John Carlos Baez on Nostr: nprofile1q…yp3dv - yes! It's my paper "Getting to the bottom of Noether's theorem" ...
nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqulfpffdgvk9f09te46a7ckukfsp3vek5urnfn2ptxskv6sw9tuvsjyp3dv (nprofile…p3dv) - yes!
It's my paper "Getting to the bottom of Noether's theorem" in the book "Philosophy and Physics of Noether's Theorems: A Centenary Conference on the 1918 Work of Emmy Noether". It's here:
https://arxiv.org/abs/2006.14741
The introduction should be enough to give you the big ideas:
Noether's theorem says that (in a nice kind of theory) there's a correspondence between *observables* and *symmetry generators*, and if the observable A is preserved by the symmetry generated by B, then then observable B is preserved by the symmetry generated by A.
So, the theorem itself has a symmetrical form. In the language of Lie algebras it simply says
[A,B] = 0 ⇔ [B,A] = 0
But the correspondence between observables and symmetry generators is nonobvious, and this is why quantum mechanics needs the number i.
It's my paper "Getting to the bottom of Noether's theorem" in the book "Philosophy and Physics of Noether's Theorems: A Centenary Conference on the 1918 Work of Emmy Noether". It's here:
https://arxiv.org/abs/2006.14741
The introduction should be enough to give you the big ideas:
Noether's theorem says that (in a nice kind of theory) there's a correspondence between *observables* and *symmetry generators*, and if the observable A is preserved by the symmetry generated by B, then then observable B is preserved by the symmetry generated by A.
So, the theorem itself has a symmetrical form. In the language of Lie algebras it simply says
[A,B] = 0 ⇔ [B,A] = 0
But the correspondence between observables and symmetry generators is nonobvious, and this is why quantum mechanics needs the number i.