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Incompatibility between Realism and Quantum Mechanics: A Simple Example

Pablo L. Saldanha

Published May 14, 2018• 0 citations
OpenAlex

Abstract

We show that it is not possible to ascribe an objective reality to a property of a quantum system even if the system is in an eigenstate of the corresponding observable and a measurement of the property is certain to result in a particular value. This kind of incompatibility between realism and quantum mechanics is theoretically demonstrated with a simple example where sequential angular momentum measurements are performed on a quantum system. We discuss the relation of this result with other investigations about realism and quantum mechanics. In particular, we show that the Einstein-Podolsky-Rosen criterion for physical reality is incompatible with the quantum theory.

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We show that it is not possible to ascribe an objective reality to a property of a quantum system even if the system is in an eigenstate of the corresponding observable and a measurement of the property is certain to result in a particular value. This kind of incompatibility between realism and quantum mechanics is theoretically demonstrated with a simple example where sequential angular momentum measurements are performed on a quantum system. We discuss the relation of this result with other investigations about realism and quantum mechanics. In particular, we show that the Einstein-Podolsky-Rosen criterion for physical reality is incompatible with the quantum theory.
In recent notes by Einstein, Podolsky and Rosen and by Bohr, attention has been called to the fact that certain results of quantum mechanics are not to be reconciled with the assumption that a system has independently real properties as soon as it is free from mechanical interference. We here investigate in general, and in abstract terms, the extent of this disagreement. When suitably formulated, such an assumption gives to certain types of questions the same answers as does quantum mechanics; this is true of the formulas usually given in discussions of the theory of measurement. There exists, however, a general class of cases in which contradictions occur. That such contradictions are not restricted to the abstract mathematical theory, but can be realized in the commonest physical terms, is shown by the working out of an example..
Based on (i) the physical principle of local causality and (ii) a certain notion of elements of reality, Einstein, Podolsky, and Rosen put forward an argument showing that physical instances may exist in which two noncommuting observables can be joint elements of the physical reality. Here, we introduce a new criterion of joint reality. We demonstrate that according to this criterion, quantum mechanics generally prevents noncommuting observables from having joint elements of reality. In addition, we introduce a measure to quantify the extent to which the criterion is violated and explore the implications of such a measure in connection with incompatibility and correlations. Our findings suggest new manners of interpreting quantum phenomena.
Over fifty years ago Einstein, Podolsky, and Rosen published a striking argument that quantum theory provides only an incomplete description of physical reality – that is, that some elements of physical reality fail to have a counterpart in quantum-theoretical description. What made this a challenge to the quantum-theoretical Weltanschauung was the very mild character of the sufficient condition for the reality of a physical quantity on which their argument hinged: “If, without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.” The argument consists in pointing out that it is possible to construct a quantum-mechanical state ψ with the following properties: The state ψ describes two noninteracting systems (I and II). In almost all discussions the two systems are taken to be two particles, and the absence of relevant interaction is built in by taking ψ to assign negligible probability to finding the particles closer together than some macroscopically large distance. By measuring an observable A of system I, one can predict with certainty the result of a subsequent measurement of a corresponding observable P of system II. If, instead, one chooses to measure a different observable B of system I, one can predict with certainty the result of a subsequent measurement of a corresponding observable Q of system II. The observables P and Q are represented in quantum theory by noncommuting operators, which means that they cannot both have definite values.
Quantum mechanics is widely believed to be inconsistent with local realism because J.S. Bell proved the contradiction between quantum mechanics and the hidden variable theories based on reality and locality of matter. As described herein, the relation between quantum mechanics and local realism is discussed. This paper presents the question of whether any version of local realism is contradicted by quantum mechanics. The answer is negative. An interpretation is proposed by which the contradiction is explained using physical variables of two types: (1) physical variables of the first type, such as positions and angles (i.e. coordinates), are realistic variables and always possess definite values independently of measurements; (2) those of the second type, such as momenta, angular momenta, and spins (i.e., conserved quantities), are non-realistic variables, which possess no value before measurement. Value definiteness of the first type provides a reliable basis to physical reality of matter, and non-reality of the second type might solve the problem of inconsistency between quantum mechanics and local realism.