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I've seen Charge, Parity, and Time symmetries talked about, but how come never rotational symmetry? E.g. if the entire universe was rotated 90 degrees, would any physical phenomenon behave differently?

Is such a rotational symmetry believed to be true, or known to be false? And why isn't it lumped with CPT?

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    $\begingroup$ What do you make of angular momentum and Lorentz Invariance? $\endgroup$ Commented Sep 16, 2022 at 19:43
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    $\begingroup$ en.wikipedia.org/wiki/Symmetry_(physics) You’ve somehow learned about discrete symmetries but not about continuous symmetries. $\endgroup$
    – Ghoster
    Commented Sep 16, 2022 at 19:50
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    $\begingroup$ From Noether’s Theorem one has that “invariance with respect to rotation gives the law of conservation of angular momentum”. Other continuous symmetries lead to other conservation laws. $\endgroup$
    – Ghoster
    Commented Sep 16, 2022 at 19:55
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    $\begingroup$ @Ghoster Make an answer. The question isn't "what is it", it's "why isn't it lumped in with CPT", the answer is: CPT are the discrete symmetries. Moreover, violations of C, P, T were surprising at the time, but they don't break physics. Losing translations or rotations would be a real headache. $\endgroup$
    – JEB
    Commented Sep 16, 2022 at 23:35

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C, P, and T are all discrete symmetries with eigenvalues $\pm 1$. At one point they were all thought to be fundamental symmetries of nature, but the weak interaction disabused the Standard Model of that idea.

Lumping them with continuous symmetries doesn't make a lot of sense.

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