Bounds on an Energy-Dependent and Observer-Independent Speed of Light from Violations of Locality

We show that models with deformations of special relativity that have an energy-dependent speed of light have nonlocal effects. The requirement that the arising nonlocality is not in conflict with known particle physics allows us to derive strong bounds on deformations of special relativity and rule out a modification to first order in energy over the Planck mass.

Figure 1

Earth frame. The GRB (thick solid line) emits at the same time a low-energetic photon (thin, long dashed line) and a highly energetic, slowed-down photon (dotted line). The slowed-down photon crosses the worldline of an electron (solid line) that was emitted nearby the detector (shaded area). A satellite flies by towards the GRB.

Figure 2

Satellite frame. Same as in Fig. 1, as seen from the satellite frame. The highly energetic photon is slowed down further and does not meet the electron in the detector.