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We study the interplay of non-locality and Lorentz invariance in a version ofdeformed or doubly special relativity (DSR) based on kappa-Minkowski spacetime.We find that Einstein's procedure for an inertial observer to assigncoordinates to distant events becomes ambiguous for sufficiently distantevents. The accuracy to which two clocks can be synchronized turns out todepend on the distance between them. These are consequences of thenon-commutativity of space and time coordinates or a dependence of the speed oflight on energy in relativistic theories. These ambiguities grow with distanceand only become relevant for real observations for the description ofcosmologically distant events. They do not afflict the interpretation of thedetection of gamma rays in stationary or moving frames near the detector.Consequently there is no disagreement between the principles of DSR and theobservation that interactions in nature are local down to currently observablescales.

On limitations of the extent of inertial frames in non-commutative relativistic spacetimes