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We make a critical comparison of relativistic and non-relativistic classicaland quantum mechanics of particles in inertial frames and of the open problemsin particle localization at the two levels. The solution of the problems of therelativistic center of mass, of the clock synchronization convention needed todefine relativistic 3-spaces and of the elimination of the relative times inthe relativistic bound states leads to a description with a decoupled non-local(non-measurable) relativistic center of mass and with only relative variablesfor the particles (single particle subsystems do not exist). We analyze theimplications for entanglement of this relativistic spatial non-separability notexisting in non-relativistic entanglement. Then we try to reconcile the twovisions showing that also at the non-relativistic level in real experimentsonly relative variables are measured with their directions determined by theeffective mean classical trajectories of particle beams present in theexperiment. We discuss some of the existing problems with the observers andtheir reference frames, leaving to the future the discussion in non-inertialframes.

On Relativistic Entanglement and Localization of Particles and on their Comparison with the Non-Relativistic Theory