On the Physical Significance of the Locality Conditions in the Bell Arguments

Philippe H. Eberhard

Travis Norsen

A new formulation of the EPR argument is presented, one which uses John Bell’s mathematically precise local causality condition in place of the looser locality assumption which was used in the original EPR paper and on which Niels Bohr seems to have based his objection to the EPR argument. The new formulation of EPR helps clarify the relation between this argument and Bell’s Theorem. The relation between these two arguments — in particular, the role of EPR as part one of Bell’s two‐part argument for nonlocality — is also discussed in detail.

Abner Shimony

The study of hidden-variable interpretations of quantum mechanics was transformed by two papers of Bell. In his 1966 paper in Reviews of Modern Physics [1] he analysed the argument of von Neumann [2] and the more powerful arguments of Jauch and Piron [3] and of Gleason [4], all leading to similar conclusions about the nonassignability of simultaneous values to all the observables of a nontrivial quantum system; and he showed that these arguments do not exclude what may be called “contextualistic” hidden-variable theories, in which the value of an observable O is allowed to depend not only upon the hidden state λ, but also upon the set C of compatible observables measured along with O . In Bell's 1964 paper in Physics [5] (written later than the other, in spite of the earlier publication date) he gave a new kind of argument against a hidden-variable interpretation of quantum mechanics, by showing that no hidden-variables theory which satisfies a certain condition of locality can agree with all the statistical predictions of quantum mechanics. The main purpose of this lecture is to discuss an experiment, designed by Clauser, Horne, Holt and myself [6], which is based on Bell's proof of the incompatibility of quantum mechanics and local hidden-variable theories. Before doing this, however, I wish to make several comments.

Aleksandr V. Belinskii

Tomasz Placek

The objective of the paper is to present a comprehensive picture of Bell-type theorems, by giving both the theorems and the proofs of them.Special care is given to specifying the assumptions of the arguments and their physical or metaphysical significance. Taking the EPR argument as a point of departure, the paper discusses four probabilitic Bell-type theorems,which are then followed by two versions on non-probailitic (GHZ) arguments.The final section provides the reader with a classification of the assumptions, which specifies which assumption is used in which proof.

Peter J. Lewis