John Carlos Baez on that article: <a href="https://mathstodon.xyz/@johncarlosbaez/113964127171705485" rel="nofollow">https://mathstodon.xyz/@johncarlosbaez/113964127171705485</a>
I recommend the book Einstein’s Tutor” which came out last year.<p><a href="https://lee-phillips.org/noether/" rel="nofollow">https://lee-phillips.org/noether/</a><p>This is probably the best layman’s approach to Noether, her impact, and how she probably didn’t think much about the theorem later because she wasn’t interested in physics and abstract mathematics was her consuming passion.
Here is a cosmological issue from Noether's Theorem. An expanding universe shows time asymmetry, therefore it might not have conservation of energy.<p>This looks like it actually happens. Photons going through empty space go through cosmological redshift, reducing their energy over time. The energy does not appear to go anywhere - it is just gone.<p>I have no idea why this example is not more widely discussed.
TLDR: Do an experiment, then move 10 meters to the left (or rotate 90 degrees, or wait a few days) and do it again. The results don’t change, because the laws of physics don’t change. This realization alone is enough to produce conservation laws. Translational and rotational symmetries produce conservation of linear and angular momentum, and the time symmetry produces conservation of energy. Each symmetry you find leads to new physics.<p>It's such an aha moment.<p>PBS Space Time: <a href="https://www.youtube.com/watch?v=04ERSb06dOg" rel="nofollow">https://www.youtube.com/watch?v=04ERSb06dOg</a>
I've never understood why Marie Curie is so celebrated in the popular press, but Noether is largely ignored. Noether's work is much more important, IMHO.
> In the fall of 1915, the foundations of physics began to crack. Einstein’s new theory of gravity seemed to imply that it should be possible to create and destroy energy, a result that threatened to upend two centuries of thinking in physics.<p>Not just seem to imply, but they do imply[0]. Does that mean that we can build a machine that generates energy and negentropy forever (e.g. an artificial Sun), thus, we can outlive the heat-death of the rest of the Universe? Yes, absolutely. But there are other existential threats, like the collapse of false-vacuum. In the end, it is not known if we have limited or unlimited time here, but Noether's theorem doesn't answer that.<p>[0] : <a href="https://www.google.com/search?q=general+relativity+and+conservation+of+energy" rel="nofollow">https://www.google.com/search?q=general+relativity+and+conse...</a>
If you would like to know more about her:<p>Her legacy
<a href="https://www.mathgenealogy.org/id.php?id=6967" rel="nofollow">https://www.mathgenealogy.org/id.php?id=6967</a><p>About her
<a href="https://en.wikipedia.org/wiki/Emmy_Noether" rel="nofollow">https://en.wikipedia.org/wiki/Emmy_Noether</a><p>Where she lived and studied
<a href="https://thonyc.wordpress.com/2011/05/07/the-house-where-emmy-lived/" rel="nofollow">https://thonyc.wordpress.com/2011/05/07/the-house-where-emmy...</a>
The article begins with claims of violation of conservation of energy but no examples. Then it posits that violations of energy conservation are explained by symmetries. What does that mean in English? Is there something else that changes in concert with changes of energy?
"Like most Jewish academics in Germany, Emmy Noether was fired after the Nazis came to power in 1933. She left later that year for Bryn Mawr College in the U.S [...]"<p>Compared to what's happening now, it's totally frightening.