Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

TL;DR

This paper presents a local hidden variable model using geometric algebra that reproduces the quantum prediction for the singlet state's spin correlations, supported by computational simulation.

Contribution

It introduces a novel local realistic model employing geometric algebra to replicate quantum singlet correlations, challenging traditional nonlocal interpretations.

Findings

Successfully reproduces quantum singlet correlations with local functions

Uses geometric algebra for a novel derivation approach

Validated results through computational simulation in Mathematica

Abstract

We deduce the quantum mechanical prediction of $-{\bf a}\cdot{\bf b}$ for the singlet spin state employing local measurement functions following Bell's approach. This result represents the quantum mechanical expectation value for the joint measurement of spin projections in the singlet state. And is equal to the negative cosine of the angle between vectors {\bf a} and {\bf b}. Our derivation is corroborated through a computational simulation conducted in the Mathematica programming environment using geometric algebra.