  Recent work has argued that the concepts of entanglement and nonlocality must
be taken seriously even in systems consisting of only a single particle. These
treatments, however, are nonrelativistic and, if single particle entanglement
is fundamental, it should also persist in a relativistic description. Here we
consider a spin-1/2 particle in a superposition of two different velocities as
viewed by an observer in a different relativistically-boosted inertial frame.
We show that the entanglement survives right up to the speed of light and that
the boosted observer would see single-particle violations of Bell's inequality.
We also discuss how quantum gates could be implemented in this way and the
possible implications for quantum information processing.
