On limitations of the extent of inertial frames in non-commutative relativistic spacetimes Lee Smolin" arXiv:submit/0071700 [gr-qc] 7 Jul 2010 Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2J 2Y5, Canada July 7, 2010 Abstract 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 de- tection 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. ismolineperimeterinstitute.ca 1 EFTA_R1_00151758 EFTA01805311