Related papers: George Boole and the Bell inequalities
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…
I review the relation of the Bell inequalities - characteristic of (classical) probabilities defined on Boolean logics - with noncontextual and local hidden variables theories of quantum mechanics and with quantum information.
Since John S. Bell demonstrated the interest of studying linear combinations of probabilities in relation with the EPR paradox in 1964, Bell inequalities have lead to numerous developments. Unfortunately, the description of Bell…
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
Many issues combine for consideration when speaking of Bell's Inequalities: nonlocality, realism, hidden variables, incompatible measures, wave function collapse, other. Each of these issues then may be viewed from several viewpoints:…
The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found ten years earlier by…
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…
The Bell inequality is derived under the assumption of three physical data sets, random or deterministic. The data sets represent a laboratory realization of the three probability based variables used by Bell. For physical data as can be…
A Bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers, measurement settings or measurement outcomes. In this article, such "liftings" of Bell inequalities are…
We provide an overview of the connections between Bell's inequalities and algebraic structure.
Bell's inequalities can be understood in three different ways depending on whether the numbers featuring in the inequalities are interpreted as classical probabilities, classical conditional probabilities, or quantum probabilities. In the…
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…
In 1862, George Boole derived an inequality for variables, now known as Boolean variables, that in his opinion represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the…
Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and…
Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results.…
We analyse the proof of Bell's inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatics, 1933. We found a (numerical) statistical correction…
Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier…
It is shown that Bell's counterfactuals admit joint quasiprobability distributions (i.e. joint distributions exist, but may not be non-negative). A necessary and sufficient condition for the existence among them of a true probability…
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use…