Inequality-free proof of Bell's theorem

TL;DR

This paper presents an inequality-free proof of Bell's theorem, directly comparing quantum and local realistic correlations, confirming their incompatibility without relying on inequalities.

Contribution

It introduces a novel proof method using Fourier series to demonstrate Bell's theorem without inequalities, enhancing conceptual clarity.

Findings

Confirms local realism is incompatible with quantum mechanics

Provides a new inequality-free proof technique

Strengthens the foundational understanding of quantum nonlocality

Abstract

Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. Most proofs of Bell's theorem, are based on inequalities. In this paper we present an alternative proof which does not involve inequalities, but only a direct comparison between correlation functions calculated using quantum mechanics on the one hand, and those calculated according to local realistic hidden-variable theories on the other. Our proof is based on a physically motivated use of Fourier series for periodic functions, and confirms that local realistic hidden-variable theories are incompatible with quantum mechanics.