Locality and Bell's Theorem

Karl Raimund Popper

Jiří Souček

The standard Bell’s theorem states that quantum mechanics (QM) cannot be locally realistic. Here we prove the strong Bell’s theorem which states that QM cannot be realistic. In the proof we use the Mermin’s form of the Bell’s theorem. Our result solves the old dilemma: non-locality or non-realism. Then we discuss the consequences of the strong Bell’s theorem, e.g. that no Bell non-locality of QM exists and that quantum theory is local and non-realistic.

B. Schulz

This article contains a review of Nelson's analysis of Bell's theorem. It shows that Bell's inequalities can be violated with a theory of local random variables if one accepts that the outcomes of these variables are not predetermined prior to measurement. The article describes the relation between Bell's theorem and the Strong Free Will theorem of Conway and Kochen. Then, the original articles of Bell are analyzed in detail. Following an article of Faris, it is explained that Bell's work on the hidden variable question in fact describes two separate theorems. Bell's first theorem says that there can be no model for the singlet state where an outcome does not depend locally on the settings of the detector where the outcome was measured. Bell's second theorem shows that Bell's inequalities can be violated by a theory that is either not deterministic, or violates causality in the sense of relativity or the free will assumption of the experimenters. It is shown in detail where Bell implicitly makes the various locality assumptions that Nelson has shown to be necessary for deriving Bell's inequality. The article closes by relating the various assumptions needed to derive Bell's theorem with the reality criterion of EPR

Aleksandr V. Belinskii

Charles P. Tresser

We prove here a version of Bell Theorem that does not assume locality. As a consequence classical realism, and not locality, is the common source of the violation by nature of all Bell Inequalities.

Charles P. Tresser