The spin 1/2

Particles with spin 1/2, like the electron, must perform two 360° rotations to return to their initial state. This concept is hard to visualize but, basically, if we imagine the electron wavefunction with α spin rotated by 360° it will become a β wavefunction. Just after another 360° rotation the electron can return to the initial state.

But why? These two videos help by illustrating the reason:

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