Proposal of a second generation of quantum-gravity-motivated Lorentz-symmetry tests: sensitivity to effects suppressed quadratically by the Planck scale

Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity scenarios even the strongest quantum-spacetime effects are suppressed by at least two powers of the Planck length, and many authors have argued that it would be impossible to test these quadratically-suppressed effects. I here observe that advanced cosmic-ray observatories and neutrino observatories can provide the first elements of an experimental programme testing the possibility of departures from Lorentz symmetry that are quadratically Planck-length suppressed. The recent interest in the possibility that (classical) Lorentz symmetry might be only an approximate symmetry of quantum spacetime was originally ignited by phenomenological analyses based on mostly-heuristic arguments [1, 2, 3, 4]. It has now matured into a detailed technical understanding of the fate of Lorentz symmetry in quantum-gravity approaches based on noncommutative geometry [5, 6, 7] and we also have several insightful results concerning the loop-quantum-gravity approach [8, 9, 10, 11]. In approaches involving spacetime discretization, such as loop quantum gravity, we are essentially finding [8, 9, 10, 11] that the discretized spacetime observables are incompatible with continuous Lorentz-symmetry transformations. Lorentz symmetry remains a good approximate symmetry, since it is violated only by correction terms whose magnitude is governed by the This essay received an “honorable mention” in the 2003 Essay Competition of the Gravity Research Foundation.