
Colloquium: A Century of Noether's Theorem - sohkamyung
https://arxiv.org/abs/1902.01989
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keypusher
Emmy Noether was also recently the subject of In Our Time, a fantastic BBC
roundtable discussion program. She seems to have had a remarkable skill for
invariants and finding symmetries in complex math, perhaps even some kind of
intuition that allowed her to make incredible leaps in different academic
areas around the topic. She played a crucial part in helping Einstein and
Hilbert lay the groundwork for the theory of general relativity, as well as
making significant advances in abstract algebra. The scope of her
contributions is only recently starting to be truly appreciated and I would
highly recommend listening to the show.

[https://www.bbc.co.uk/programmes/m00025bw](https://www.bbc.co.uk/programmes/m00025bw)

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ssivark
Emmy Noether's story is an interesting perspective on the sociology of the
scientific establishment a hundred years ago. But (in case the reader doesn't
appreciate the importance of the ideas) it's also worth focusing on what is a
fantastic and profound result regarding symmetries and how they make problem-
solving easy (in a very concrete operational sense). The ideas are so deep
that they're not only applicable when there are exact symmetries, but degrade
gracefully to also give approximate answers when symmetries are approximate.

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ars
A bit off topic, but anyone know what the symmetries for Conservation of
Gravity and Conservation of Magnetic charge are?

i.e. gravity can not be created or destroyed, it can only be moved (works just
like Conservation of Charge).

And a Magnetic monopole can not be created unless you create both sides at the
same time.

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semi-extrinsic
I don't understand what you mean by conservation of gravity. Do you mean
conservation of mass? There is literally nothing else than mass and some
universal constants that determine the gravitational force.

As for "no magnetic monopoles" \- this one isn't actually a law, there's
nothing in any of our physical theories that says you cannot have magnetic
monopoles, it's just that experimentally nobody's ever found one (and we've
looked pretty hard).

It's important to note about magnetic monopoles that the magnets we know are
_not_ made up of magnetic monopoles, they are made up of magnetic dipoles. No
matter how small pieces you break a magnet into, even going down towards atom-
sized bits, the pieces still have a north and a south pole.

~~~
titanomachy
Isn't divB=0 one of Maxwell's equations? That seems to be "one of our physical
theories" claiming the impossibility of magnetic monopoles.

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semi-extrinsic
Ah, but this is indeed just us saying "hey, we don't see any monopoles
anywhere, so let's simplify the equations to divB=0". The "full" equations
have a divB={stuff that's perfectly symmetric to divE RHS}, and also a
modified curlE term to make the "full" set of equations completely symmetric
for electricity and magnetism. You can see these equations at

[https://en.wikipedia.org/wiki/Magnetic_monopole](https://en.wikipedia.org/wiki/Magnetic_monopole)

~~~
titanomachy
Interesting! I guess I've never learned much physics more recent than 1904.

