Bell's paradoxes without the introduction of hidden variables

A. Gamba

Florentín Smarandache, Victor Christianto

Aleksandr V. Belinskii

A hidden-variable theory is the traditional, but not unique, basis for constructing various types of Bell's theorem. The starting point may also be a recognition of the existence of a positive-definite probability distribution function. This assumption alone is used to formulate and prove Bell's paradoxes of different types. A specific example is used to show that a formal quantum calculation can sometimes give negative values of the joint probabilities that are used in the proof. An attempt is made to identify the physical meaning of this result and an algorithm for determination of negative joint probabilities of this type is proposed.

Philippe H. Eberhard

Mary Bell, Kurt Gottfried, Martinus J. G. Veltman

This book is the most complete collection of John S Bell's research papers, review articles and lecture notes on the foundations of quantum mechanics. Some of this material has hitherto been difficult to access. The book also appears in a paperback edition, aimed at students and young researchers. This volume will be very useful to researchers in the foundations and applications of quantum mechanics. Contents: (1) On the Problem of Hidden Variables in Quantum Mechanics; (2) On the Einstein-Podolsky-Rosen Paradox; (3) The Moral Aspect of Quantum Mechanics; (4) Introduction to the Hidden-Variabl

Jaykov Foukzon, Менькова Елена Романовна, Alexander A Potapov

Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.