A simple proof of Bell's inequality

TL;DR

This paper presents an extremely simple and visual proof of Bell's inequality, making the fundamental concept more accessible and transparent for educational and conceptual purposes.

Contribution

It provides a straightforward, single-figure proof of Bell's inequality, enhancing understanding and teaching of quantum mechanics foundations.

Findings

The proof is extremely simple and visual.

It clarifies the assumptions behind Bell's inequality.

It facilitates teaching and understanding of quantum nonlocality.

Abstract

Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an extremely simple proof of Bell's inequality: a single figure suffices. This simplicity may be useful in the unending debate of what exactly the Bell inequality means, since the hypothesis at the basis of the proof become extremely transparent. It is also a useful didactic tool, as the Bell inequality can be explained in a single intuitive lecture.