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There are two major alternatives for violating the (usual) Lorentz invarianceat large (Planckian) energies or momenta - either not all inertial frames (inthe Planck regime) are equivalent (e.g., there is an effectively preferredframe) or the transformations from one frame to another are (non-linearly)deformed (``doubly special relativity''). We demonstrate that the natural (andreasonable) assumption of an energy-dependent speed of light in the lattermethod goes along with violations of locality/separability (and eventranslational invariance) on macroscopic scales.  PACS: 03.30.+p, 11.30.Cp, 04.60.-m, 04.50.+h.Comment: 5 pages RevTeX, several modification

Large-scale nonlocality in “doubly special relativity” with an energy-dependent speed of light