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Cited by 1,415Quantum Mechanics and ApplicationsQuantum Information and CryptographyAdvanced Thermodynamics and Statistical Mechanics

Environment-induced superselection rules

Zurek, W. H.·1982·Physical Review D
DOI 10.1103/physrevd.26.1862
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Abstract

We show how the correlations of a quantum system with other quantum systems may cause one of its observables to behave in a classical manner. In particular, "reduction of the wave packet," postulated by von Neumann to explain definiteness of an outcome of an individual observation, can be explained when a realistic model of an apparatus is adopted. Instead of an isolated quantum apparatus with a number of states equal to the number of possible distinct outcomes of the measurement, discussed by von Neumann, we consider an apparatus interacting with other physical systems, described here summarily as "environment." The interaction of the quantum apparatus with the environment results in correlations. Correlations impose effective superselection rules which prevent apparatus from appearing in a superposition of states corresponding to different eigenvalues of the privileged pointer observable. It is the propagation of the correlations with the pointer basis states which is ultimately responsible for the choice of the pointer observable. It can be thought of as a process of amplification in which the state of many distinct physical systems becomes correlated with the pointer basis state. Whether these environment systems are regarded as a part of the apparatus setup, or as a part of its environment is irrelevant. What is crucial is the redundancy of the record concerning the pointer observable which is imprinted into the correlations. Eigenspaces of the pointer observable provide a natural basis for the pointer of the quantum apparatus and determine the to-be-measured observable of the quantum system. Decay of those elements of the apparatus-system density matrix, which are off-diagonal in the pointer observable, is caused by the natural evolution of the combined system-apparatus-environment object. For a hypothetical finite environment with $N$ distinct eigenvalues of the apparatus-environment interaction Hamiltonian, off-diagonal terms will decay to become of the order of ${N}^{\ensuremath{-}\frac{1}{2}}$, and will recur only on a Poincar\'e time scale. No recurrences will be observed in realistic circumstances. As the correlations spread through the environment on a time scale typically much shorter than the recurrence time scale calculated for the environment already correlated with the pointer observable, the measurement becomes effectively irreversible. Relevance of this model of the measurement process for the understanding of the second law of thermodynamics and its relation to Bohr's "irreversible act of amplification" is briefly discussed. The emergence of the pointer observable can be interpreted as a clue about the resolution of the measurement problem in case of no environment. It points towards the possibility that properties of quantum systems have no absolute meaning. Rather, they must be always characterized with respect to other physical systems.

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  • Owing to interactions expressed in Schrödinger's equation among many degrees of freedom, the amount of y-disjointness in supports of Φ and Ψ⊥ will typically tend to increase dramatically as time goes on, with more and more degrees of freedom participating.

    “In fact, owing to the interactions-expressed in Schr¨ odinger's equation-among the many degrees of freedom, the amount of y-disjointness in the supports of Φ and Ψ ⊥ will typically tend to increase dramatically as time goes on, with, as in a chain reaction, more and more degrees of freedom participating in this disjointness (see [13,42,64,38]; see also [ 12 ])).”

    From Quantum equilibrium and the origin of absolute uncertainty (1992) · cites this paper as [64]

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Authors
Zurek, W. H.
Affiliations
California Institute of Technology (US)
Corresponding author
Zurek, W. H.
ORCID
Zurek, W. H.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1982-10-15
Volume
26
Issue
8
Pages
1862-1880
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.26.1862
OpenAlex
W2089610453
Cited by
1,415
References
47
Citations by year
2026: 46 · 2025: 27 · 2024: 42 · 2023: 46 · 2022: 50 · 2021: 59 · 2020: 53 · 2019: 34 · 2018: 38 · 2017: 32 · 2016: 33 · 2015: 31 · 2014: 41 · 2013: 45 · 2012: 32
FWCI
3.61
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
superselection rules, measurement problem, wave packet reduction, projective measurement, environmental decoherence, quantum-classical correspondence, Poincaré recurrence, second law of thermodynamics, emergence of classicality, quantum-to-classical transition

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