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If i rotate a physical system by say 10 degrees it is equivalent to my self rotate -10 degrees.

but if i rotate an electron 360 degrees it spin state have a detectable minus sing. now if instead of the electron myself rotate in opposite direction i think there will be no detectable change in electron. it is same as before "I" rotate.

so i can ask is my note is true? or equivalently: do one-half spin phenomena breakdown equivalence of between active and passive transformation?

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  • $\begingroup$ The statement "if I rotate an electron 360 degrees it spin state have a detectable minus sing" [sic] is an oversimplification, see this answer of mine. That minus sign is not detectable unless as a relative phase, i.e. compared to another state that is not being rotated, and this is a rotation in Hilbert space, not physical space. That said, I am not sure what exactly your question is - can you elaborate where you see this "breakdown"? $\endgroup$ – ACuriousMind Apr 21 '18 at 13:31
  • $\begingroup$ I think active and passive transformations are mainly different things. so i'm thinking about an experiment which shows this difference. @ACuriousMind $\endgroup$ – moshtaba Apr 21 '18 at 17:45

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