  We describe the spin and momentum degrees of freedom of a system of two
massive spin--$\tfrac{1}{2}$ particles as a 4 qubit system. Then we explicitly
show how the entanglement changes between different partitions of the qubits,
when considered by different inertial observers. Although the two particle
entanglement corresponding to a partition into Alice's and Bob's subsystems is,
as often stated in the literature, invariant under Lorentz boosts, the
entanglement with respect to other partitions of the Hilbert space on the other
hand, is not. It certainly does depend on the chosen inertial frame and on the
initial state considered. The change of entanglement arises, because a Lorentz
boost on the momenta of the particles causes a Wigner rotation of the spin,
which in certain cases entangles the spin- with the momentum states. We
systematically investigate the situation for different classes of initial spin
states and different partitions of the 4 qubit space.
  Furthermore, we study the behavior of Bell inequalities for different
observers and demonstrate how the maximally possible degree of violation, using
the Pauli-Lubanski spin observable, can be recovered by any inertial observer.
