Your Daily Equation #25: Noether's Amazing Theorem: Symmetry and Conservation

Episode 25 #YourDailyEquation: In 1918, the phenomenal German mathematician Emmy Noether discovered a deep link between symmetries and conserved quantities, which has proven to be one of the most influential mathematical results in the development of physical laws. Join Brian Greene for an explanation of Noether's insight and the mathematical argument--in the simplest case--establishing that it is true.

Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.

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[phtinc]

at 51yrs of age, I’ve long since forgotten what it’s like to be in a classroom but only wish I’d had teachers with 1/5th the talent you possess in articulating and conveying your thoughts and ideas. You are a true gem, Professor. We all benefit greatly from your knowledge and expertise. God bless. Stay safe 😷 and best wishes...

[yuma]

I must say that Brian‘s handwriting is frickin beautiful

[jeffk]

I've heard about Noether's Theorem for years and knew it was about 'proving certain quantities are conserved as a consequence of specific symmetries', or whatever. Now I actually understand where this comes from. Eyes open! I've never seen how the math works out until now. Thank you Professor Greene.

[gerardopc]

With regards to Noether's theorem (1915), if we want to be more specific and inclusive, Emmy Noether was not the first person to discover the fundamental link between symmetries and conserved currents (energy, momentum, angular momentum, etc.). Many people in the physics community ignore this fact, but the intimate connection between symmetries and conservation laws was first noticed in classical mechanics by Jacobi in 1842. In his paper, Jacobi showed that for systems describable by a classical Lagrangian, invariance of the Lagrangian under translations implies that linear momentum is conserved, and invariance under rotations implies that angular momentum is conserved. Still later, Ignaz Robert Schütz (1897) derived the principle of conservation of energy from the invariance of the Lagrangian under time translations. Gustav Herglotz (1911) was the first to give a complete discussion of the constants of motion assiciated with the invariance of the Lagrangian under the group of inhomogeneous Lorentz transformations. Herglotz also showed that the Lorentz transformations correspond to hyperbolic motions in R3. What Noether did, was to put every case into the generalized and firm framework of a mathematical theorem.

[laaradee]

I quite addicted to watching these, it’s like learning German by listening to a newscast, with one better - the manipulation of symbols - so some visual input as well. I suppose I need to start at a beginning - whatever that means. The historical and sociological significances are so——??? Well for example, !today I tried to imagine what it would be like to be a female who liked mathematics in 1890’s, ....thanks for this!

[niyantadeshpande]

Thank you Dr. Greene as always!! Your notoriety is well deserved. You’re a rock star!!!

[PetraKann]

It's absolutely astonishing how much innovation and science emerged from Germany from that golden period of less than a century. Noether is a prime another example of this creative thought.

[gedlangosz]

I first came across Noether's theorem on a course I was doing about the Higgs Boson. Of course this famously breaks symmetry to achieve the required results!

[hubertheiser]

Again you made it look so easy. Thanks for another great explanation!

[samali]

This is fantastic. Professor, you make things so easy to understand, that one starts loving physics. Thank you!!!

[arnavmishra]

Sir please upload the DIRAC EQUATION too!🙏🏻

[ReidarWasenius]

Greetings from Finland. THANKS for producing these videos!!

[daydreamer]

Physicist on YouTube with their knowledge is revolution in science.

[kyleklassen]

Dr. Brian Greene,

you explain it perfectly!

[chritophergaafele]

Professor can you explain mach's principle and its application in general relativity

[christophertamina]

I an so impressed by your ability to explain the Noether's Theorem in such simple terms. You are Brian green, so I am not surprised. 😘

[mohameda.]

You drank the junk of tea leaves leftover for science :) and here I give you the least we can, a subscription to your channel, a comment and a like on your video... Hope many can do... for science :)

[tryphonsoleflorus]

Thank you so much;great explanation for us amateur physicists not quite on the level of theoretical physics!

[mehdibaghbadran]

each universes has huge turning around themeselves and at the same momentum stars and planet acting the same, and this live movment beautiful

[dabrownone]

Can you describe how Noether's Theorem relates to gauge theory? I think it is important but don't understand how it works there