2003/12/30 by Giovanni Amelino-Camelia, Jerzy Kowalski-Glikman, Gianluca Mandanici +2 · 108 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Doubly special relativity #Four-force #Lorentz covariance #Lorentz transformation #Noncommutative and Quantum Gravity Theories #Phenomenology (philosophy) #Physics #Planck #Planck energy #Planck scale #Quantum #Quantum gravity #Quantum mechanics #Spacetime #Theoretical physics #Theory of relativity #gr-qc
paper · pdf · doi:10.1142/s0217751x05028569
published in International Journal of Modern Physics A 20(26), 6007-6037 (World Scientific) · 22 pages, LaTex
arxiv created 2003/12/30 · openalex publication_date 2005/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Investigations of the possibility that some novel "quantum" properties of space–time might induce a Planck-scale modification of the energy/momentum dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry, with an associated reduced n-parameter (n<6) rotation-boost symmetry group. More recently several studies have also considered the possibility of a "doubly special relativity," in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a 6-parameter group of rotation-boost symmetry transformations (a deformation of the Lorentz transformations). For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. Here we show that the analysis of the experimental limits could be significantly different in a doubly-special-relativity framework. We find that the study of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, should not provide significant constraints on a doubly-special-relativity parameter space. However, certain types of analyses of gamma-ray bursts should be sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-special-relativity framework. This result also allows us to characterize more sharply the differences between the doubly-special-relativity framework and the framework of κ-Poincaré Hopf algebras, two frameworks which are often confused with each other in the literature.