Bell's theorem without the hypothesis of locality

Willy De Baere, A. Mann, M. Revzen

Aleksandr V. Belinskii

One of the Bell's assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., of 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 local realism. In this paper, Bell's inequality is derived in its traditional form, without resorting to the hypothesis of locality, the only assumption being that the probability distributions are nonnegative. These probability distributions are calculated, for a specific optical experiment, in the framework of quantum theory and it is shown that they can take on negative values. This can therefore be regarded as a rigorous proof that the hypothesis of locality is not relevant to violations of Bell's inequalities. The physical meaning of the obtained results is examined.

Geoffrey Paul Hellman

As was remarked two years ago at a symposium of the PSA on locality and hidden variables (Shimony 1981), the Bell theorems together with experiments supporting the quantum correlations (violating the inequalities of the theorems) provide a rather remarkable opportunity for philosophy. Shimony summed this up in the nice phrase, “experimental metaphysics”. For, as he pointed out, arguments based on Bell-type theorems, concluding that certain experiments should exhibit correlations obeying a certain inequality, generally employ premises of a metaphysical character, e.g., that the systems in question are deterministic (in the experimental observables). If, in fact, the experimental predictions are violated, and if one has reason to believe any other premises involved, then one must give up the metaphysical hypothesis.

Charles P. Tresser

Karl Raimund Popper

Abner Shimony

‘Bell's Theorem’ is the collective name for a family of arguments, which more accurately should be referred to as ‘Theorems of Bell's Type’, all being variants of the remarkable argument given by J. S. Bell (1964). All of these arguments have the format E & H → I, where E is a description of a type of experimental setup involving pairs of particles emitted from a common source, H is a physical hypothesis which typically expresses some version of “realism” and some version of “locality”, and I is an inequality concerning correlations between particles of a pair. There are differences among theorems of Bell's type regarding the details of the inequality I , which are important in actually carrying out experimental tests. There are differences regarding the arrow—i.e., the procedure whereby I is inferred from E & H.