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The British Journal for the Philosophy of Science

Separable Hidden Variables Theory to Explain Einstein-Podolsky-Rosen Paradox

Shaurya Bhave

Published Dec 1, 1986• 4 citations
Publisher

Abstract

A realist separable hidden variables theory in conformity with Einstein's principle of causality is developed in this paper to explain the Einstein-Podolsky-Rosen paradox, and the experimental results (including those in Aspect's four polarizers experiment) obtained so far with a view to test the non-separability of quantum mechanics.

DOI
10.1093/bjps/37.4.467

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Abstract Einstein's severe critique of quantum mechanics took its ultimate form in the so‐called Einstein Podolsky Rosen (EPR) paradox. The latter remained a subject of mere dispute, until a remarkable progress was initiated in 1964 by Bell who showed that quantum mechanical correlations specific for an EPR type experiment cannot be reproduced in any local hidden—variables theory. Afterwards, realistic versions of EPR experiments have been conceived and, in fact, carried out. The objective of the present paper is to give a review of this recent exciting development, both theoretical and experimental, which reveals one of the most striking features of quantum theory, the “quantum interconnectedness of distant systems”.

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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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After a brief summary of mathematical formalism of quantum theory and double slit experiment, the famous Einstein-Podolsky-Rosen paradox has been described. Bell’s inequalities have been derived and tests has been discussed. It is concluded that local hidden variable theories are wrong.

•Jan 1, 1988•0 citations
A realist separable hidden variables theory in conformity with Einstein's principle of causality is developed in this paper to explain the Einstein-Podolsky-Rosen paradox, and the experimental results (including those in Aspect's four polarizers experiment) obtained so far with a view to test the non-separability of quantum mechanics.
Abstract Einstein's severe critique of quantum mechanics took its ultimate form in the so‐called Einstein Podolsky Rosen (EPR) paradox. The latter remained a subject of mere dispute, until a remarkable progress was initiated in 1964 by Bell who showed that quantum mechanical correlations specific for an EPR type experiment cannot be reproduced in any local hidden—variables theory. Afterwards, realistic versions of EPR experiments have been conceived and, in fact, carried out. The objective of the present paper is to give a review of this recent exciting development, both theoretical and experimental, which reveals one of the most striking features of quantum theory, the “quantum interconnectedness of distant systems”.
Introduction The paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts to show that even without such a separability or locality requirement no ‘hidden variable’ interpretation of quantum mechanics is possible. These attempts have been examined elsewhere and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory has been explicitly constructed. That particular interpretation has indeed a grossly non-local structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions. Formulation With the example advocated by Bohm and Aharonov, the EPR argument is the following. Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stern–Gerlach magnets, on selected components of the spins σ 1 and σ 2 .
As a criterion between quantum mechanics and local hidden-variable theories, the so-called Einstein-Podolsky-Rosen paradox is mainly tested in the form of the statistical correlation between polarizations of photons issuing from a cascade transition. It has been stated more than once that an improved form of the test would make use of polarizers, the orientation of which would change randomly in a time comparable with the time of flight of the two photons; the Bell locality assumption could then be replaced by a weaker assumption also considered by Bell: The Einstein principle of separability. However, to our knowledge, no workable experimental scheme has yet been proposed, and we believe the one described in this paper to be a workable one. After explaining the difference between the Bell locality assumption and the Einstein principle of separability, we briefly discuss the theoretical implications of the modified experiment. The overall scheme of the apparatus we are proposing is described, and the generalized Bell inequalities, modified for our case, are derived. As in previous experiments, supplementary assumptions are made in order to derive experimentally testable inequalities. Finally, we describe the device we intend to use to carry out the proposed scheme.
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.
The EPR experiment is analysed in terms of ordinary quantum mechanics and shown to be compatible with the orthodox interpretation of this theory. There is no need to refer to Bohrs resolution of the EPR paradox, nor is it necessary to assume any further unusual properties of the quantum physical reality. In particular, it is shown that the EPR experiment does not contradict the fact that incommensurable properties cannot be objectivized simultaneously in a quantum mechanical system, and that the measuring process can be understood in terms of quantum theory as an interaction of the measuring apparatus and the object system. From these results it follows that there is no reason to search for modifications of the quantum theory which might be more convenient for a realistic interpretation of the EPR experiment. Furthermore, the EPR experiment cannot be used as a motivation for introducing hidden variables into the quantum theory. Experimental investigations which try to test quantum mechanics in respect to the possibility of introducing local hidden variables can therefore not be justified by the EPR paradox.