  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.
