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I am thinking something which could be similar as Gödel's works - but not with axioms of logical systems, but with symmetries of (theoretical) physical systems.

Such a proof would mean, that adding any new symmetry, would either contradict the others, or it could be derived from them.

I think, having such a proof would mean, that a theory is "ready". For example, I think the Newtonian Mechanics and the SR are probably "ready" in this sense, but I can't proove it.

Furthermore, applying the Noether theorem, it would also mean, that all conserved quantities of a theory were already found.

peterh
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  • Just throwing it out there: If you could prove you had a particular number of D.O.F, you could find a maximal number of independent generators of a global continuous symmetry. The same cannot be said for global discrete symmetries, and perhaps also not for gauge symmetries. – Omry Sep 10 '17 at 15:07
  • If you like this question you may also enjoy reading this Phys.SE post. – Qmechanic Sep 10 '17 at 15:33

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