General covariance

General Invariance

The core tenet of general relativity is that the laws of gravity can be applied identically from all perspectives. In other words, general covariance means that we can freely change coordinate systems regardless of our position in the universe. (

Stress–energy–momentum pseudotensor)

General covariance and

Conservation of Energy cannot coexist completely. However, energy conservation holds locally. This is because general covariance states that the laws of physics should remain invariant regardless of changes in the coordinate system.

아인슈타인도 몰랐던 상대성이론의 구멍 (양자역학 영상을 보셨다면 이것도 보셔야 합니다!)

에너지 보존 법칙은 틀린 걸까요? 레전드, 그리고 또 레전드 영상. 세상을 바라보는 눈이 달라질 겁니다. (고립계에선 항상 유효합니다) 처로님 멤버십 가입 감사합니다. ▀▀▀ A huge thank you to Prof. Geraint Lewis, Prof. Melissa Franklin, Prof. David Kaiser, Elba Alonso-Monsalve, Richard Behiel, Prof. Leo Stein and Jakob Schwintenberg for their invaluable expertise and contributions to this video. Special thanks to Alessandro from ScienceClic for his help on animations and input on the script. Check out his excellent video on Noether’s theorem here: • The Symmetries of the universe ▀▀▀ 0:00 대칭성이란 무엇인가? 4:25 에미 뇌터와 아인슈타인 7:33 일반 공변성 11:59 최소 작용의 원리 15:29 뇌터의 제1정리 18:24 연속 방정식 23:20 뇌터의 뒷이야기 24:49 표준 모형 - 힉스, 쿼크 등등 ▀▀▀ References: MathHistory Biography - Emmy Amalie Noether via mathshistory.st-andrews.ac.uk - https://ve42.co/BioNoether Bartlett, J. G. (2021). The Standard Cosmological Model and CMB Anisotropies. New Astron.Rev. 43 (1999) 83-109 - https://ve42.co/CosmoCMB Kimberling, C. (1982). Emmy Noether, Greatest Woman Mathematician. Mathematics Teacher, March 1982, Volume 84, Number 3, pp. 246–249. - https://ve42.co/NoetherGreat Blunck, A., et al. (2016). Mathematik und Gender. Verlag Franzbecker - https://ve42.co/MathGender Evans, R. J. (1976). The Feminist movement in Germany, 1894-1933. Sage Publications - https://ve42.co/FeministGer Without Emmy Noether, there would be a huge gap in mathematics and its understanding via www.mpg.de - https://ve42.co/NoetherGap Dihedral group of order 6 via Wikipedia - https://ve42.co/Dihedral6 Emmy Noether University of Erlangen via Wikipedia - https://ve42.co/Erlangen Timeline of women in mathematics via Wikipedia - https://ve42.co/WomenMath Elizaveta Litvinova via Wikipedia - https://ve42.co/LitvinovaE Sofya Kovalevskaya via Wikipedia - https://ve42.co/KovalevskayaS Charlotte Scott via Wikipedia - https://ve42.co/ScottC Cornelia Fabri via Wikipedia - https://ve42.co/FabriC Emmy Noether, the renowned mathematician who taught 20 years of unpaid classes just because she was a woman via english.elpais.com - https://ve42.co/NoetherPay Noether, E. (1908). Über die Bildung des Formensystems der ternären biquadratischen Form. Reimer - https://ve42.co/NDissert Noether, E. (1983). Invariante Variationsprobleme. Gott.Nachr.1918:235-257,1918; Transp.Theory Statist.Phys.1:186-207,1971 - https://ve42.co/InvarProb Noether, E. (2018). M. A. Tavel’s English translation of “Invariante Variationsprobleme”. arXiv - https://ve42.co/InvarProbEn Byers, N. (1998). E. Noether’s Discovery of the Deep Connection Between Symmetries and Conservation Laws*. Mod.Phys.Lett. A14 (1999) 99-104 - https://ve42.co/SymCon De Haro, S. (2021). Noether’s Theorems and Energy in General Relativity. Cambridge University Press, 2021 - https://ve42.co/EnergyGR Rowe, D. E. (2019). Emmy Noether on Energy Conservation in General Relativity. arXiv - https://ve42.co/EnergyCon Branding, K. (2005). A Note on General Relativity, Energy Conservation, and Noether’s Theorems. Springer - https://ve42.co/GRanEC Additional References: https://ve42.co/NoethersAdRefs ▀▀▀ Special thanks to our Patreon supporters: Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Autodidactic Studios, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Greg Scopel, iRick, Jon Jamison, Juan Benet, Keith England, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, TTST, Tj Steyn, Ubiquity Ventures, wolfee ▀▀▀ Directed by Matthew Davies Written by Matthew Davies, Casper Mebius, Derek Muller and Pablo Rovetto Edited by Trenton Oliver, Peter Nelson and Nick Lear Animated by Fabio Albertelli, Emma Wright, Andrew Neet, Alessandro Roussel and Ivy Tello Illustrations by Jakub Misiek, Cainejan Esperanza, Tommy Stevens, Maria Gusakovich and Emma Wright Additional research by Henry van Dyck, Gabe Strong and Darius Garewal Produced by Matthew Davies, Casper Mebius, Derek Muller, Zoe Heron, Rob Beasley Spence and Tori Brittain Thumbnail contributions by Jakub Misiek, Ren Hurley, Ben Powell and Peter Sheppard Additional video/photos supplied by Getty Images and Pond5 Music from Epidemic Sound Translated by Mingi Kwon, CineLingo Dubbed by Mingi Kwon

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General covariance

In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws. While this concept is exhibited by general relativity, which describes the dynamics of spacetime, one should not expect it to hold in less fundamental theories. For matter fields taken to exist independently of the background, it is almost never the case that their equations of motion will take the same form in curved space that they do in flat space.

https://en.wikipedia.org/wiki/General_covariance

General covariance

General Invariance

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