[twiceaday]

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.

It's such an aha moment.

PBS Space Time: https://www.youtube.com/watch?v=04ERSb06dOg

[immibis]

Symmetries produce conservation laws if you accept and understand Lagrangian mechanics. That's a big asterisk IMO especially if you've never heard of Lagrangian mechanics and then you try to understand Noether's theorem.

Doesn't getting from Newton to Lagrange already rely on the existence of conservation laws? Apparently if we take Lagrange as fundamental, then it works, and a variation of it works in quantum mechanics, so it does seem to be fundamental, but if you're trying to get from Newton's laws to Noether's theorem, you can't get from here to there without fully grasping Lagrange first.

[eru]

It also works backwards: for (most) conserved quantities, you can also find a symmetry.

> Each symmetry you find leads to new physics.

There's a few caveats and asterisks for that. Eg Noether's theorem only applies to continuous symmetries. Eg Noether's theorem has nothing to say about mirror symmetry or time reversal symmetry.

[gauge_field]

Another point to appreciate is how universal this principle of symmetry is. It is used in every branch of physics going from Classical Physics (Lagrangian Formulation) to quantum physics (with Feynman's Path Integral Formulation), from conservation of momentum to conservation of electric charge in (U(1) Symmetry) of fundamental particles. The fact that she was able to do this as a woman 100 years agos is also amazing.

[mckirk]

I wonder what the conservation law is connected to the 'analysis invariance', i.e. the fact that no matter how well you've thought through everything beforehand, there will still be some recalcitrant pocket of the experiment that behaves confusingly. Maybe that's the 'conservation of surprise'.

[wholinator2]

Well i have heard the term 'conservation of misery' quite a few times since starting my PhD