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