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Zeitschrift für Naturforschung A

Über das Einstein-Podolsky-Rosen Paradoxon / On the Einstein-Podolsky-Rosen Paradox

Peter Mittelstaedt

Published Apr 1, 1974• 1 citation
Publisher

Abstract

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.

DOI
10.1515/zna-1974-0401

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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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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.
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”.
In 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen ('EPR') reported on a thought experiment that they believed showed that quantum theory provided an incomplete description of reality. Today we know that quantum theory is a complete and correct description of Nature (in flat space-time). The EPR thought experiment is predicted by quantum theory and has since been experimentally confirmed. However, EPR experiments have no physical pictorial explanation, and are considered part of a "paradox". Here I resolve the "paradox". I show independently of any interpretation of quantum theory that EPR (thought) experiments are a direct and compelling consequence of the existence of true randomness and the conservation of energy. It becomes obvious why EPR (thought) experiments allow for the precise prediction of truly random measurement values. Local hidden variables are not motivated.
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 .
A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the statistical independence between two measurements space - like separated. This assumption is valid only with the additional one that statistical dependence between two measurements requires a causal connection between them. This additional assumption rules out the possibility that statistical dependence may due to an intrinsic property of the physical system under study. Therefore, hidden variables theories are built up with a restriction which leads them to be disproved by experiment. Quantum mechanical non - locality, invoked for describing EPR - type experiments, is strictly connected to the hypothesis (NDV hypothesis) according to which the twin photons of entangled pairs do not have a definite polarization before measurements. Both hypotheses are used only for describing EPR experiments and not for making predictions. Therefore, they can be dropped without reducing the predictive power of quantum mechanics concerning entangled photons pairs. Furthermore, both hypotheses can be experimentally tested by a modification of a standard experimental apparatus designed for studying entangled photons pairs.
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.
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.