Bell’s theorem depends crucially on counterfactual reasoning, and is mistakenly interpreted as ruling out a local explanation for the correlations which can be observed between the results of measurements performed on spatially-separated quantum systems. But in fact the Everett interpretation of quantum mechanics, in the Heisenberg picture, provides an alternative local explanation for such cor...

Bell’s theorem states that quantum correlation function of two spins can not be represented as an expectation value of two classical random variables. Spin is described in Bell’s model by a single scalar random variable. We discuss another classical model of spin in which spin is described by a triple of classical random variables. It is shown that in this model the quantum correlation function...

Two examples are given that substantially simplify the no-hidden-variables theorem of Kochen and Specker, greatly reducing the number of observables considered and requiring no intricate geometric argument. While one of the examples also obeys a more powerful version of Bell's theorem, the other does not. The examples provide a new perspective on both of these fundamental theorems and on the re...

The famous Doignon-Bell-Scarf theorem is a Helly-type result about the existence of integer solutions to systems of linear inequalities. The purpose of this paper is to present the following quantitative generalization: Given an integer k, we prove that there exists a constant c(n, k), depending only on the dimension n and k, such that if a bounded polyhedron {x ∈ Rn : Ax ≤ b} contains exactly ...

A proof of Bell's theorem without inequalities is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem using an entangled state of 2n qubits (with n odd) shared between two distant observers. In two recent papers[1,2], Cabello gave a proof of Bell's theorem without inequalities by usi...

A proof of Bell's theorem without inequalities is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem using an entangled state of 2n qubits (with n odd) shared between two distant observers. In two recent papers[1,2], Cabello gave a proof of Bell's theorem without inequalities by usi...

A proof of Bell's theorem without inequalities is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem using an entangled state of 2n qubits (with n odd) shared between two distant observers. In two recent papers[1,2], Cabello gave a proof of Bell's theorem without inequalities by usi...

In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion form...

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 Bass and stated in full generality by Vorob’ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequal...