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Optics and Spectroscopy

Quantum uncertainty and a counterexample of nonlocal classical “realism”

Aleksandr V. Belinsky

Published Sep 1, 2017• 0 citations
Publisher

Abstract

We analyze the scheme of an experiment in which, by examining suppression effects of the cross correlation of photons in a beamsplitter and by preparing squeezed states, it is proven that the phase difference of photons in Fock states cannot acquire a certain value, since, otherwise, the simultaneous existence of these two effects would be impossible. We show that this reveals an intrinsic inconsistency of the nonlocal classical interpretation of quantum mechanics on the basis of nonlocal classical “realism.”

DOI
10.1134/s0030400x17090077

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We analyze the scheme of an experiment in which, by examining suppression effects of the cross correlation of photons in a beamsplitter and by preparing squeezed states, it is proven that the phase difference of photons in Fock states cannot acquire a certain value, since, otherwise, the simultaneous existence of these two effects would be impossible. We show that this reveals an intrinsic inconsistency of the nonlocal classical interpretation of quantum mechanics on the basis of nonlocal classical “realism.”
Abstract This paper reviews the schemes of experiments in which it was possible to prove, based on measured photon cross-correlation suppression effects in a beam splitter and preparing squeezed states, the nonexistence of a definite value of the photon phase difference in Fock states (otherwise, these two effects cannot exist simultaneously). It is shown that this conclusion emphasizes the internal inconsistency of interpreting the quantum mechanics in the spirit of classical nonlocal ‘realism’ — in the sense that measured physical quantities have no definite values a priori , i.e., before the instant of measurement.
Accepting nonlocal quantum correlations requires us to reject special relativity and/or probability theory. We can retain both by revising our interpretation of quantum mechanics regarding the handling of separated systems, as quantum mechanics conflicts with local realism only in its treatment of separated systems. We cannot use the joint probability formula for cases of separated measurements. We use the marginals (partial traces) together with whatever priors we have from an understanding of the system. This program can reconcile quantum mechanics with local realism. An apparent obstacle to this program is the experimental evidence, but we argue that the experiments have been misinterpreted, and that when correctly interpreted they confirm local realism. We describe a local realistic account of one important Einstein-Poldosky-Rosen-Bohm (EPRB) experiment (Weihs et al6) that claims to demonstrate nonlocal entanglement. We present a local realistic system (experiment) that can be calibrated into both quantum and classical correlation domains via adjustment of parameters (‘hidden variables’) of the apparatus. Weihs incorrectly dismisses these parameters as uncritical. Nonlocal entanglement is seen to be an error. The rest of quantum mechanics remains intact, and remains highly valued as a powerful probability calculus for observables. Freed from the incoherent idea of nonlocal entanglement, we can leverage powerful classical ideas, such as semiclassical radiation theory, stochastic dynamics, classical noncommutativity/contextuality, measurement effects on state, etc., to augment or complement quantum mechanics. When properly interpreted and applied, quantum mechanics lives in peaceful harmony with the local realist conception, and both perspectives offer useful paradigms for describing systems.
We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states. The same concerns the entangled states of compound quantum systems. In the {\it existing} quantum mechanics, introducing Bell's inequalities is fully legal. However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation. Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm. They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.
I consider the extent to which the applicability of the concept of classical realism is constrained, irrespective of the validity or not of the quantum formalism, by existing experiments both in the EPR–Bell setup, including recent experiments testing ‘nonlocal realistic’ theories, and in the area of ‘macroscopic quantum coherence’. Unless we are willing to sacrifice one or more other intuitively plausible notions such as that of the conventional ‘arrow of time’, it appears impossible, in either context, to maintain the classical notion of realism.
The EPR paradox was caused by the provision that quantum variables must have pre-existing values. This type of "hidden property realism" was later falsified by Bell's Theorem. Accordingly, the physical basis for action-at-a-distance between entangled quanta was removed. Yet, modern interpretations present Bell's inequality as a Locality Criterion, as if Bell violations can only happen at the quantum level, and only with remote interactions. This is a questionable practice, considering that classical joint measurements also violate such inequalities for mutually exclusive wave properties. In particular, consecutive measurements of polarization produce the same coefficients of correlation as parallel measurements with entangled quanta, yet they are explicitly local. Furthermore, it is possible to combine parallel and consecutive measurements of Type I polarization-entangled photons in a single experiment, conclusively showing that quantum Bell violations can be local. Surprisingly, classical phenomena also require nonlocal interpretations if pre-existing properties are taken for granted. Hence, the solution is to reject the models with pre-existing properties for both classical and quantum wave-like phenomena.