Interpretations of quantum mechanics, and interpretations of violation of Bell's inequality

De Muynck, W M

Published Feb 12, 2001• 35 citations

Abstract

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.

Related papers

INTERPRETATIONS OF QUANTUM MECHANICS, AND INTERPRETATIONS OF VIOLATION OF BELL'S INEQUALITY

WILLEM. M. DE MUYNCK

arXiv:quant-ph/0102066Foundations of probability and physicsDec 1, 200114 citations

Violation of Bell Inequalities: Mapping the Conceptual Implications

Brian Drummond

This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of these are definite. The violations constrain possible prequantum (underlying) theories, but do not rule out the possibility that such theories might reconcile at least one understanding of locality and realism to quantum mechanical predictions. Violation might reflect, at least partly, failure to acknowledge the contextuality of quantum mechanics, or that data from different probability spaces have been inappropriately combined. Many claims that there are definite implications reflect one or more of (i) imprecise non-mathematical language, (ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment of measurement statistics and (iv) underlying philosophical assumptions.

arXiv:2106.14767Jun 28, 20213 citations

Is quantum mechanics nonlocal?

Jānis Ruža

A factual inconsistency of the nonlocality theory is demonstrated via a careful analysis of the conceptual and formal contents of Bell's theorem and the inequalities associated with it. The conceptual inconsistency of the theory follows from the consideration that it is, in principle, impossible to formulate quantum mechanics in terms of local hidden variables. The formal inconsistency of the nonlocality theory follows from the facts that: (i) nonlocality is not a physical property that can be represented by a function or an operator; (ii) it is impossible to derive Bell's inequality in a mathematically consistent way; and (iii) Bell's definition of locality is incorrect. Therefore, Bell's theorem cannot serve as the foundation for the introduction of the nonlocality notion in quantum mechanics.

Physica ScriptaNov 4, 20100 citations

Is a Deterministic and Local Interpretation of Quantum Mechanics Possible?… First Steps

Eduardo Nahmad-Achar, Natalia Sánchez-Kuntz

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].

Journal of Physics Conference SeriesApr 1, 20200 citations

Quantum Mechanics as a Classical Theory III: Epistemology

L. S. F. Olavo

The two previous papers developed quantum mechanical formalism from classical mechanics and two additional postulates. In the first paper it was also shown that the uncertainty relations possess no ontological validity and only reflect the formalism's limitations. In this paper, a Realist Interpretation of quantum mechanics based on these results is elaborated and compared to the Copenhagen Interpretation. We demonstrate that von Neumann's proof of the impossibility of a hidden variable theory is not correct, independently of Bell's argumentation. A local hidden variable theory is found for non-relativistic quantum mechanics, which is nothing else than newtonian mechanics itself. We prove that Bell's theorem does not imply in a non-locality of quantum mechanics, and also demonstrate that Bohm's theory cannot be considered a true hidden variable theory.

arXiv:quant-ph/9503022Mar 28, 19950 citations

Contrasting Implications of the Frequentist and Bayesian Interpretations of Probability when Applied to Quantum Mechanics Theory

James L. Beck

An examination is made of the differing implications from applying the two mainstream interpretations of probability, frequentist and Bayesian, to QM (quantum mechanics) theory for the Bohm-EPR experiment. The joint probability distribution for the possible spin outcomes for two particles with coupled spins is examined. Contrasting conclusions are made: (i) Under the frequentist interpretation, the QM spin distribution implies a widely-discussed non-locality because probabilistic conditioning on a spin measurement is viewed as corresponding to a causal influence. Under the Bayesian interpretation, this conditioning is viewed as providing information relevant to the spin probabilities and the argument for non-locality loses its force. (ii) The frequentist interpretation leads to the locality condition used by John Bell in 1964 to establish conditions for the existence of hidden variables behind the spin probability distribution but this condition is not consistent with the product (Bayes) rule of probability theory. Under the Bayesian interpretation, there is no motivation for this locality condition and a new stochastic hidden-variable model is given that reproduces the spin distribution. (iii) Bell's original 1964 inequality provides a necessary condition for the existence of a third-order joint probability distribution for three spin variables that is compatible through marginalization with the second-order joint distributions for the three possible spin pairs. Bell's inequality is logically equivalent to the 1969 CHSH inequality that involves expectations of four pairs of four spin variables; the CHSH inequality must be satisfied in order for a fourth-order joint probability distribution for the four spin variables to exist. When any of these inequalities are violated, a joint probability distribution for three spin outcomes fails to be valid because some probabilities are negative.

arXiv:1804.02106Apr 6, 20181 citation