- 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.
John Carlos Baez /
npub1nf…3nqe4
2025-02-07 19:12:52
in reply to nevent1q…u6h4
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npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4Published at
2025-02-07 19:12:52Event JSON
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"content": "- yes! \n\nIt'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:\n\nhttps://arxiv.org/abs/2006.14741\n\nThe introduction should be enough to give you the big ideas:\n\nNoether'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.\n\nSo, the theorem itself has a symmetrical form. In the language of Lie algebras it simply says\n\n[A,B] = 0 ⇔ [B,A] = 0\n\nBut the correspondence between observables and symmetry generators is nonobvious, and this is why quantum mechanics needs the number i.",
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