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

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 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.

arXiv comment21 pages, Latex, no figures, Section 4 argument improved strengthening limit on synchronization; recent critique addressed

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Cited by in corpus (13)

• Minimal Length Scale Scenarios for Quantum Gravity
• Quantum Spacetime Phenomenology
• Taming nonlocality in theories with Planck-scale-deformed Lorentz symmetry
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity
• The Soccer-Ball Problem
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Experimental Search for Quantum Gravity
• The emergence of Special and Doubly Special Relativity
• The black hole information paradox and relative locality
• Comment on arXiv:1007.0718 by Lee Smolin
• Quantum superpositions of the speed of light
• Born's prophecy leaves no space for quantum gravity