On the Significance of the Bell Inequalities for the Locality Problem in Different Realistic Interpretations of Quantum Mechanics

Abstract

AbstractThe relation between the Bell inequalities, locality and the existence of joint probability distributions is discussed in different realist interpretations of quantum mechanics. We distinguish four realist interpretations, viz., the objectivistic one, the contextualistic one, the strictly nonobjectivistic and the quasi‐objectivistic interpretation. Conclusions are differing largely in different interpretations. We also distinguish between two kinds of locality, viz, macrolocality and Einstein/Bell locality. From a classical model of stochastic measuring processes a definition of Einstein/Bell locality is derived that differs from the Bell/Clauser/Horne/Shimony factorizability condition. It is demonstrated that only in the quasi‐objectivistic interpretation the Einstein/Bell locality condition plays a role in the derivation of a Bell inequality for quantities that are experimentally relevant. It is argued that even in this interpretation it is not possible to arrive at the conclusions that the Bell inequalities stem from the locality condition because of the tacit assumption of an additional property, namely the existence of probability distributions conditionalized on the dispersionfree states of the hidden variables. Consideration of a phase space representation of the Schrödinger equation demonstrates that this latter assumption is at odds with the statistics of quantum systems.