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Philosophy of Science

Pair Distributions and Conditional Independence: Some Hints about the Structure of Strange Quantum Correlations

N. David Mermin

Published Sep 1, 1983• 5 citations
Publisher

Abstract

Some statistical questions that arise in studies of Einstein-Podolsky-Rosen correlations are given precise and complete answers for a very simple but artificial set of pair distributions. Some recent results and conjectures about hidden variable representations of the more complex distributions that describe the Einstein-Podolsky-Rosen experiment are examined in the light of the behavior of the simple model.

DOI
10.1086/289124

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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.

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Some statistical questions that arise in studies of Einstein-Podolsky-Rosen correlations are given precise and complete answers for a very simple but artificial set of pair distributions. Some recent results and conjectures about hidden variable representations of the more complex distributions that describe the Einstein-Podolsky-Rosen experiment are examined in the light of the behavior of the simple model.
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.
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.
ASPECTS OF THE DEBATE The debate between Niels Bohr and Albert Einstein concerning the interpretation of quantum mechanics extended from the fifth Solvay Conference in 1927 until the end of Einstein's life. The most dramatic exchange occurred in 1935, when Einstein, in collaboration with B. Podolsky and N. Rosen, published a paper in Physical Review entitled “Can quantum-mechanical description of physical reality be considered complete?”, concluding with a negative answer, and Bohr replied in the same journal, with a paper of the same title but giving a positive answer. Their arguments were restated, in some respects with greater clarity, in the Library of Living Philosophers volume on Einstein in 1949. The disagreements between Bohr and Einstein concerned not only the physical question expressed in the common title of their papers, but also philosophical questions about physical reality and human knowledge. Much light was thrown upon the Bohr–Einstein debate by the theorem of J. S. Bell (1964) and the experiments which it inspired. Bell showed that any physical theory which applies to a pair of spatially separated systems (as considered in the thought experiment of Einstein, Podolsky, and Rosen) and satisfies a certain locality condition will, in certain circumstances, disagree statistically with quantum mechanics. Consequently, the supplementation of the quantum mechanical description envisaged by Einstein and his collaborators (usually referred to as a “hidden variables theory”) must either violate the locality condition or clash with quantum mechanical predictions.