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  • $\begingroup$ Thank you, this is helpful and addresses my question. I will look at the paper. In the meantime, would you agree to the statement "rotating a particle has no simple, immediate operational meaning (unlike translating it)", or is that a mis-reading on my part? $\endgroup$ Commented Dec 1, 2018 at 20:38
  • $\begingroup$ @Melissa I don't have a clear yes or no answer -- this is exceeding the limits of my intuition! The best I've been able to do (so far, at least) is to think about how a given transformation affects a state-vector (like applying a rotation to just one of the two terms in a superposition) and then thinking about how the resulting state-vector would be prepared experimentally. That probably doesn't qualify as a "simple, immediate operational meaning"; but just because I haven't thought of one doesn't mean there isn't one. This is a great question! $\endgroup$ Commented Dec 1, 2018 at 21:34