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

How to make quantum mechanics look like a hidden-variable theory and vice versa

Marlan O. Scully

Published Nov 15, 1983• 53 citations
Publisher

Abstract

The quantum theory of a singlet spin-\textonehalf{} system is developed in terms of angular variables using a quantum-distribution-function technique. These calculations demonstrate a much closer correspondence between quantum mechanics and certain hidden-variable theories than was previously appreciated. It is found that a new type of hidden-variable theory is suggested by the quantum-distribution-function treatment of the Einstein-Podolsky-Rosen-Bohm spin-spin correlation problem which is in agreement with quantum theory but is "nonlocal."

DOI
10.1103/physrevd.28.2477

Related papers

A tutorial on quantum distribution functions for spin-12 systems and Einstein-Podolsky-Rosen correlations

Marlan O. Scully, Hwang Lee, Eduardo García Gómez +1 more

In earlier paper entitled How to make quantum mechanics look like a hidden-variable theory and vice versa, Phys. Rev. D 28, 2477 (1983) [1], we developed a quantum distribution function analysis for spin-12 systems, which had many of the characteristics of a hidden variable theory but was rigorously quantum mechanical. In the same paper, we also presented a hidden variable theory which was modeled after the Wigner like quantum distribution analysis and which agreed with the predictions of Einstein-Podolsky-Rosen (EPR) experiments but was non-local. These considerations are useful in understanding various subtle aspects of locality and reality in EPR type experiments. This has not been widely appreciated by students of philosophy and of the foundations of quantum mechanics. This is at least in part no doubt because the mathematical underpinnings are of a somewhat different nature than those usually associated with quantum mechanics. That is, the elements of quantum distribution theory are not the usual material of quantum mechanics course. The main goal of the present notes is therefore to provide a tutorial on quantum distribution theory as applied to spin one half particles. To that end, the original Phys. Rev. paper is included, as are our extensions of that paper. The technical variations, which are naturally included in an abbreviated form in the Phys. Rev. paper, are here presented as a series of worked problems.

AIP conference proceedings•Jan 1, 1999•0 citations

Reply to "Comment on `How to make quantum mechanics look like a hidden-variable theory and vice versa' "

Marlan O. Scully

Milonni reconsiders our recent work based on a singlet spin-\textonehalf{} system in terms of photon polarization correlations. His conclusions are in agreement with ours and provide a simple example showing why nonlocal hidden-variable theories are unappealing. We extend his arguments in order to emphasize that spin-\textonehalf{} physics is in some ways closer to classical intuition than that based on "few photon" physics.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Aug 15, 1985•1 citation

Comment on "How to make quantum mechanics look like a hidden-variable theory and vice versa"

Peter W. Milonni

The hidden-variable theory considered by Scully is discussed in the context of photon polarization correlations.Received 17 January 1984DOI:https://doi.org/10.1103/PhysRevD.32.1040©1985 American Physical Society

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Aug 15, 1985•5 citations

Angular-momentum measurement and nonlocality in Bohm’s interpretation of quantum theory

Christopher Dewdney, Z. Malik

We present the Bohm theory of hydrogenlike atoms, the measurement of orbital angular momentum, and Einstein-Podolsky-Rosen angular momentum correlations. We use the illustrations to discuss the arguments of von Neumann [described in M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974)] and Kochen and Specker [J. Math. Mech. 17, 59 (1967)] against hidden variables.

Physical Review A•Nov 1, 1993•19 citations

Hidden Variables and Nonlocality in Quantum Mechanics

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In this paper, we show that Erwin Schroedinger's generalization of the Einstein Podolsky Rosen argument can be connected to certain mathematical theorems - Gleason's and also Kochen and Specker's - in a manner analogous to the relation of EPR itself with Bell's theorem. In both cases, the conclusion is quantum nonlocality, as we discuss. The "Schroedinger nonlocality" proofs share some features with the Greenberger, Horne, and Zeilinger quantum-nonlocality work, yet also differ in significant ways. For clarity and completeness, we begin with a detailed discussion of the topic of hidden variable theorems. We argue, in agreement with John S. Bell, that 'impossibility' does not follow.

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Hidden-variable model for the Bohm Einstein-Podolsky-Rosen experiment

Kenneth Howard Schatten

We consider a hidden-variable model for the Einstein, Podolsky, and Rosen experiment [Phys. Rev. 47, 777 (1935)] as modified by Bohm $[---Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951)]. We provide a nonlocal random-vector model that mimics the same statistical behavior as quantum mechanics and conforms with Bell's theorem. Angular momentum conservation appears to require the nonlocal correlations.

Physical Review A•Jul 1, 1993•7 citations
The quantum theory of a singlet spin-\textonehalf{} system is developed in terms of angular variables using a quantum-distribution-function technique. These calculations demonstrate a much closer correspondence between quantum mechanics and certain hidden-variable theories than was previously appreciated. It is found that a new type of hidden-variable theory is suggested by the quantum-distribution-function treatment of the Einstein-Podolsky-Rosen-Bohm spin-spin correlation problem which is in agreement with quantum theory but is "nonlocal."
In earlier paper entitled How to make quantum mechanics look like a hidden-variable theory and vice versa, Phys. Rev. D 28, 2477 (1983) [1], we developed a quantum distribution function analysis for spin-12 systems, which had many of the characteristics of a hidden variable theory but was rigorously quantum mechanical. In the same paper, we also presented a hidden variable theory which was modeled after the Wigner like quantum distribution analysis and which agreed with the predictions of Einstein-Podolsky-Rosen (EPR) experiments but was non-local. These considerations are useful in understanding various subtle aspects of locality and reality in EPR type experiments. This has not been widely appreciated by students of philosophy and of the foundations of quantum mechanics. This is at least in part no doubt because the mathematical underpinnings are of a somewhat different nature than those usually associated with quantum mechanics. That is, the elements of quantum distribution theory are not the usual material of quantum mechanics course. The main goal of the present notes is therefore to provide a tutorial on quantum distribution theory as applied to spin one half particles. To that end, the original Phys. Rev. paper is included, as are our extensions of that paper. The technical variations, which are naturally included in an abbreviated form in the Phys. Rev. paper, are here presented as a series of worked problems.
In this paper, we show that Erwin Schroedinger's generalization of the Einstein Podolsky Rosen argument can be connected to certain mathematical theorems - Gleason's and also Kochen and Specker's - in a manner analogous to the relation of EPR itself with Bell's theorem. In both cases, the conclusion is quantum nonlocality, as we discuss. The "Schroedinger nonlocality" proofs share some features with the Greenberger, Horne, and Zeilinger quantum-nonlocality work, yet also differ in significant ways. For clarity and completeness, we begin with a detailed discussion of the topic of hidden variable theorems. We argue, in agreement with John S. Bell, that 'impossibility' does not follow.