Bell’s Inequalities Experiments

Andrei Yu. Khrennikov

We analyze 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 from 1933. We found a (numerical) statistical correction to Bell’s inequality. Such an additional term εφ on the right-hand side of Bell’s inequality can be considered as a probability invariant of a quantum state φ. This is a measure of nonreproducibility of hidden variables in different runs of experiments. Experiments to verify Bell’s inequality can be considered as just experiments to estimate the constant εφ. It seems that Bell’s inequality could not be used as a crucial reason to deny local realism. We consider deterministic as well as stochastic hidden variables models.

Alain Aspect, Philippe Grangier

Robert R. Tucci

This paper presents a new, computer-implementable algorithm for determining Bell inequalities. The algorithm is very general: one can use it to derive the Bell inequalities for any of the experiments that are usually considered for this purpose, such as the Bohm-Bell experiment, the Clauser-Horne experiment, or the experiments with spin 1, 3/2, 2 and 5/2 particles proposed by Mermin, Schwarz and Garg. As an example, this paper applies the algorithm to the Clauser-Horne experiment. The algorithm, which is based on simple notions from n-dimensional Euclidean geometry, gives a simple geometrical interpretation to the Bell inequalities. The algorithm allows one to demonstrate that a set of Bell inequalities is complete. The algorithm uses special hidden variables that were first used by Wigner and Belinfante. This paper also shows how to use finite group theory to express a set of Bell inequalities in a form that makes its invariance under relabellings explicit.

Alain Aspect

Alain Aspect

Eugene Scarzafava

Abstract Claims that entanglement, or non-local interaction ("spooky action-at-a-distance), has been experimentally proven are false. The claims are based entirely on the fact that the results of experiments performed to test that issue (EPR-Bohm experiments) violate various theoretical inequalities (Bell Inequalities).The various Bell Inequalities used to interpret the results of EPR-Bohm experiments are shown to be inappropriate for such experiments. The inequalities do not correctly provide for the correlation between the particles in each pair, which is the essence of such experiments; and therefore the inequalities are irrelevant. Claims that the results of such experiments, because they violate the inequalities, require the conclusion that the measurement of one particle in an "entangled" pair can instantly affect the state of its partner, even at great distances, are untrue and need to be modified.