noether's theorem

[Anonymous No.10223416]

what is the most conceptually important theorem in theoretical physics, and why is the answer noether's theorem?

honestly, symmetry and conservation bros. this is how we understand quantum field theory and general relativity and fucking everything in physics. wikipedia "quantum chromodynamics" and this is how it starts:
>In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3).
symmetry groups are so fucking important, conservation laws are so fucking important, and noether is the one who uncovered this relationship.

how did she BTFO every male in history? seriously, is there a reason why the most fundamental mathematical principle in physics was missed by the male-dominated field and Emmy was the one to find it?

[Tuba Jam No.10223436]

>>10223416
bump. good women in stem don't get nearly the attention they deserve thanks to all the karlie klosses out there

[Anonymous No.10223472]

>>10223436
>thanks to all the karlie klosses out there
I want to have sex in the missionary position for the purposes of procreation with that lanky biddy.

[Anonymous No.10223491]

>>10223416
>was missed

Noether and Artin (Emil Artin, father of Michael Artin who wrote your undergrad Algebra book) literally invented Abstract Algebra as we know it.

Many people think Newton was the first one to try to write mathematical laws of physics but they are wrong. Newton was just the first one to have the calculus necessary to do it.

[Anonymous No.10223519]

>>10223416
>tfw went through a math degree without using a single theorem attributed to a woman
The only reason why I know about Noether is because I tried using some insane algebra about Noetherian rings to try to prove something in my number theory homework that didn't even require that heavy duty machinery

>>10223491
Excuse you? We used Fraleigh's book
#notmyalgebraist

[Anonymous No.10223540]

>>10223519
well maybe her math stuff was too hard for mathfags, but for sure every physicist who studies (quantum) field theory learns it at least in passing (pic related from Weinberg's classic QFT text)

[Anonymous No.10223555]

>>10223519
>Fraleigh's
Found the brainlet cs major taking the "Abstract Algebra for Ed majors" version

[Anonymous No.10223867]

>>10223540
Math undergrads (often) don't see her stuff because actually proving her results requires advanced undergrad/graduate level understanding. We often don't use results that we don't have the machinery to prove yet in school (with exceptions). I assume physicists use whatever the fuck they want as long as they know that someone out there in the world managed to prove it. But I just know that this is the case for her algebra when I had to do some digging about commutative rings.

>>10223555
I've never even heard of that class, or any other math class that is custom tailored for teachers in training at the undergraduate level. We take all the same versions of classes as pure math majors do.

[Anonymous No.10223872]

>>10223867
We as in math majors with secondary ed concentration that is. I don't like CS people either

[Anonymous No.10223902]

>>10223416
Conservation laws aren't nearly as important as you think they are. Sure conserved quantities are nice, but you can have infinitely many conservation laws even in non-solvable models and non-local conserved quantities does not give you global integral leaves on which you can do symplectic reduction. Besides, the theorem itself is often abused and at best misused by physicists (e.g. assume the unproven converse or disregard regularity conditions required). Also it's just a trivial consequence of the theory of compact Lie [math]G[/math]-bundles and the principle of least action, it's very mathematically unenlightening (Noether would agree with me on this, I've met her).
Goldstone's theorem comes more to mind than Noether's. It guarantees gapless modes for every generator of the unbroken symmetry group which makes the construction of effective field theories extremely straightforward; this is the entire foundation of Ginzburg-Landau. On top of that Mermin-Wagner is also quite important.
Aside from these, things like Coleman-Mandula, Bogolyubov edge-of-the-wedge and Schrader-Osterwalder are basically huge patches of Flex Tape that seals major foundational holes in QFT in what most physicists ignore on a daily basis. They may not be "conceptually" important but they're important in the sense that if they don't exist then much of QFT is garbage-in-garbage-out nonsense.

[Anonymous No.10224092]

>>10223416
>Giving a shit about algebra
lmao brainlet

[Anonymous No.10224386]

>>10223491
>Noether and Artin literally invented Abstract Algebra
>If we ignore Euler, Gauss, Kronecker, and Ruffinin because they were straight, white, Christian males.

[Anonymous No.10224390]

>>10223416
Noether's Theorem is utterly tautological and irrelevant. Other than theorists in physics paying it mere lip service, it has zero meaningful applications. It does not tell us when a symmetry finds use in physics, and it does not tell us when a physical quantity is universally conserved. Momentum is conserved in time as surely as energy is. Noether's Theorem does not predict this, and indeed cannot explain the apparently contradiction. She found a very cumbersome way of saying that a quantity is conserved if it is conserved.

[Anonymous No.10224498]

>>10223540
>for sure every physicist who studies (quantum) field theory learns it
Yeah, for sure. Except what you posted is not the Noether theorem, but just the most simple special case of it, i.e. on the 1-jet.

[Anonymous No.10225061]

>>10224386
Not that guy but Noether was the person who axiomatized algebraic structures and did do a lot of development for the field. Galois was the person with the first big insight that founded the field so he should be mentioned at some point as well.

[Anonymous No.10225067]

>>10224390
Everything after axioms is just tautological if one would be precise

Shit argument

[Anonymous No.10225087]

>>10225067
nice job reading 5 words into his post, good job stopping right before he actually talks about the specifics

shit argument

[Anonymous No.10225093]

>>10223416
>Praises a theorem about global symmetries
>Cites a local symmetry as an example
You can’t be this retarded can you /sci/?

[Anonymous No.10225119]

Women not being smart is an American nerd myth you only see on fly on 4chan. Also programmers seem to believe this, but they're all brainlet manchildren so is it surprising that they resort to those explanations instead of rightfully blaming themselves for their virginity.

But I get it. Until you experience women mopping the floor with you in mathematics it's easy to live in denial.

The most amazed I've ever been was this girl who was bored during a lecture until the professor asked for an explanation of some combinatorial black magic even he didn't get at that point, and it took her like a couple of minutes to construct an extremely elaborate solution. Mind you this wasn't some standard discrete math problem.

[Anonymous No.10225121]

>>10223902
>Noether would agree with me on this, I've met her
Stupid roleplayer.

[Anonymous No.10225133]

>>10225119
why do you feel the need to lie?

[Anonymous No.10225798]

>>10223902
>They may not be "conceptually" important but they're important in the sense that if they don't exist then much of QFT is garbage-in-garbage-out nonsense.
It makes predictions that are experimentally verified, who gives a fuck about rigour?

[Anonymous No.10227447]

>every phisics fanboi knows about Noether
>Not a single femanist complaining , about lack of woman in the history of phisics knkw her
Why? Why do they ignore her? Look at lists of strong dependent woman in stem and they even have girls that did nothing more than stamp out the holes in punch cards men marked who they then claim pioneered computers, yet not Noether?

[Anonymous No.10227458]

>>10223867
Bullshit, I don't know if there's a more general case that might need more math, but I remember we derived the results In one of our undergrad qm courses using just linear algebra, basic group theory, and calculus.

[Anonymous No.10227917]

>>10225798
>It makes predictions that are experimentally verified
Yeah until the ~130th term in the perturbative expansion right? After which the QED S-matrix diverges without bound. And darn where's that chiral Goldstone boson in QCD??? It must be here somewhere because who [math]cares[/math] about rigour?? Right??? xddXDDdxd

[Anonymous No.10227957]

>>10227917
based yukari-poster

btw are you in grad school for you doctorate now or did you get a job in industry?

[Anonymous No.10228015]

>>10227447
because ada lovelace was quirky and cute, by contrast Noether probably intimates them.

[Anonymous No.10228034]

>>10227957
I'm doing a PhD

[Anonymous No.10229065]

>>10228015
>Noether probably intimates them.
L-lewd!

[Anonymous No.10229078]

>>10223416

[Anonymous No.10229082]

>>10225061
Burnside founded the field tbqh.
>>10228034
>i will never score extra on tests by sketching chen on it because I'm not studying qft

[Anonymous No.10229196]

Noethers theorem is dated at 1915.
The proof is so small and follows relatively quickly out of the lagrangian formalism.
How the fuck was it not discovered earlier?
It almost seems like (((they))) want us to believe that this result was found by a woman when in fact it was known long ago under a different name.
Just kidding, but it does seem weird to me.

[Anonymous No.10230053]

>>10229196
It was just one of those fairly obvious results that no one had gotten around to publishing or proving rigorously because it's too small-time.

[Anonymous No.10230478]

>>10229082
>Burnside founded the field tbqh.
Then why isn't it called Burnside theory?

[Anonymous No.10230539]

>>10227917
>~130th term in the perturbative expansion right

dude, what are cutoffs, lol. a PHYSICAL explanation will come along soon enough and it'll all be ok, in the interim, matching experimental predictions is more than sufficient, it doesn't matter if it has ten thousand free parameters.

[Anonymous No.10230547]

>>10223491
Newton was the first to have a comprehensive system of causality. nothing like the Principia has been seen before

Leibniz (one of Newton's worst rival) literally said that if you took all "the mathematics from antiquity to the time of Newton and compared it to Newton, the latter was greater"

[Anonymous No.10230556]

Grothendieck surpassed Noether

[Anonymous No.10232225]

bump

[Anonymous No.10232427]

>>10228034
You're a more algebra/TQFT oriented guy, right? Could you give me your opinion on a lecture that I found on the nlab about perturbative QFT?

https://ncatlab.org/nlab/show/geometry+of+physics+--+perturbative+quantum+field+theory

(warning: the software used is apparently not up to the task of an ~400p online manuscript, loading might take a while)

[Anonymous No.10232449]

>>10232427
I took a brief look and it seems pretty decent.

[Anonymous No.10232629]

>>10232449
Thanks! I really hope that the (faint) trend of rigurously writing down QFT/quantization lecture notes doesn't die off.

[Anonymous No.10232640]

>>10232629
I doubt it will. It's an ever-developing field after all, and one that's getting more and more attention what with all the applications of gauge theory to pure topology.

[Anonymous No.10232657]

>>10232640
well fuggg

In a not too distant future, all of the "big" guys like Witten, Yau and so on will be dead and it'll be even more of a buttfuckery to write proper introductury texts to QFT/stringstuff/sugra.

t. suffering mathfag