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We saw in class that rotating a spin state with an angle of 2pi returns minus the state, and so it has to be rotated 4pi rad in order to return to the original state.

However, we also saw that the expected value of the spin DOES return to its original value after a rotation of 2pi rad.

My question is- Being that we can only measure expected values, and not the states themselves, what physical meaning is there to the "double rotation" symmetry of a spin state?

I mean, how is this theoretical result manifested in experiments ?

thanks

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# Spin-1/2 rotational symmetry

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