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CRC Press eBooks

The Einstein-Podolsky-Rosen Problem

Bernard d’Espagnat

Published Mar 5, 2018• 0 citations
Publisher

Abstract

The difference between the conceptual framework of classical physics and that of quantum physics which is due to the nonseparability property of the latter theory is better understood in specific examples. This chapter uses some specific examples to test the validity, both in classical and in quantum mechanics, of two conceptual principles. First is Reality Principle . The very concept of a reality may be criticized by philosophically minded empiricists. A widespread opinion, however, is that somehow a physical reality does exist, which should not just amount to the talks we give about it. In their search for a criterion that would make it possible to recognize elements of reality, A. Einstein, B. Podolsky, and N. Rosen had to take such considerations into account. Second, Principle of the Separability of Mechanically Isolated Systems, one can easily guess that this second principle, which remains somewhat implicit in the work of Einstein and his colleagues may well be the source of insuperable difficulties.

DOI
10.1201/9780429501449-11

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In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper [17] in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete.That is, there must exist some elements of reality that are not described by quantum mechanics.There must be, they concluded, a more complete description of physical reality behind quantum mechanics.There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality.Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities).The paradox consists in the fact that quantum probabilities do not satisfy these inequalities.And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades.The problem is still open and hotly debated among both physicists and philosophers.It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.

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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.

•May 14, 2018•0 citations
The difference between the conceptual framework of classical physics and that of quantum physics which is due to the nonseparability property of the latter theory is better understood in specific examples. This chapter uses some specific examples to test the validity, both in classical and in quantum mechanics, of two conceptual principles. First is Reality Principle . The very concept of a reality may be criticized by philosophically minded empiricists. A widespread opinion, however, is that somehow a physical reality does exist, which should not just amount to the talks we give about it. In their search for a criterion that would make it possible to recognize elements of reality, A. Einstein, B. Podolsky, and N. Rosen had to take such considerations into account. Second, Principle of the Separability of Mechanically Isolated Systems, one can easily guess that this second principle, which remains somewhat implicit in the work of Einstein and his colleagues may well be the source of insuperable difficulties.
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.
This chapter examines the A. Einstein, B. Podolsky, and N. Rosen (EPR) argument and the opinion toward interpretational matters from various noted quantum physicists. The paradox of EPR can equally well be tested by polarization properties of pairs of photons. “When the momentum of a particle is known, its coordinate has no physical reality” is an essential component of the EPR argument. A useful pragmatic perspective on quantum mechanics is provided by N. G. Van Kampen. He argues that the difficulties in quantum mechanics only surface when one starts philosophizing: “this philosophizing has given rise to a number of ‘interpretations’, in which ψ is endowed with more physical significance than is needed”. There is a plethora of interpretations of quantum mechanics. Among the most prominent interpretations one finds are the Copenhagen interpretation and the many-worlds interpretation.
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.
In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete. That is, there must exist some elements of reality that are not described by quantum mechanics. There must be, they concluded, a more complete description of physical reality behind quantum mechanics. There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality. Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities). The paradox consists in the fact that quantum probabilities do not satisfy these inequalities. And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades. The problem is still open and hotly debated among both physicists and philosophers. It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.
In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper [17] in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete.That is, there must exist some elements of reality that are not described by quantum mechanics.There must be, they concluded, a more complete description of physical reality behind quantum mechanics.There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality.Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities).The paradox consists in the fact that quantum probabilities do not satisfy these inequalities.And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades.The problem is still open and hotly debated among both physicists and philosophers.It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.
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.