Electron spin correlations: a geometric representation

TL;DR

This paper provides a geometric and probabilistic analysis of electron spin correlations, clarifying concepts like contextuality and measurement dependence, and deriving quantum formulas for spin correlations with potential physical interpretations.

Contribution

It introduces a geometric representation of electron spin correlations based on probability distributions, offering a clearer probabilistic understanding and physical insight into electron spin behavior.

Findings

Derived quantum formulas for spin correlations using geometric probability models

Clarified the concepts of contextuality and measurement dependence in electron spins

Suggested a possible physical interpretation of electron spin based on the geometric approach

Abstract

An analysis is made within the quantum formalism of the probabilistic features of the electron spin correlation, with the purpose of clarifying the concepts of contextuality and measurement dependence. The quantum formulas for the spin correlation are then derived on the basis of a probability distribution function and its associated geometric representation, both for a pair of projections of a single-particle spin and for the bipartite system in singlet spin state. This endows the spin correlation with a clear probabilistic meaning and leaves the door open for a possible physical image of the electron spin, as discussed at the end of the paper.