When a math trick turns out to be real

What this strange quantum effect reveals about potentials. Sponsored by Planet Wild. Want to restore the planet’s ecosystems and see your impact in monthly videos? The first 150 people to join Planet Wild will get the first month for free at: https://planetwild.com/r/veritasium/join If you want to get to know them better first, check out their project stopping plastic waste before it reaches the ocean: https://planetwild.com/r/veritasium/m34 If you’re looking for a molecular modelling kit, try Snatoms, a kit I invented where the atoms snap together magnetically - https://ve42.co/SnatomsV Sign up for the Veritasium newsletter for weekly science updates - https://ve42.co/Newsletter ▀▀▀ Chapters: 0:00 The 3 Body Problem 4:16 Potential Energies 7:09 What is the curl in mathematics? 11:59 Bohm and Oppenheimer 14:36 Potentials in the Schrödinger Equation 18:40 The Aharonov-Bohm Effect 22:59 The Physics Community Responds 25:29 The Donut Experiment 27:49 But What Does it Mean? 33:51 The Gravitational Aharonov-Bohm Effect ▀▀▀ A special thank you to Prof. Yakir Aharonov for discussing your own original research with us. And a huge thank you to Prof. David Kaiser, Prof. Steven Strogatz, Dr Peter Asenbaum, Prof. Olival Freire Jr., and Prof. Yuval Gefen for your invaluable expertise and contributions to this video. ▀▀▀ References - https://ve42.co/ABRefs Image refs - https://ve42.co/Ty ▀▀▀ Special thanks to our Patreon supporters: Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Armedtoe, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Data Don, Dave Kircher, David Johnston, David Tseng, EJ Alexandra, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Hayden Christensen, Ibby Hadeed, Jeromy Johnson, Jesse Brandsoy, Jon Jamison, Juan Benet, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Mark Heising, Martin Paull, Meekay, meg noah, Michael Bush, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Robson, Sam Lutfi, Shalva Bukia, Sinan Taifour, Tj Steyn, Ubiquity Ventures, Vahe Andonians, wolfee ▀▀▀ Writers: Daniel Leonard, Casper Mebius & Derek Muller Producer and Director: Daniel Leonard Presenters: Derek Muller, Casper Mebius & Gregor Čavlović Editor: Jack Saxon Additional Editor: James Stuart Animators: Emma Wright, Fabio Abertelli, Andrew Neet & Ivy Trello Illustrators: Jakub Misiek, Grace Nemanic & Isaac McRee Researchers: Gabe Strong & Callum Cuttle Thumbnail designers: Abdallah Rabah, Ren Hurley & Ben Powell Production Team: Josh Pitt, Matthew Cavanagh, Anna Milkovic, Katy Southwood & Jess Bishop-Laggett Executive Producers: Derek Muller, Casper Mebius & Gregor Čavlović Additional video/photos supplied by Getty Images and Pond5 Music from Epidemic Sound