgebras of Quantum-Mechanical Observables
• Representations of Spacetime Alternatives and Their Classical Limits
• Night Thoughts of a Quantum Physicist
• Some Recent Developments in the Decoherent Histories Approach to Quantum Theory
• Quantum Measurement, a coherent description
• Fully polarized states and decoherence
• What Connects Different Interpretations of Quantum Mechanics?

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• A model-theoretic interpretation of environmentally-induced superselection
• Some Consequences of the Thermodynamic Cost of System Identification
• On the classical limit of quantum mechanics, fundamental graininess and chaos: compatibility of chaos with the correspondence principle
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• Quantum Edge Detection for Image Segmentation in Optical Environments
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• Optimal Estimation of States in Quantum Image Processing
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• Introduction to Quantum Mechanics and the Quantum-Classical transition
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• Extending cosmological natural selection
• Manifold Coordinates with Physical Meaning
• On the relation between geometric and deformation quantization
• Macroscopic observables and the Born rule
• Quantization and superselection sectors III: Multiply connected spaces and indistinguishable particles
• The Spacetime Picture in Quantum Gravity
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• Contextuality, Witness of Quantum Weirdness
• Quantum image processing?
• Interpretation Neutrality in the Classical Domain of Quantum Theory
• "'Formal' vs. 'Empirical' Approaches to Quantum-Classical Reduction"
• Bohr-Sommerfeld Star Products
• Justifying the Classical-Quantum Divide of the Copenhagen Interpretation
• Gradient expansion of the non-Abelian gauge-covariant Moyal star-product
• The relation between classical and quantum electrodynamics
• Quantum Boolean Image Denoising