Noether's Theorem and The Symmetries of Reality

Conservation laws are among the most important tools in physics. They feel as fundamental as you can get. And yet they’re wrong - or at least they’re only right sometimes. These laws are consequences of a much deeper, more fundamental principle: Noether’s theorem.

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Conservation laws are the cheat codes of physics. They make it possible to solve physics problems that would otherwise be painfully difficult, or even impossible. More than cheat codes – conservation laws are close to the source code – they emerge from profound and simple truths about the basis of reality. They emerge from the fundamental symmetries of nature. The connection between conservation laws and symmetry is encapsulated in Noether’s theorem. But before we dive into this extremely elegant idea, let’s talk about the seeming paradox that inspired it, and the genius who discovered it.

Written and hosted by Matt O'Dowd
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[alexanderf]

Favorite Noether story. Hilbert wanted her to teach a university class but they refused to hire a woman. So he hired her as a teaching assistant and never showed up to the class.

[orthochronicity]

It's also worth noting that she didn't really step in to tackle the energy problem that was dogging early general relativity: Klein asked her for her input after being prompted by a colleague. When he did, he was surprised to learn that she had already worked out most of the solution but had put it by the wayside for more important mathematics.

When she did publish it, Einstein supposedly remarked that he had no idea that anyone could think about gravity in such a general way. In true mathematics fashion, her work was far more general than anything we deal with in physics. The universe was basically just a special case.

It's hard to overstate just how amazing of a mathematician she was.

[fep_ptcp]

I'm not lazy, i'm just following the universal principle of least action

[usmanadil]

The mathematics department at my university is called Noether Wing. I always wondered who that was. Now, I do. Thank you, PBS Space-time.

Edit: I made this comment 3 years ago and forgot about it. It just popped in my notifications and boy am I surprised. I am a graduate now, and have studied Noether's theorem in Quantum Field Theory. Its absolutely beautiful and she's easily my most admired woman from the 20th century.

[kroyhevia]

"Einstein also called her a genius" greatest line for a resume ever

[buxeessingh]

Emmy Noether is one of the greatest intellects of all time. She was just awe-inspiring.

[GustavoValdiviesso]

If every scientist have at least one academic hero or heroine, mine has always been Emmy Noether. Not just her genius mind, but also the hardships and illness she had to face make her one tough person. She doesn't get nearly enough recognition, even among science outreach lecturers.

[Aufenthalt]

Thanks for the enormous effort in trying to to bring very advanced subjects to the public without diluting them in oversimplification of. I cannot believe there are 14 people disliking this video.

[SophiaAstatine]

Noether's story is so sad. And her legacy is really great. Glad this episode is a thing.

[ejejej]

Space time videos are a gift to the world. A huge thank you to everyone that make these videos possible.

[BrendanBlake]

I think I pulled my Landau-Lifshitz Pseudotensor once at the gym.

[MrRolnicek]

It's pretty unfair. When there's a genius mathematician we don't hear a word from them. But as soon as they dip a single toe into physics, giving us even 1/10th the contribution they bring into maths, we get collectively fascinated.

[tombombadillo]

Lost my shit at the ending hahahah.

Didn't expect my reading of the preface of LOTR in grade 9 would ever become relevant again.

[grimwatcher]

You know you're smart when Einstein calls you a genius

[Stoic]

Thank you... Its awesome any time I see recognition given to one of the many, many women who have made major contributions to science yet have been over looked by history....

[cheaterman]

Hahahahaha, etymology of Middle Earth languages as a prerequisite, awesome :D

[ogliara]

Noether is such a personal hero of mine. What an absolutely wonderful inspiration.

[ramirosilveira]

This has been on my mind since I took an introductory course to general relativity this year, now this video comes out and it even has Tolkien references. Perfection.

[thatdude_]

"Her work in abstract algebra redefined entire fields..." didn't you mean to say Rings? I'll see myself out

[Ikbeneengeit]

I'm so glad you did more on Noether's Theorem!! This is mind-blowing stuff.