  We show that a pair of massive relativistic spin-1/2 particles prepared in a
maximally entangled spin state in general is not capable of maximally violating
the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities without a
post-selection of the particles momenta, representing a major difference in
relation to non-relativistic systems. This occurs because the quantization axis
of the measurements performed on each particle depends on the particle
velocity, such that it is not possible to define a reduced density matrix for
the particles spin. We also show that the amount of violation of the CHSH
inequality depends on the reference frame, and that in some frames the
inequality may not be violated.
