A note on Penrose's Spin-Geometry Theorem and the geometry of `empirical quantum angles'

TL;DR

This paper provides a straightforward proof of Penrose's Spin Geometry Theorem within quantum mechanics and explores the structure of a model for the space of quantum directions based on $SU(2)$-invariant observables.

Contribution

It offers a direct proof of Penrose's Spin Geometry Theorem and models the quantum directions space using elementary $SU(2)$-invariant observables.

Findings

A simple proof of the Spin Geometry Theorem is presented.

A model of the space of quantum directions is sketched.

The structure of quantum directions is linked to $SU(2)$-invariant observables.

Abstract

In the traditional formalism of quantum mechanics, a simple direct proof of (a version of) the Spin Geometry Theorem of Penrose is given; and the structure of a model of the `space of the quantum directions', defined in terms of elementary $SU(2)$-invariant observables of the quantum mechanical systems, is sketched.