Approaches to Quantum Gravity

442 G. Amelino-CameliaA theory will be compatible with the DSR principles if there is complete equivalenceof inertial observers (Relativity Principle) and the laws of transformationbetween inertial observers are characterized by two scales, a high-velocity scaleand a high-energy/short-length scale. Since in DSR one is proposing to modify thehigh-energy sector, it is safe to assume that the present operative characterizationof the velocity scale c would be preserved: c is and should remain the speed ofmassless low-energy particles. 6 Only experimental data could guide us toward theoperative description of the second invariant scale λ, although its size is naturallyguessed to be somewhere in the neighborhood of the Planck length L p .As a result of the “historical context” described in the preceding subsectionmost authors have explored the possibility that the second relativistic invariant beintroduced through a modifications of the dispersion relation. This is a reasonablechoice but it would be incorrect at present to identify (as is often done in the literature)the DSR proposal with the proposal of observer-independent modificationsof the dispersion relation. For example, the dispersion relation might not be modifiedbut there might instead be an observer-independent bound on the accuracyachievable in the measurement of distances.In the search for a first example of formalism compatible with the DSR principlesmuch work has been devoted to the study of κ-Minkowski. There are goodreasons for this [25; 26; 31], but once again it would be incorrect to identify theDSR idea with κ-Minkowski. Of course we may one day stumble upon a very differentformalism which is compatible with the DSR principles. And even withinresearch on κ-Minkowski it must be noticed that the same mathematics can beused to obtain pictures which very clearly violate the DSR principles. For example,some authors introduce theories in κ-Minkowskiinawaythatleadstoalawof conservation of energy-momentum based on a naive substitution of the usualsum rule with the “coproduct” sum rule, but this amounts [25; 26; 31] to breaking(rather than deforming) the Poincaré symmetries.22.5 More on the phenomenology of departures from Poincaré symmetryIn this section I comment on some aspects of recent phenomenology work ondepartures from Poincaré symmetry, mostly as codified in modifications of theenergy-momentum dispersion relation. I will start by stressing that the same modifieddispersion relation can be introduced in very different test theories, leadingto completely different physical predictions. But I also argue that, for most of the6 Note, however, the change of perspective imposed by the DSR idea: within Special Relativity c is the speedof all massless particles, but Special Relativity must be perceived as a low-energy theory (as viewed from theDSR perspective) and in taking Special Relativity as starting point for a high-energy deformation one is onlybound to preserving c as the speed of massless low-energy particles.