Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

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.