Assumption-Free Derivation of the Bell-Type Criteria of Contextuality/Nonlocality.

Ehtibar N Dzhafarov

doi:10.3390/e23111543

Abstract

Bell-type criteria of contextuality/nonlocality can be derived without any falsifiable assumptions, such as context-independent mapping (or local causality), free choice, or no-fine-tuning. This is achieved by deriving Bell-type criteria for inconsistently connected systems (i.e., those with disturbance/signaling), based on the generalized definition of contextuality in the contextuality-by-default approach, and then specializing these criteria to consistently connected systems.

Highlights

Another assumption is that experimenters choose what they measure independent of the background events determining measurement outcomes
There, we generalize the definition of contextuality/nonlocality to inconsistently connected systems, and show that the generalized Bell-type criteria in this generalized conceptual setting can be derived with no assumptions
We have seen that if one does not make any constraining assumptions about how a measurement outcome in a system depends on settings, local or remote, and if one adopts the contextuality-by-default approach (CbD) definition of generalizedcontextuality, the derivation of the traditional criteria ofcontextuality follows with no ontological assumptions, by specializing the definition in question to consistently connected systems

Summary

Introduction

There, we generalize the definition of contextuality/nonlocality to inconsistently connected systems (those with disturbance or signaling), and show that the generalized Bell-type criteria in this generalized conceptual setting can be derived with no assumptions. Instead they are derived from a classificatory definition of (non)contextuality based on the notion of the difference between random variables. The term is used to designate a special case of contextuality, for systems where contexts are formed by spacelike separated components.

Contextuality for Consistently Connected Systems

Contextuality in Inconsistently Connected Systems

Conclusions