Suppose a detector that can be rotated measures a particle in which the probabilities of detecting some state are affected by the rotation of the detector. When the system is rotated through 360°, the observed output and physics are the same as initially but the amplitudes are changed for a spin- particle by a factor of −1 or a phase shift of half of 360°. When the probabilities are calculated, the −1 is squared, (−1)2 =  1, so the predicted physics is the same as in the starting position. Also, in a spin- particle there are only two spin states and the amplitudes for both change by the same −1 factor, so the interference effects are identical, unlike the case for higher spins. The complex probability amplitudes are something of a theoretical construct which cannot be directly observed.