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AIP conference proceedings

Locality and simultaneous elements of reality

Giuseppe Nisticò, Angela Sestito

Published Jan 1, 2012• 0 citations
Publisher

Abstract

We show that the extension of quantum correlations stemming from a “strict" interpreta- tion of the criterion of reality raises the failure of Hardy’s non-locality theorem. Then, by suggesting an ideal experiment, we prove that such an extension, though strictly smaller than the one derived by Einstein, Podolsky and Rosen and usually adopted, allows for the assignment of simultaneous objective values of two non-commuting observables.

DOI
10.1063/1.4773170

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We show that the extension of quantum correlations stemming from a “strict" interpreta- tion of the criterion of reality raises the failure of Hardy’s non-locality theorem. Then, by suggesting an ideal experiment, we prove that such an extension, though strictly smaller than the one derived by Einstein, Podolsky and Rosen and usually adopted, allows for the assignment of simultaneous objective values of two non-commuting observables.
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.
According to the orthodox interpretation of quantum mechanics (Bohr being its leading voice), the attributes of a physical object (position, momentum, spin, etc.) can be assigned only when they have been measured. Einstein advocated the local realist viewpoint that an object had definite attributes whether they had been measured or not. The Copenhagen school view that measurement actually produces an object’s property would imply that the measurement of one part of an entangled quantum state can instantaneously fix the value of another part, no matter how far the two parts have been separated. Einstein, Podolsky, and Rosen devised a thought experiment to shine a light on this “spooky action-at-a-distance” feature; its discussion and debate have illuminated the meaning of quantum mechanics (QM). It led later to Bell’s theorem showing that these seemingly philosophical questions can lead to observable results. The experimental vindication of the orthodox theory has sharpened our appreciation of the nonlocal features of quantum mechanics. Nevertheless, the counter-intuitive QM picture of objective reality still troubles many, leaving one to wonder whether quantum mechanics is ultimately a complete theory.
The notion of the Einstein-Podolsky-Rosen (EPR) "element of reality" is much discussed in the literature on the foundations of quantum mechanics. Recently, it has become particularly relevant due to a proposed criterion of the physical reality of a given quantum mechanical observable [A. L. O. Bilobran and R. M. Angelo, Europhys. Lett. 112, 40005 (2015)]. We examine this proposal and its consequently related measure of non-locality [V. S. Gomez and R. M. Angelo, Phys. Rev. A 97, 012123, (2018)] and argue that the criterion is ill-described as quantifying physical reality without introducing serious inconsistency with the basic notions of realism that under-gird enquiry. We agree that this reality criterion demonstrates, along with the famous GHZ results, that general quantum observable values make for poor elements of reality. However, we also argue that this does not mean no such elements of reality are to be found in quantum theory. By arguing for, and adopting, probability distributions as these elements of reality instead, we demonstrate that the criterion of physical reality is actually one of observable predictability. We then examine the relationship of realism-based non-locality to the Bell form and find that, despite the flawed premise, this measure does indeed codify non-locality that is not captured by Bell inequalities.
The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Sixty five years ago, the most significant paper questioning a fundamental aspect of quantum phenomena was written by Einstein, Podolsky and Rosen (EPR) [1]. They addressed the question whether the wave-function represented a complete description of reality in quantum mechanics, and argued that it didn’t. Bohr’s reply to this paper [2] was not sufficient to resolve the fundamental issues raised by EPR. Decades later, Bohm rephrased the EPR problem [3] in terms of particles correlated in their spin and this helped enormously in analyzing the problem with clarity. John Bell analyzed the EPR problem in the early sixties and established the Bell’s inequalities obeyed by
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.