On the left is the (2D real part of) the mathematical model. On the right is the 3D physical spin vector (sometimes called a "Bloch sphere").

• The moving green vector in the sphere is the physical spin vector that corresponds to the moving state vector in the mathematical space on the left.
• Note that for any spin state $|\psi\rangle$ the state vector $-|\psi\rangle$ will correspond to the the same physical spin vector as $|\psi\rangle$
• Therefore, the the physical vector goes all the way around twice, for every one time the state vector goes around.

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