Velocity-like maximum polarization: irreversibility and quantum measurements

The polarization emerging in the subsequent scattering processes can never exceed $1$ which corresponds to the fully polarized pure state. This property is shown to be provided by the addition rule similar to that for relativistic velocities never exceeding the speed of light. The cases of spin $1/2$ and $1$ are considered. The photon linear polarization in Thomson scattering is monotonically increasing. This directness is shown to be a consequence of spin measurement procedure and may be the particular example of ithe anticipated relation between quantum measurement and time irreversibility. The emergent polarization may be considered as a case of opposing time's arrows corresponding to microscopic (spin) and macroscopic (momentum) degrees of freedom, respectively.