Taming nonlocality in theories with Planck-scale-deformed Lorentz symmetry

We report a general analysis of worldlines for theories with deformed relativistic symmetries and momentum dependence of the speed of photons. Our formalization is faithful to Einstein's program, with spacetime points viewed as an abstraction of physical events. The emerging picture imposes the renunciation of the idealization of absolutely coincident events, but is free from some pathologies which had been previously conjectured.