Detecting the sign change when a spinor rotates through 360 degrees

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wnvl2
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When a spinor is rotated through 360◦, it is returned to its original direction, but it also picks up an overall sign change. This sign has no consequence when spinors are examined one at a time, but it can be relevant when one spinor is compared with another. Is there an experiment to make an electron interact with another electron that has a fase factor of -1 because of that 'rotation'?
 
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