# Violation of the Bell's type inequalities as a local expression of incompatibility

## TL;DR

This paper argues that Bell's inequalities are essentially tests of local incompatibility of quantum observables, akin to interference experiments, rather than evidence of nonlocality, clarifying their foundational significance.

## Contribution

It reinterprets Bell's inequalities as tests of local incompatibility, challenging the common view of them as proof of quantum nonlocality.

## Key findings

- Bell's test is a local incompatibility test, similar to interference experiments.
- Bell's inequalities do not necessarily imply nonlocality, but test local observable incompatibility.
- Clarifies the foundational interpretation of Bell's inequalities in quantum mechanics.

## Abstract

By filtering out the philosophic component we can be said that the EPR-paper was directed against the straightforward interpretation of the Heisenberg's uncertainty principle or more generally the Bohr's complementarity principle. The latter expresses contextuality of quantum measurements: dependence of measurement's output on the complete experimental arrangement. However, Bell restructured the EPR-argument against complementarity to justify nonlocal theories with hidden variables of the Bohmian mechanics' type. Then this Bell's kind of nonlocality - {\it subquantum nonlocality} - was lifted to the level of quantum theory - up to the terminology {\it "quantum nonlocality"}. The aim of this short note is to explain that Bell's test is simply a special {\it test of local incompatibility of quantum observables}, similar to interference experiments, e.g., the two-slit experiment.