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Journal of Physics A Mathematical and General

Interpretations of quantum mechanics and some claimed resolutions of the EPR paradox

M. A. B. Whitaker, Ishwar S Singh

Published Aug 1, 1982• 4 citations
Publisher

Abstract

The authors discuss a number of papers which claim that the EPR 'paradox' may be resolved using density-matrix methods. They first show that it is only inside the Copenhagen interpretation that the EPR experiment has any appearance of paradox; inside an ensemble interpretation, or hidden-variable theory, it may be analysed in a straightforward way. They then show that these 'resolutions' are implicitly using an ensemble interpretation.

DOI
10.1088/0305-4470/15/8/017

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The authors discuss a number of papers which claim that the EPR 'paradox' may be resolved using density-matrix methods. They first show that it is only inside the Copenhagen interpretation that the EPR experiment has any appearance of paradox; inside an ensemble interpretation, or hidden-variable theory, it may be analysed in a straightforward way. They then show that these 'resolutions' are implicitly using an ensemble interpretation.
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.
Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with an arbitrary axis of quantization. This axis acts as a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state. Whether or not the EPR spin pairs retain entanglement or disentangle, however, the statistical ensemble interpretation resolves the EPR paradox and gives a mechanism for quantum "teleportation" without the need for instantaneous action-at-a-distance.
The purpose of this paper is to resolve two paradoxes, which occur in quantum theory, by using the discussion of the theory of measurement presented in two earlier papers by the author [3], [4], [5]. The two paradoxes discussed will be the Schrödinger cat paradox and the Einstein, Podolski, Rosen paradox [2]. An introductory section will be included which summarizes the relevant results from the author's previous papers. Also a discussion will be made regarding the author's interpretation of the density operator.
In the normal presentation of the EPR problem a comparison is made between the (weak) Copenhagen interpretation of quantum mechanics which seems to suggest that at times action at a distance may take place, and the hidden parameter interpretation which must satisfy Bell's inequality, in contradiction to the predictions of quantum mechanics. In this paper, we consider a relativistic approach to the paradox. However, the frame of reference under consideration is not the usual Lorenz frame but rather the spin frame of reference which is invariant with respect to the SU(2) group.