Geometric model for the electron spin correlation

TL;DR

This paper develops a geometric local model for electron spin correlations that reproduces quantum predictions, providing a concrete probabilistic interpretation consistent with locality and measurement settings.

Contribution

It introduces a geometric model based on a generic probability distribution that reproduces quantum spin correlations without nonlocality.

Findings

The model reproduces the quantum spin correlation formula.

Partitioning based on measurement settings prevents transfer of spin projections.

The approach offers a local realistic interpretation of quantum spin correlations.

Abstract

The quantum formula for the spin correlation of the bipartite singlet spin state, $C_{Q}(\boldsymbol{a},\boldsymbol{b})$, is derived on the basis of a probability distribution $\rho(\phi)$ that is generic, i. e., independent of $(\boldsymbol{a},\boldsymbol{b})$. In line with a previous result obtained within the framework of the quantum formalism, the probability space is partitioned according to the sign of the product $A=\alpha\beta$ of the individual spin projections $\alpha$ and $\beta$ onto $\boldsymbol{a}$ and $\boldsymbol{b}$. A specific partitioning and a corresponding set of realizations {$ \phi$} are associated with every measurement setting $(\boldsymbol{a},\boldsymbol{b})$; this precludes the transfer of $\alpha$ or $\beta$ from $C_{Q}(\boldsymbol{a},\boldsymbol{b})$ to $C_{Q}(\boldsymbol{a},\boldsymbol{b'})$, for $\boldsymbol{b'}\neq\boldsymbol{b}.$ A geometric model that reproduces the spin correlation serves to validate our approach, giving a concrete meaning to the quantum result in terms of a (local random variable) probability distribution.