Related papers: Wigner's inequality for conditional probabilities …
In this work, we show that Bell's inequality violation of arise from the fact that the condition imposed upon the development of inequality is not respected when it is applied in the idealized experiment. Such a condition is that the…
We show that by taking into account randomness of realization of experimental contexts it is possible to construct common Kolmogorov space for data collected for these contexts, although they can be incompatible. We call such a construction…
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…
We show that paradoxical consequences of violations of Bell's inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional description (due to Bell) is based on a…
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…
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 statistics behind Bell's inequality is demonstrated to allow a Kolmogorovian (i.e. classical) model of probabilities that recovers the quantum covariance.
We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…
We compare the classical Kolmogorov and quantum probability models. We show that the gap between these model is not so huge as it was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule,…
We revisit the Bell--CHSH scenario for two spin-\(\tfrac{1}{2}\) particles and isolate the precise algebraic origin of the Bell contradiction. On the quantum side, spin-\(\tfrac{1}{2}\) is described by a noncommutative spinor (Clifford)…
We derive a new class of time-dependent Bell inequalities in Wigner form under the assumption of locality in the framework of Kolmogorov's probability theory. We consider violation of the obtained inequalities for three cases: spin…
By formulating the axioms of quantum mechanics, von Neumann also laid the foundations of a "quantum probability theory". As such, it is regarded a generalization of the "classical probability theory" due to Kolmogorov. Outside of quantum…
It is not generally known, that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of plus and minus 1s that are writable on paper.This surprising fact is not…
We present a detailed analysis of the set theoretical proof of Wigner for Bell type inequalities with the following result. Wigner introduced a crucial assumption that is not related to Einstein's local realism, but instead, without…
The celebrating theorem of A. Fine implies that the CHSH inequality is violated if and only if the joint probability distribution for the quadruples of observables involved the EPR-Bohm-Bell experiment does not exist, i.e., it is impossible…
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…
We present a classical probability model appropriate to the description of quantum randomness. This tool, that we have called stochastic gauge system, constitutes a contextual scheme in which the Kolmogorov probability space depends upon…
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…
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…
Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the…