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Journal of the Japan Association for Philosophy of Science

Holistic Ensemble Interpretation of Quantum Mechanics and Bell’s Inequalities

Hisato Shirai

Published Jan 1, 2021• 0 citations
Publisher

Abstract

The ensemble interpretation (EI) of quantum mechanics has been proposed by physicists and philosophers (e.g., A. Einstein, K. R. Popper, and A. Lande). However, it is not accepted widely among modern scientists. This is because the EI is regarded as a kind of the hidden variable theories. The scientists believe that the EI is inconsistent with violation of Bell's inequalities. The present paper points out that there are various types of the EI. Several of them can be consistent with the violation. The non-local type of the EI proposed by Shirai in 1998 is also consistent. We call it “holistic ensemble interpretation (HEI).” The non-locality in the HEI includes a temporal non-locality (i.e., a future dependence), implying that the present distributions depend on the future conditions. The concept of the future dependence would be so controversial that we discuss it deeply in the latter half of the paper. Many scientists may think of it as a doubtful concept, because it disagrees with the concept of “free will.” However, there are several reasons why we should consider the future dependence.

DOI
10.4288/kisoron.49.1_15

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The ensemble interpretation (EI) of quantum mechanics has been proposed by physicists and philosophers (e.g., A. Einstein, K. R. Popper, and A. Lande). However, it is not accepted widely among modern scientists. This is because the EI is regarded as a kind of the hidden variable theories. The scientists believe that the EI is inconsistent with violation of Bell's inequalities. The present paper points out that there are various types of the EI. Several of them can be consistent with the violation. The non-local type of the EI proposed by Shirai in 1998 is also consistent. We call it “holistic ensemble interpretation (HEI).” The non-locality in the HEI includes a temporal non-locality (i.e., a future dependence), implying that the present distributions depend on the future conditions. The concept of the future dependence would be so controversial that we discuss it deeply in the latter half of the paper. Many scientists may think of it as a doubtful concept, because it disagrees with the concept of “free will.” However, there are several reasons why we should consider the future dependence.
Einstein was never satisfied with quantum mechanics. He argued that quantum mechanics was incomplete for two main reasons; it violated the locality principle and the separability principle. The violation of separability is an unavoidable consequence of quantum interactions. Non-separability can be seen in quantum entanglement. Non-locality, however, is more controversial. Einstein and his associates published the EPR paper in order to argue for the incompleteness of quantum mechanics. Years later, John Bell formulated what became known as the Bell Inequalities in response to the EPR paper. The Bell Inequalities are seen as a major obstacle for quantum locality. I will argue that non-locality is not a necessary implication of the Bell Inequalities. The Bell Inequalities were developed using Bell’s locality requirement as a major premise. Bell’s locality requirement can be described in terms of two conditions, parameter independence and outcome independence. A violation of either condition will lead to a violation of the Bell inequalities. Parameter independence is not violated by the results of experimental quantum physics. So, it can be argued that violations of the Bell inequalities are caused by the violation of outcome independence. Such a violation of outcome independence does not imply non-locality if we accept some form of holism or non-separability. Thus, by including some form of holism or non-separability into our picture of the quantum realm we can develop a theory that does not conflict with locality. This paper will discuss different types of holism and non-separability and how they can be used to help understand quantum phenomena.
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.
Abstract Quantum states in superposition cannot be observed, suggesting that they merely embody information on possible measurement results. Yet, we think of them as describing physical systems that evolve in time according to given mathematical equations. Furthermore, evolution takes place in physical space-time, and local causality is imposed on space-time by Special Relativity (a sequence of cause and effect that constitutes a fundamental principle by which we think about and do scientific work). It is therefore strange that there is non–locality and violation of causality embedded in Quantum Mechanics. We try to give here a first step to see whether a deterministic and local interpretation is possible. We will show that Bell’s inequality is not conclusive about the non–local nature of Quantum Mechanics, in that there exists an interpretation of reality (which we put forward) which is local and in which Bell’s inequality cannot be derived. Assuming determinism and locality a new Bell-like inequality is derived, which is always satisfied by Quantum Mechanics and which allows for local hidden variables [1].
Various interpretations of quantum mechanics, favored (or neglected) by John Bell in the context of his nonlocality theorem, are compared and discussed. Varenna 1970 I met John Bell for the first time at the Varenna conference of 1970 [1]. I had been invited on the suggestion of Eugene P. Wigner, who had already helped me to publish my first paper on the concept that was later called decoherence – to appear in the first issue of Foundations of Physics a few months after the conference [2]. This concept arose from my conviction, based on many applications of quantum mechanics to composite systems under various conditions, that Schrödinger's wave function in configuration space, or more generally the superposition principle, is universally valid and applicable. In particular, stable narrow wavepackets can represent classical configurations, while their superpositions define novel individual properties – such as “momentum,” defined as a plane wave superposition of different positions. Superpositions of macroscopically different properties, on the other hand, are regularly irreversibly “dislocalized” (distributed over many degrees of freedom) by means of interactions described by the Schrödinger equation. The corresponding disappearance of certain local superpositions (“decoherence”) seems to explain the phenomenon of a classical world as well as the apparent occurrence of quantum jumps or stochastic “events” – see Sect. 20.4 or [3] for a historical overview of the conceptual development of quantum theory. So I had never felt any motivation to think of “hidden variables” or any other physics behind the successful wave function. Therefore, I was very surprised on my arrival in Varenna to hear everybody discuss Bell's inequality. It had been published a few years before the conference, but I had either not noticed it or not regarded it as particularly remarkable until then. As this inequality demonstrates that the predictions of quantum theory would require any conceivable reality possibly underlying the nonlocal wave function to be nonlocal itself, I simply found my conviction that the latter describes individual reality confirmed. For example, I had often discussed the conservation of total spin or angular momentum in an individual decay process, which requires nonlocal entanglement between the fragments at any distance in a form that was later called a “Bell state”.
The conceptually puzzling features of quantum mechanics as a statistical theory all have their source in the impossibility of relating the probability assignments defined by the quantum state to distributions over determinate values of the physical magnitudes. While some interpretations of quantum mechanics, as well as “hidden variable” modifications of the theory, have proposed several constructions for assigning values to magnitudes (beyond the value assignments defined by the quantum state alone), a variety of theorems exist which impose severe restrictions on such theoretical constructions. This note will deal with Bell's proof (in [2]), that any hidden variable theory satisfying a physically reasonable locality condition is characterized by an inequality which is inconsistent with the quantum statistics. Bell's result has initiated a series of experiments designed to refute the entire class of local hidden variable theories. We show that Bell's inequality actually characterizes a feature of hidden variable theories which is much weaker than locality in the sense considered physically motivated.
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and empiricist interpretations of the mathematical formalism of quantum mechanics, iii) the distinction between measurement and preparation. It will be demonstrated that an interpretation of violation of Bell's inequality by quantum mechanics as evidence of non-locality of the quantum world is a consequence of a particular choice between these alternatives. Also a distinction must be drawn between two forms of realism, viz. a) realist interpretations of quantum mechanics, b) the possibility of hidden-variables (sub-quantum) theories.