
Emmy Noether changed the course of physics - yk
http://arstechnica.com/science/2015/05/the-female-mathematician-who-changed-the-course-of-physics-but-couldnt-get-a-job/1/
======
cbd1984
Noether’s Theorem is something I wish was introduced a lot earlier than it
ever seems to be: I think a simple, restricted, but still enlightening form of
it can be introduced as soon as students have a basic mastery of derivatives
and the idea that a derivative of zero means the function is constant with
respect to that variable. You don't need to introduce the idea of generalized
coordinates to give a flavor of how powerful this notion is.

Here's a few simple examples:
[http://www.sjsu.edu/faculty/watkins/noetherth.htm](http://www.sjsu.edu/faculty/watkins/noetherth.htm)

Nothing about this requires math beyond undergrad calculus.

~~~
carlob
IIRC when I studied physics I think they tried to tell us that there was
something profound about the fact that time-invariant systems conserve kinetic
energy and space-invariant systems conserve momentum, … during the first year,
but I don't think anyone was mindblown. Then during the second year we started
learning about generalized coordinates and Lagrangians and I think we did
learn the Noether theorem then (probably just about one semester later).

However I think I really fell in love with it when I understood gauge
invariance.

In general I think you can always try to tell your students things a little
early to impress them, but it rarely works until they can work out the math
themselves. I remember our professor in introductory quantum mechanics saying
something along the lines of: "and now you see why quantum mechanics is just
Markov chains in imaginary time", but until another professor showed us the
Wick rotation in the context of path integrals nobody really appreciated that
even if it could have been in our grasp earlier.

I guess this has come out way denser than I meant it to be, but my point is
that you can always try to introduce something a little bit earlier, but
you'll often find that your students don't want to learn some diluted crap,
they want the real deal!

~~~
diego898
I've never heard of QM being presented like that. Do you have a reference I
could read? Thanks!

~~~
carlob
You can start here:

[http://en.wikipedia.org/wiki/Wick_rotation](http://en.wikipedia.org/wiki/Wick_rotation)

and there was this on HN some time ago

[https://news.ycombinator.com/item?id=8377680](https://news.ycombinator.com/item?id=8377680)

Though I didn't find Scott Aaronson to be as clear as the professor who
finally showed us the Wick rotation. Unfortunately he passed away a few years
back right after having missed being awarded the Nobel prize by an inch.

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

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drjesusphd
Here's my favorite way of thinking about Noether's theorem:

In physics, we have to assume the laws of nature are the same everywhere and
for all time. Otherwise, we're wasting our time. Because of Noether's theorem,
this means there are some conserved quantities. Whatever these happen to be is
what we _call_ momentum and energy. If the laws of physics change (they are
still the same everywhere, just modified based on an improved theory), then we
have to change our definitions of what is conserved.

If you define kinetic energy as mv^2/2, then when you take into account
relativity, you realize that's not conserved any more. However, because the
physical law that relatively predicts still does not change over time, then
_something_ must be conserved. So we call that energy instead. Until the next
iteration, of course.

~~~
lucozade
I actually think it may be a little more prosaic than that.

In order for us to have a scientifically verifiable theory, or at least a
consequence of a theory that is scientifically verifiable, that
theory/consequence must be invariant under translations in space, time and
rotation. Otherwise there would be no repeatability of any related experiment.

As such, by Noether's theorem, that theory/consequence must conserve momentum,
energy and angular momentum. At the very least.

So any theory that didn't conserve these quantities couldn't be scientifically
verifiable. So it's sort of a tautology that scientific theories conserve
these quantities.

~~~
tjradcliffe
It is nothing of the kind.

It is a matter of perfectly ordinary empirical fact that we live in a universe
that, so far as we can tell, is translationally, temporally and rotationally
invariant. There is absolutely nothing in Noether's theorem that forbids us
from having theories that violate momentum, energy or angular momentum
conservation if they happen to describe a universe that has aspects that
violate those invariance conditions.

There have been theories that do so, like Dirac's weird large number thing.
These are completely legitimate theories, and are entirely subject to
absolutely ordinary observational, experimental and inferential verifiability
(which is why we know Dirac's large number thing is likely false.)

~~~
lucozade
Yes indeed. However, for us to be able to scientifically verify those
theories, something about them must be invariant in space, time and rotation.
That's pretty much the definition of a scientifically verifiable theory.

My point isn't that there can't be theories without those properties nor that
the universe necessarily has them (or not). Just that, if it doesn't, we
couldn't verify it scientifically.

~~~
abecedarius
According to Feynman there once were people saying that since experiments need
to be repeatable, to be scientific the laws of physics must be deterministic,
by pure logic. Oh, quantum mechanics? Oops.

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calstad
She was also very instrumental in the discovery of the functorality of
homology in algebraic topology, which led to the explosion of homological
algebra. She was definitely a great polymath

~~~
jackmaney
Also, a class of rings, called Noetherian rings[1], are named after her.
Noetherian rings are of great importance in ring theory.

[1]:
[http://en.wikipedia.org/wiki/Noetherian_ring](http://en.wikipedia.org/wiki/Noetherian_ring)

------
avmich
Now, who can explain the Noether's theorem binding conservation law with an
invariant better than "Structure and Interpretation of Classical Mechanics"?
:)

~~~
psykotic
That depends on what you mean by "explain". The proof is simple calculus:
[http://math.ucr.edu/home/baez/noether.html](http://math.ucr.edu/home/baez/noether.html)

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tsotha
When these periodic "let's put a woman on a bill" come up Noether is my choice
for the subject. Her work had a huge influence on the shape of the world today
and few people outside physics and mathematics have heard of her.

~~~
qmalxp
Unfortunately, she was not American.

~~~
tsotha
That's not an issue unless she wanted to be president. She taught in the US,
and that's good enough for me.

~~~
tzs
And she's dead and has a name, which is good enough for the Department of the
Treasury. That's the only legal restriction I could find on who may appear on
US currency and securities [1]:

 _United States currency has the inscription “In God We Trust” in a place the
Secretary decides is appropriate. Only the portrait of a deceased individual
may appear on United States currency and securities. The name of the
individual shall be inscribed below the portrait._

See the FAQ [2] at the Bureau of Engraving and Printing site for some
interesting information on how the current choices came about.

[1] 31 USC §5114(b)

[2]
[http://www.moneyfactory.gov/faqlibrary.html](http://www.moneyfactory.gov/faqlibrary.html)

------
sasvari
Here's a NY Times article about Emmy Noether from 2012 [0] and the HN
discussion [1]:

[0] The Mighty Mathematician You’ve Never Heard Of
[http://www.nytimes.com/2012/03/27/science/emmy-noether-
the-m...](http://www.nytimes.com/2012/03/27/science/emmy-noether-the-most-
significant-mathematician-youve-never-heard-of.html)

[1]
[https://news.ycombinator.com/item?id=3760447](https://news.ycombinator.com/item?id=3760447)

------
stefantalpalaru
Noether made important contributions worth talking about, but I'd reserve the
"changed the course of physics" qualification for Einstein and those oh his
level.

~~~
andrepd
Precisely. She didn't "change the course of physics" at all. Nothing in her
work was a massive paradigm shift. She didn't shape the field for decades to
come. Einstein did that, with special and general relativity. Him, Planck, de
Broglie and all that crowd did that with quantum theory. Noether's theorem is
beautiful, powerful and amazingly profound, and she definitely deserves way,
way more recognition than she gets. But it's wrong to say that she "changed
the course of physics".

~~~
drjesusphd
> Nothing in her work was a massive paradigm shift. She didn't shape the field
> for decades to come.

I disagree. Quantum field theories are often expressed as a collection of
symmetries. The ever-successful Standard Model is:

SU(3) × SU(2) × U(1)

Everything else follows because of Noether's theorem. And by "everything", I
mean, "every phenomena in the universe that we are aware of except for
gravity".

~~~
cdwhite
Well, to be fair, you actually also have to put in some numbers, too: masses,
mixing angles, coupling constants, and the Higgs vacuum expectation value.
(See
[https://en.wikipedia.org/wiki/Standard_Model#Construction_of...](https://en.wikipedia.org/wiki/Standard_Model#Construction_of_the_Standard_Model_Lagrangian)
.) But, yeah, that symmetry description is incredibly powerful.

