American Journal of Modern Physics

Assumptions of Metric Variable-Type in Bell’s Theorem

Fosco Ruzzene

Published Jan 1, 2013• 1 citation

Abstract

An analysis of both the original and the CHSH Bell inequalities is presented. Two additional mathematical assumptions are identified in the theorem. These are: all variables in the inequalities have a field algebraic structure, and all variables have measurability as a mathematical property. This means the variables are of metric-type, mathematically indistinguishable from those of classical theories. The consequences of attributing the violation of Bell’s theorem to these assumptions are examined.

DOI: 10.11648/j.ajmp.20130206.22

Related papers

The Bell Inequalities: Identifying What Is Testable and What Is Not

Louis Sica

The Bell theorem and inequality were derived as consequences of seemingly reasonable physical and statistical hypotheses. Bell’s assumptions were used to deduce cross-correlations of three spin measurements on two entangled particles neglecting non-commutation. The assumed correlation functions, later confirmed for certain quantum measurements, violate the Bell inequality. The present paper reviews a more general derivation of the Bell inequality showing that it is identically satisfied by finite data sets whether deterministic or random, after assuming merely that they exist. It is thereafter concerned with the consequences of this result for interpretations of the inequality that result in its violation. A primary finding is that correlation functions have differing forms due to quantum commutation, non-commutation, and conditions of measurement, and result in satisfaction of the Bell inequality used consistently with its derivation. A stochastic process having the same correlation function for all variable pairs is shown to be inconsistent with experimentally reported data. The logic of the three and four variable inequalities is shown to be similar. Finally the inequalities in probabilities are shown to follow from those in correlations with quantum mechanical results satisfying either when properly implemented.

arXiv:1903.02116Journal of Modern PhysicsJan 1, 20209 citations

Hidden assumptions in the derivation of the theorem of Bell

K. Hess, Hans A. De Raedt, Kristel F. L. Michielsen

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.

Jan 1, 201217 citations

Hidden assumptions in the derivation of the theorem of Bell

Karl Hess, Hans A. De Raedt, Kristel Michielsen

arXiv:1108.3583Physica ScriptaNov 1, 201222 citations

A Bell Theorem with no locality assumption

Charles P. Tresser

We prove here a version of Bell Theorem that does not assume locality. As a consequence classical realism, and not locality, is the common source of the violation by nature of all Bell Inequalities.

arXiv:quant-ph/0608008Aug 1, 20060 citations

Assumptions underlying Bell s inequalities

Angel G Valdenebro

There are several versions of Bell's inequalities (BI), proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and loosely use formulations of others. The issue, to judge from recent publications, continues to cause misunderstandings. We present a very simple but general proof of BI, identifying explicitly the complete set of assumptions required.

arXiv:quant-ph/0208161European Journal of PhysicsSep 1, 200222 citations

Review of Nelson's analysis of Bell's theorem

B. Schulz

This article contains a review of Nelson's analysis of Bell's theorem. It shows that Bell's inequalities can be violated with a theory of local random variables if one accepts that the outcomes of these variables are not predetermined prior to measurement. The article describes the relation between Bell's theorem and the Strong Free Will theorem of Conway and Kochen. Then, the original articles of Bell are analyzed in detail. Following an article of Faris, it is explained that Bell's work on the hidden variable question in fact describes two separate theorems. Bell's first theorem says that there can be no model for the singlet state where an outcome does not depend locally on the settings of the detector where the outcome was measured. Bell's second theorem shows that Bell's inequalities can be violated by a theory that is either not deterministic, or violates causality in the sense of relativity or the free will assumption of the experimenters. It is shown in detail where Bell implicitly makes the various locality assumptions that Nelson has shown to be necessary for deriving Bell's inequality. The article closes by relating the various assumptions needed to derive Bell's theorem with the reality criterion of EPR

arXiv:1302.4180Feb 18, 20130 citations