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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Interaction between classical and quantum systems: A new approach to quantum measurement. II. Theoretical considerations

T. N. Sherry, E. C. G. Sudarshan

Published Aug 15, 1979• 47 citations
Publisher

Abstract

We develop further a new approach to the quantum measurement process. In this approach, which we proposed in a recent paper, the apparatus is treated as a classical system; however, the classical apparatus is directly coupled to the quantum system. A principle of integrity, which requires that the observables of the classical apparatus retain their classical integrity, is introduced. We examine the constraints which this principle places upon the coupling between the apparatus and the quantum system. To illustrate our approach we use a model loosely based on the Stern-Gerlach experiment. For this model we exhibit a coupling which satisfies the principle of integrity.

DOI
10.1103/physrevd.20.857

Related papers

Interaction between classical and quantum systems: A new approach to quantum measurement.I

T. N. Sherry, E. C. G. Sudarshan

We introduce an unconventional approach to the measurement problem in quantum mechanics: we treat the apparatus as a classical system belonging to the macroworld. To describe the quantum measurement process we must couple the classical apparatus to the quantum system. In this paper we explain how this is to be done: we embed the classical apparatus into a larger quantum-mechanical structure, making use of a superselection principle. The apparatus can now be coupled to the quantum system in a straightforward manner. We discuss what constraints should be placed on the coupling so that an interpretation of the interaction as a measurement results. We require that unambiguous information of the values of a quantum observable should be transferred to the variables of the apparatus. We also require that the apparatus should retain its classical identity. This latter requirement is formulated as a principle of integrity, in both weak and strong forms.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Dec 15, 1978•70 citations

Interaction between classical and quantum systems: A new approach to quantum measurement. III. Illustration

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Following the approach to quantum measurement, proposed in an earlier paper, in which the apparatus is treated as a purely classical instrument to be described by the laws of classical mechanics we examine some simple experiments for the purpose of illustration. The Stern-Gerlach experiment is examined in detail, within our approach, and we see explicitly how the relevant information is transferred to the apparatus variables. We also examine a magnetic interferometer arrangement and a crossed-field arrangement. Consideration of these experiments leads us to the inclusion of an extra procedural step in our approach. This extra step is necessary so that an observer may measure the classical apparatus variables at will after the interaction is completed.

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Quantum measurement theory and the Stern–Gerlach experiment

M. Hannout, S. Hoyt, A. Kryowonos +1 more

The Stern–Gerlach experiment was one of the early illustrative examples of the Bohr view of quantum mechanics. In the Bohr view, a measurement is an interaction between a quantum object and an apparatus which acts in a classical fashion. There are still open problems with this concept, many of which enter into the discussion of the original Stern–Gerlach measurement.

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Model interactions between classical and quantum systems are briefly discussed. These include: general measurement-like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, SQUID-tank model.

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From Quantum Probabilities to Classical Facts

Ph. Blanchard, Arkadiusz Jadczyk

Model interactions between classical and quantum systems are briefly reviewed. These include: general measurement - like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, piecewise deterministic Markov processes and meaning of the wave function.

arXiv:hep-th/9311090•Nov 16, 1993•8 citations

A modern analysis of the Stern–Gerlach experiment

Daniel E. Platt

While the Stern–Gerlach experiment is an old and familiar problem, no analysis of this experiment is presented in the pedagogical literature using modern quantum mechanical techniques. Expositions of the Stern–Gerlach experiment are usually based on ‘‘old quantum theory,’’ i.e., semiclassical Bohr–Sommerfeld quantum mechanics. The experiment is also a popular one in discussions of the postulate of quantum measurement, which asserts that the process of measuring an observable forces the state vector of the system into an eigenvector of that observable, and the value measured will be the eigenvalue of that eigenvector. The most enduring of the philosophical arguments associated with quantum mechanics ultimately revolves around the mechanism of quantum measurement. Since the postulate of quantum measurement is expressed in terms well outside the realm of the old quantum mechanics, the traditional analysis of the Stern–Gerlach experiment cannot reveal any information about the relationship between dynamics and measurement. Therefore, a modern analysis of the Stern–Gerlach experiment must be made if this experiment is to reveal any information about the relationship between dynamics and the mechanism of quantum measurement. This paper presents such an analysis, and develops some of the implications for the theory of quantum measurement.

American Journal of Physics•Apr 1, 1992•48 citations
We develop further a new approach to the quantum measurement process. In this approach, which we proposed in a recent paper, the apparatus is treated as a classical system; however, the classical apparatus is directly coupled to the quantum system. A principle of integrity, which requires that the observables of the classical apparatus retain their classical integrity, is introduced. We examine the constraints which this principle places upon the coupling between the apparatus and the quantum system. To illustrate our approach we use a model loosely based on the Stern-Gerlach experiment. For this model we exhibit a coupling which satisfies the principle of integrity.
We introduce an unconventional approach to the measurement problem in quantum mechanics: we treat the apparatus as a classical system belonging to the macroworld. To describe the quantum measurement process we must couple the classical apparatus to the quantum system. In this paper we explain how this is to be done: we embed the classical apparatus into a larger quantum-mechanical structure, making use of a superselection principle. The apparatus can now be coupled to the quantum system in a straightforward manner. We discuss what constraints should be placed on the coupling so that an interpretation of the interaction as a measurement results. We require that unambiguous information of the values of a quantum observable should be transferred to the variables of the apparatus. We also require that the apparatus should retain its classical identity. This latter requirement is formulated as a principle of integrity, in both weak and strong forms.
Following the approach to quantum measurement, proposed in an earlier paper, in which the apparatus is treated as a purely classical instrument to be described by the laws of classical mechanics we examine some simple experiments for the purpose of illustration. The Stern-Gerlach experiment is examined in detail, within our approach, and we see explicitly how the relevant information is transferred to the apparatus variables. We also examine a magnetic interferometer arrangement and a crossed-field arrangement. Consideration of these experiments leads us to the inclusion of an extra procedural step in our approach. This extra step is necessary so that an observer may measure the classical apparatus variables at will after the interaction is completed.
While the Stern–Gerlach experiment is an old and familiar problem, no analysis of this experiment is presented in the pedagogical literature using modern quantum mechanical techniques. Expositions of the Stern–Gerlach experiment are usually based on ‘‘old quantum theory,’’ i.e., semiclassical Bohr–Sommerfeld quantum mechanics. The experiment is also a popular one in discussions of the postulate of quantum measurement, which asserts that the process of measuring an observable forces the state vector of the system into an eigenvector of that observable, and the value measured will be the eigenvalue of that eigenvector. The most enduring of the philosophical arguments associated with quantum mechanics ultimately revolves around the mechanism of quantum measurement. Since the postulate of quantum measurement is expressed in terms well outside the realm of the old quantum mechanics, the traditional analysis of the Stern–Gerlach experiment cannot reveal any information about the relationship between dynamics and measurement. Therefore, a modern analysis of the Stern–Gerlach experiment must be made if this experiment is to reveal any information about the relationship between dynamics and the mechanism of quantum measurement. This paper presents such an analysis, and develops some of the implications for the theory of quantum measurement.