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 quantities taken by probability must be non negative, and such a condition is represented by $|\cal{P(w)}|=\cal{P(w)}$ . We will also show that, when trying to define the values of the joint probabilities of $ (Z_1, Z_2, Z_3) $, through the values obtained from the $ (Z_j, Z_k) $ pairs, we find that these values are negative, so not Kolmogorov's axiom is respected: $\cal{P(w)}\geq0$ in cases where Bell's inequality is violated, and we also show that only such violation is possible if Wigner's inequality, in a certain arrangement, is violated, and that both violations are related to the violation of one of Kolmogorov's axioms. At the end of the paper, we suggest a new interpretation of the probabilities involved, in order to avoid the situation of negative probabilities and the violation of Bell's inequality and, consequently, Wigner's inequality.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 quantities taken by probability must be non negative, and such a condition is represented by $|\cal{P(w)}|=\cal{P(w)}$. We will also show that, when trying to define the values of the joint probabilities of $ (Z_1, Z_2, Z_3) $, through the values obtained from the $ (Z_j, Z_k) $ pairs, we find that these values are negative, so not Kolmogorov's axiom is respected: $\cal{P(w)}\geq0$ in cases where Bell's inequality is violated, and we also show that only such violation is possible if Wigner's inequality, in a certain arrangement, is violated, and that both violations are related to the violation of one of Kolmogorov's axioms. At the end of the paper, we suggest a new interpretation of the probabilities involved, in order to avoid the situation of negative probabilities and the violation of Bell's inequality and, consequently, Wigner's inequality.

arXiv:2006.08066Jun 15, 20200 citations

Bell's inequality in terms of probabilities

Thomas V Marcella

Bulletin of the American Physical SocietyMar 15, 20210 citations

NONADDITIVE 'PROBABILITIES' AND BELL'S INEQUALITY

M. I. Shirokov

Journal of Physics A Mathematical and TheoreticalJan 1, 19830 citations

Bell's Theorem and "Classical" Probability Theory

H. Razmi, Mohammad Golshani

Using CH model of Bell’s theorem and only by applying the conditional probability definition in ”classical ” probability theory,without imposing the locality condition,we are able to show that the stochastic realistic (CH) model cannot reproduce all of the predictions of quantum mechanics. PACS number: 03.65.Bz It is generally claimed that Bell inequalities are inconsistent with experimental data and with the predictions of quantum mechanics.A condition often used in the derivation of Bell inequalities is the so-called locality condition.The temptation is to attribute Bell inequalities violation to the violation of locality. In this paper we are goingUsing CH model of Bell’s theorem and only by applying the conditional probability definition in ”classical ” probability theory,without imposing the locality condition,we are able to show that the stochastic realistic (CH) model cannot reproduce all of the predictions of quantum mechanics. PACS number: 03.65.Bz It is generally claimed that Bell inequalities are inconsistent with experimental data and with the predictions of quantum mechanics.A condition often used in the derivation of Bell inequalities is the so-called locality condition.The temptation is to attribute Bell inequalities violation to the violation of locality. In this paper we are going

arXiv:quant-ph/9811072Nov 25, 19980 citations

Conditionals, Probability and Bell’s Theorem

Henry Krips

Springer eBooksJan 1, 19891 citation

Wigner's inequality for conditional probabilities and nonexistence of a realistic model for the two dimensional Hilbert space

Andrei Yu. Khrennikov

We perform the analysis of probabilistic assumptions of Bell's approach. We emphasize that J. Bell wrote about probability without to specify the concrete axiomatics of probability theory. The careful analysis demonstrated that (surprisingly) J. Bell did not apply the classical probability model (Kolmogorov) to describe ``classical physical framework.'' In fact, he created his own probabilistic model and compared it with the quantum one. The crucial point is that J. Bell did not pay attention to {\it conditional probabilities.} We show that conditional probability in his model cannot be defined by classical Bayes' formula. We also use the approach based on Bell-type inequalities in the conventional probabilistic approach, Kolmogorov model. We prove an analog of Wigner's inequality for conditional probabilities and by using this inequality show that predictions of the conventional and quantum probability models disagree already in the case of noncomposite systems (even in the two dimensional case).We perform the analysis of probabilistic assumptions of Bell's approach. We emphasize that J. Bell wrote about probability without to specify the concrete axiomatics of probability theory. The careful analysis demonstrated that (surprisingly) J. Bell did not apply the classical probability model (Kolmogorov) to describe ``classical physical framework.'' In fact, he created his own probabilistic model and compared it with the quantum one. The crucial point is that J. Bell did not pay attention to {\it conditional probabilities.} We show that conditional probability in his model cannot be defined by classical Bayes' formula. We also use the approach based on Bell-type inequalities in the conventional probabilistic approach, Kolmogorov model. We prove an analog of Wigner's inequality for conditional probabilities and by using this inequality show that predictions of the conventional and quantum probability models disagree already in the case of noncomposite systems (even in the two dimensional case).

arXiv:quant-ph/0308078Aug 14, 20033 citations

|\cal{P(w)}|=\cal{P(w)}

. We will also show that, when trying to define the values of the joint probabilities of $ (Z_1, Z_2, Z_3) $, through the values obtained from the $ (Z_j, Z_k) $ pairs, we find that these values are negative, so not Kolmogorov's axiom is respected:

\cal{P(w)}\geq0

in cases where Bell's inequality is violated, and we also show that only such violation is possible if Wigner's inequality, in a certain arrangement, is violated, and that both violations are related to the violation of one of Kolmogorov's axioms. At the end of the paper, we suggest a new interpretation of the probabilities involved, in order to avoid the situation of negative probabilities and the violation of Bell's inequality and, consequently, Wigner's inequality.