Geometric model for the electron spin correlation

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 $ρ(ϕ)$ 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 $A=αβ$ of the individual spin projections $α$ and $β$ onto $\boldsymbol{a}$ and $\boldsymbol{b}$. A specific partitioning and a corresponding set of realizations {$ϕ$} are associated with every measurement setting $(\boldsymbol{a},\boldsymbol{b})$; this precludes the transfer of $α$ or $β$ 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.

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