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Noether's theorem

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Seonglae ChoSeonglae Cho
Created
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2024 Nov 20 1:41
Editor
Editor
Seonglae ChoSeonglae Cho
Edited
Edited
2025 Oct 6 23:18
Refs
Refs
Emmy Noether
Contracted Bianchi identities

Continuous
Symmetry of the
Action of a
Physical System with force has a corresponding
Conservation law

Symmetry indicates same physical principles against action (
Noether Current’s derivative is 0)
This shows that the
Conservation law is not absolute and inevitable, but rather a conditional property that is not absolute in all situations and depends on symmetry. In other words, it means that if symmetry is broken, conservation laws may not apply. This can be seen simply when interpreting
Redshift, where the time translation symmetry is broken, and the energy conservation law does not seem to hold due to changes in wavelength.
Einstein explained the consistency of physical laws in
General Relativity, clarified by Noether's work. This gives symmetry to spacetime transformations by fixing physical laws, including the speed of light, despite the foreign nature of spacetime. The conserved quantity for this symmetry of spacetime transformation is the
Stress-energy tensor, and it is conserved without change rate as . In other words, in redshift, while time symmetry is broken, it is interpreted that energy is redistributed in the expanded spacetime that flexibly changes with spacetime symmetry.
Because the theory of relativity explains gravity as the curvature of spacetime itself, it requires modeling the entire curved spacetime gravitational field as a
Stress–energy–momentum pseudotensor for the expression of gravitational energy.

Symmetry of physical laws under variation of the path in time

Principle of stationary action →
Euler–Lagrange equation

Conservation of Energy

For a static empty universe
However, our universe is not globally symmetric with respect to time since spacetime itself evolves. Global energy conservation does not hold, even though local conservation () still applies.

Contracted Bianchi identities

 
 
 
Noether's theorem
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems published by mathematician Emmy Noether in 1918. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle of least action. This theorem only applies to continuous and smooth symmetries of physical space.
Noether's theorem
https://en.wikipedia.org/wiki/Noether%27s_theorem
Noether's theorem
우주의 기본 원리 대칭성에 대하여(뇌터의 정리)_과학_34
우주의 기본 원리인 대칭성을 발견하고 정리한 뇌터의 정리. 아인슈타인은 그녀를 천재라고 칭송했죠. 이 영상은 주)카이스토리와 함께합니다. #대칭성 #뇌터의 정리 #물리학 석군 후원하기! 계좌이체를 통한 후원 : 우리은행 1002-149-139184(석**) 아래 링크를 클릭하면 투네이션을 통해 손쉽게 후원이 가능하십니다. https://toon.at/donate/seokuntv 채널 멤버쉽 가입하기! https://www.youtube.com/channel/UCsOm... 여러분의 소중한 후원은 더 빠른 영상 업로드에 굉장히 많은 도움이 됩니다. 비지니스 문의 : [email protected]
우주의 기본 원리 대칭성에 대하여(뇌터의 정리)_과학_34
https://www.youtube.com/watch?v=Em-cqknAFKw&t=52s
우주의 기본 원리 대칭성에 대하여(뇌터의 정리)_과학_34
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
아인슈타인도 몰랐던 상대성이론의 구멍 (양자역학 영상을 보셨다면 이것도 보셔야 합니다!)
https://www.youtube.com/watch?v=yKDq4mGlVAU
아인슈타인도 몰랐던 상대성이론의 구멍 (양자역학 영상을 보셨다면 이것도 보셔야 합니다!)
 
 
 

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