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

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 de-tection the description of gamma of cosmologically rays in stationary distant or moving events. frames They donot near the afflict detector. theinterpretationof Consequently there the is no disagreement between the principles of DSR and the observation that interactions innature are local down to currently observable scales.