The spinorial ball: a macroscopic object of spin-1/2

Abstract

Historically, the observation of half-spin particles was one of the most surprising features of quantum mechanics. They are often described as "objects that do not come back to their initial state after one turn but do after two turns". There are macroscopic implementations using constraints such as clamping a belt or ribbon that purport to show similar behavior (the "Dirac belt trick"). However, a demonstration of an unconstrained macroscopic object with half-spin behavior remains elusive. In this article, we propose to fill this gap and introduce the spinorial ball. It consists of a translucent plastic ball with internal LED illumination that behaves as a freely movable macroscopic half-spin object. It provides a new tool to introduce and visualize half-integer spins as well as the covering group homomorphism from SU(2) to SO(3), and offers in particular a clear visualization of the different homotopy classes of SO(3). We discuss its development and function, and how one can mimic quantum measurement and wave function collapse using this the spinorial ball. The entire system is open source hardware, with build details, models, 3d printing files, etc., provided under an open source license.