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Physical Review A

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

Kenneth Howard Schatten

Published Jul 1, 1993• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.48.103

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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.
1 History of the Einstein-Podolsky-Rosen Paradox.- 2 Are Faster-Than-Light Influences Necessary?.- 3 All the Inequalities of Einstein Locality.- 4 Einstein-Podolsky-Rosen Experiments Using the Decays of ?c or J/? into ??? ? ?-?p?+p?.- Chapter5 Einstein-Podolsky-Rosen Paradox for the K0-K?0 and B0-B?0 Systems.- 6 Even Local Probabilities Lead to the Paradox.- 7 The Experimental Investigation of the Einstein-Podolsky-Rosen Question and Bell's Inequality.- 8 Rapisarda's Experiment: Testing Quantum Mechanics versus Local Hidden-Variable Theories with Dichotomic Analyzers.- 9 Nonlocality and the Einstein-Podolsky-Rosen Experiment as Understood through the Quantum-Potential Approach.- 10 Interpretation of the Einstein-Podolsky-Rosen Effect in Terms of a Generalized Causality.- 11 Quantum Action-at-a-Distance: The Mystery of Einstein-Podolsky-Rosen Correlations.- 12 Particle Trajectories and Quantum Correlations.- 13 Bell's Inequality and the Nonergodic Interpretation of Quantum Mechanics.- 14 An Extended-Probability Response to the Einstein-Podolsky-Rosen Argument.- 15 The Search for Hidden Variables in Quantum Mechanics.- 16 Variable Detection Probability Models for Einstein-Podolsky-Rosen-Type Experiments.- 17 Stochastic Electrodynamics and the Einstein-Podolsky-Rosen Argument.- 18 Explicit Calculations with a Hidden-Variable Spin Model.- 19 Symmetric and Asymmetric Models for Atomic Cascade Experiments.
Bohm's spin polarization modification of the paradox of Einstein, Podolsky, and Rosen has served as the basis for numerous analyses of the roles of hidden variables and Einstein locality in quantum mechanics. The present note points out how corresponding analyses can be carried out on the original formulation of Einstein, Podolsky, and Rosen (EPR) in terms of observations of position and momentum. Concrete conceptual experiments are proposed to furnish tangible illustrations of EPR tests of reality, and a position-momentum variant of Bell's inequality is formulated. Implications regarding joint measurements of position and momentum, delayed choice experiments, and superluminal communication are discussed briefly.
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."