Dirac's belt trick, Topology, and Spin ½ particles

ANSWERS TO FREQUENTLY ASKED QUESTIONS: https://scholar.harvard.edu/files/noahmiller/files/dirac_belt_trick_faq.pdf This is my submission to 3Blue1Brown's "Summer of Math Exposition 1" #SoME1. In this video, I explain what Dirac's famous belt trick has to do with the topology of rotating spin 1/2 particles, such as electrons. I created the 3D animations using Three.js/CCapture.js, and the math animations with Manim Community v0.8.0. 00:00 Introduction 4:14 The space of rotations 9:40 Paths through the space of rotations 18:48 Group theory & the fundamental group 31:30 Quantum spin and SU(2) 39:31 SU(2) as the double cover of SO(3) 48:26 Bringing it all together 52:22 Tying up loose ends Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u Largo From Concerto No 5 Exzel Music Publishing (freemusicpublicdomain.com) Licensed under Creative Commons: By Attribution 3.0 http://creativecommons.org/licenses/by/3.0/