Is an interpretation of quantum phenomena by hidden parameters impossible?

Alexander I. Akhiezer, R.V. Polovin

Alexander I. Akhiezer, R.V. Polovin

Elemér Elad Rosinger

It is shown that, although correct mathematically, the celebrated 1932 theorem of von Neumann which is often interpreted as proving the impossibility of the existence of "hidden variables" in Quantum Mechanics, is in fact based on an assumption which is physically not reasonable. Apart from that, the alleged conclusion of von Neumann proving the impossibility of the existence of "hidden variables" was already set aside in 1952 by the counterexample of the possibility of a physical theory, such as given by what is usually called the "Bohmian Mechanics". Similar arguments apply to other two well known mathematical theorems, namely, of Gleason, and of Kochen and Specker, which have often been seen as equally proving the impossibility of the existence of "hidden variables" in Quantum Mechanics.

Roland L. Omnes

Andrey A. Gribkov

The article is dedicated to the analysis of the ontological status of the hidden parameter λ in the context of Bell's theorem and quantum correlations. In the standard formulation of Bell's inequalities, the hidden parameter is attributed to an individual pair of entangled particles: it is assumed that λ determines the measurement outcomes for each specific pair and, therefore, serves as the carrier of correlation at the level of a single event. This interpretation gives rise to a well-known dilemma: the violation of Bell's inequalities in an experiment is interpreted as evidence of the impossibility of any local realistic theory, leading to conclusions about the non-locality of nature or a rejection of realism. The subject of this study is the very legitimacy of attributing the hidden parameter to an individual pair of particles. The question is posed: is λ a property of a single pair or a characteristic of a statistical ensemble? The problem is considered in the context of the classical philosophical opposition between the singular and the general, as well as the mereological relationship between parts and the whole in relation to the quantum-mechanical description of reality. A conceptual analysis of the mathematical structure of Bell's theorem is employed, along with a comparison of the ontological assumptions of the standard and ensemble interpretations, as well as a philosophical analysis of the levels of realization of correlation. The scientific novelty of the work lies in the explicit formulation of the question regarding the level of ontological belonging of the hidden parameter—a question that is typically not addressed in standard discussions around Bell's theorem. It is shown that attributing λ to an individual pair of particles represents not an experimentally justified fact, but an ontological assumption embedded in the formalism at the stage of its construction. This assumption predetermines the interpretation of the results: the violation of Bell's inequalities is perceived as a collapse of local realism only under the condition that correlation must be realized at the level of a single pair. If the correlation is realized at the level of the ensemble—through the structure of the distribution ρ(λ)—then the violation of Bell's inequalities indicates not non-locality, but the inadequacy of an individual ontology of the hidden parameter. The conclusion is that the standard interpretation of Bell's theorem conflates two ontological levels of description, and a correct delineation of these levels removes the necessity of choosing between non-locality and a rejection of realism.

V. V. Aristov, А. В. Никулов

Many physicists limit oneself to an instrumentalist description of quantum phenomena and ignore the problems of foundation and interpretation of quantum mechanics. This instrumentalist approach results to "specialization barbarism" and mass delusion concerning the problem, how a quantum computer can be made. The idea of quantum computation can be described within the limits of quantum formalism. But in order to understand how this idea can be put into practice one should realize the question: "What could the quantum formalism describe?", in spite of the absence of an universally recognized answer. Only a realization of this question and the undecided problem of quantum foundations allows to see in which quantum systems the superposition and EPR correlation could be expected. Because of the "specialization barbarism" many authors are sure that Bell proved full impossibility of any hidden-variables interpretation. Therefore it is important to emphasize that in reality Bell has restricted to validity limits of the no-hidden-variables proof and has shown that two-state quantum system can be described by hidden variables. The later means that no experimental result obtained on two-state quantum system can prove the existence of superposition and violation of the realism. One should not assume before unambiguous experimental evidence that any two-state quantum system is quantum bit. No experimental evidence of superposition of macroscopically distinct quantum states and of a quantum bit on base of superconductor structure was obtained for the present. Moreover same experimental results can not be described in the limits of the quantum formalism.