Uploads from Dr. Jorge S. Diaz

Currently Playing: Symmetry in physics and Noether’s theorem

Buy me a coffee and support the channel: https://ko-fi.com/jkzero In this video, I present an overview of symmetries in physics, passive vs. active transformations, and how to derive Noether's theorem from the Euler-Lagrange equations. Different examples are presented in detail to show how the invariance under specific symmetries can be used to construct conserved quantities. [Related videos] ∘ Lagrangian Mechanics: when theoretical physics got real https://youtu.be/QbnkIdw0HJQ [References] ∘ C. Huygens, "A summary account of the laws of motion," Philos. Trans. R. Soc. 4, 925 (1669) ∘ G. E. Smith, "The vis viva dispute: A controversy at the dawn of dynamics," Physics Today Oct. (2006) https://physicstoday.aip.org/features/the-vis-viva-dispute-a-controversy-at-the-dawn-of-dynamics ∘ E. Noether, "Invariante Variationsprobleme," Nachr. v. d. Ges. d. Wiss. zu Göttingen, 235 (1918) [Credits] Sunflower by M. Mingle, public domain Newton's cradle by Thirdman, free use via Pexels https://www.pexels.com/video/circular-magnets-bumping-each-other-8011404/ Emmy Noether, public domain Faucault's pendulum by M. Espejo, free use via Pexels https://www.pexels.com/video/a-pendulum-display-on-public-swinging-during-daytime-6117694/ Curling stones by SHVETS production, free use via Pexels https://www.pexels.com/video/curling-stones-sliding-on-ice-rink-7560795/ LHC collision by CERN in "CERN: 50 years of Science" https://www.youtube.com/watch?v=SARgkwczvAE Cassini spacecraft by NASA in JPL and the Space Age: Triumph at Saturn https://www.youtube.com/watch?v=SY-hQJ5pMd4 Galileo Galilei's "Dialogo" by Nightryder84 under CC BY-SA 3.0 Portrait of René Descartes by Frans Hals, public domain Christiaan Huygens, the astronomer, public domain Rolling sphered fruits by M. Leonova, free use via Pexels https://www.pexels.com/video/rolling-sphered-fruits-7593078/ Philosophiae Naturalis Principia Mathematica by P. Hermans under CC BY-SA 3.0 Lagrange's Analytical Mechanics, public domain Albert Einstein, public domain Einstein's Zurich Notebook, public domain David Hilbert, public domain Felix Klein, public domain Paul Albert Gordan, public domain Clebsch-Gordan coefficients by Particle Data Group https://pdg.lbl.gov/2002/clebrpp.pdf Emmy Noether's paper via European Digital Mathematics Library Snowflake by J. Lass under CC BY 4.0 Camera in a stabilizer by A. Preciado, free use via Pexels https://www.pexels.com/video/a-video-camera-in-a-stabilizer-8081338/ Woman taking photos by A. Sandrini, free use via Pexels https://www.pexels.com/video/woman-taking-photos-in-the-desert-3010810/ Kittens learn Newton's cradle by Funny Cats and Nice Fish under CC BY 3.0 https://www.youtube.com/watch?v=4eHEEtAtFDU CC BY 3.0 https://creativecommons.org/licenses/by/3.0/ CC BY-SA 3.0: https://creativecommons.org/licenses/by-sa/3.0/deed.en CC BY 4.0: https://creativecommons.org/licenses/by/4.0/deed.en