Related papers: Non-Kolmogorov probability models and modified Bel…
The statistics behind Bell's inequality is demonstrated to allow a Kolmogorovian (i.e. classical) model of probabilities that recovers the quantum covariance.
We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation…
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This…
On one side, so far a great part of the evidence accepted as proof of the alleged quantum non-locality relied on inhomogeneous Bell inequalities involving an additional assumption (no-enhancement) whose role had not been sufficiently…
Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing…
One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim…
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 inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these…
We discuss coupling of violation of Bell's inequality and non-Kolmogorovness of statistical data in the EPR-Bohm experiment. We emphasize that nonlocalty and "death of realism" are only sufficient, but not necessary conditions of…
Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…
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…
We derive a Bell-like inequality involving all correlations in local observables with uncertainty free states and show that the inequality is violated in quantum mechanics for EPR and GHZ states. If the uncertainties are allowed in local…
Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to…
Within the Dempster-Schafer theory of evidence a non-Kolmogorovian kind of epistemic uncertainty arises, which is encoded using multi-valued maps. We analyse the possible implications such non-Kolmogorovian epistemic uncertainty may have…
We present an alternative approach to modeling Einstein-Podolsky-Rosen-Bohm (EPRB)-type experiments. The basis for our approach will be to replace the conventional Kolmogorov theory of probability, with the more general Dempster-Schafer…
The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell's arguments one can not distinguish two hypotheses: a) quantum mechanics is {\it nonlocal}, b) quantum mechanics is {\it…
Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate…
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…
We establish connections between the requirement of measurability of a probability space and the principle of complimentarity in quantum mechanics. It is shown that measurability of a probability space implies the dependence of results of…
Bell's theorem proves the incompatibility between quantum mechanics and local realistic hidden-variable theories. In this paper we show that, contrary to a common belief, the theoretical proof of Bell's theorem is not affected by…