= Noether's theorem
{c}
For every <continuous symmetry> in the system (<Lie group>), there is a corresponding conservation law.
Furthermore, given the symmetry, we can calculate the derived conservation law, and vice versa.
As mentioned at http://buzzard.ups.edu/courses/2017spring/projects/schumann-lie-group-ups-434-2017.pdf[], what the symmetry (<Lie group>) acts on (obviously?!) are the <Lagrangian> <generalized coordinates>. And from that, we immediately guess that manifolds are going to be important, because the generalized variables of the Lagrangian can trivially be <Non-Euclidean geometry>, e.g. the <pendulum> lives on an infinite cylinder.
\Video[https://www.youtube.com/watch?v=CxlHLqJ9I0A]
{title=The most beautiful idea in physics - Noether's Theorem by <Looking Glass Universe> (2015)}
{description=One sentence stands out: the generated quantities are called the generators of the transforms.}
\Video[https://www.youtube.com/watch?v=AuqKsBQnE2A]
{title=The Biggest Ideas in the Universe | 15. Gauge Theory by <Sean Carroll> (2020)}
{description=This attempts a one hour hand wave explanation of it. It is a noble attempt and gives some key ideas, but it falls a bit short of Ciro's desires (as would anything that fit into one hour?)}
\Video[https://www.youtube.com/watch?v=hF_uHfSoOGA]
{title=The Symmetries of the universe by <ScienceClic> English (2021)}
{description=https://youtu.be/hF_uHfSoOGA?t=144 explains intuitively why symmetry implies consevation!}