Approaches to Quantum Gravity

440 G. Amelino-Camelia22.4 Aside on doubly special relativity: DSR as seenby the phenomenologistIn preparation for the next section, which focuses on the phenomenology ofPlanck-scale departures from Poincaré symmetry, I find it useful to provide herea short but self-contained introduction to “doubly special relativity” (DSR). Thisis a scenario that I proposed only a few years ago [25; 26], but is already ratherextensively analyzed as an alternative to the standard scenario of Planck-scaleeffects that break Lorentz(/Poincaré) symmetry. As a result of this interest, at thispoint there are numerous attempts in the literature to review DSR research, so onemight think this section could be unnecessary. However, DSR is becoming differentthings to different authors, and the differences are rather significant for the“phenomenologist perspective on Quantum Gravity” which I am here attemptingto provide. The DSR proposal, which originally provided a physics scenario for thePlanck scale, is now often identified with a certain (rather vaguely defined) mathematicalframework, whether or not this mathematical framework turns out to becompatible with the DSR principles.This recent mathematical twist of the DSR literature may well some day matureinto a powerful tool for Quantum Gravity research, perhaps both at the conceptuallevel and for what concerns phenomenology, but at present it is certainly of no usefor phenomenology (and even the conceptual side is only at an early stage of development).Instead for the thesis presented in this chapter my original DSR proposalis rather valuable since it provides a rare example of a physics idea that is powerfulenough to make definite falsifiable predictions (even without any knowledge of thecorrect formalism that should implement it!). This is stressed in particular in thepart of the next section devoted to photon stability.22.4.1 MotivationI introduced the doubly special relativity scenario as a sort of alternative perspectiveon the results on Planck-scale departures from Lorentz symmetry which hadbeen reported in numerous articles [5; 6; 7; 8; 10; 11; 12; 29] between 1997 and2000. These studies were advocating a Planck-scale modification of the energymomentumdispersion relation, usually of the form E 2 = p 2 + m 2 + ηL n p p2 E n +O(L n+1p E n+3 ), on the basis of preliminary findings in the analysis of several formalismsin use for Planck-scale physics. The complexity of the formalisms is suchthat very little else was known about their physical consequences, but the evidenceof a modification of the dispersion relation was becoming robust. In all of therelevant papers it was assumed that such modifications of the dispersion relationwould amount to a breakup of Lorentz symmetry, with associated emergence of a