Approaches to Quantum Gravity

576 Questions and answersconsider a composite object, the deformation will then depend on the typicalsize of the object or roughly on the number of particles making the object.This option should be, however, improved in the context of field theory sincewe can have virtual particles that would then spoil this simple interpretation.The deformation inducing the non-linear realization is really dependent onthe system and not on the observer, this is why this is really a deformation ofthe usual relativity principle. In this sense the status of DSR is the same asSpecial Relativity regarding the state of motion of the observer.DSR is a (a priori effective) theory supposed to describe flat semi classicalspacetime, so that we encode approximately, effectively, some quantum andgravitational features in the kinematics. This is really a zero order approximation,where both quantum and gravitational effects are small but notnegligible, modifying the symmetry. For example as I argued shortly in thearticle, the notion of consecutive measurements can implement a non-trivialdependence of the reference frame on the system, this irrespective of the distancebetween them. This is related to entanglement and is a purely quantumfeature. Gravitational effects can also generate this deformation in a way independentto the particle distance: typically one can expect the gravitationalfluctuations to be expressed in terms of the fundamental physical scale presentthere, provided by the particle: its Compton or de Broglie lengths. For examplein the paper Phys. Rev. D74:085017 (2006), gr-qc/0607024, Aloisio et al.looked at a particle, together with some stochastic fluctuations of the gravitationalfield. The typical scale of these fluctuations being expressed as afunction of the physical scale present there is the particle de Broglie length. Itthen implied naturally a deformation of the symmetries as well as a nonlineardispersion relation.In any case, I feel that still at this stage, a better understanding of DSR isneeded. In particular to really understand what is the fundamental meaningof the deformed relativity principle, together with a better understanding ofthe DSR operational aspects are for me still open issues that deserve further(deep!) thinking.• Q - D. Oriti - to L. Smolin:I have one comment and one question. The comment is the following: it seemsto me that the quantum discreteness of geometry and the ultraviolet finitenessthat you discuss are a bit less generic than one would hope. In fact, the discretenessof geometric operators in the canonical formulation, as well as theuniqueness results that you mention for the same formulation, depend very muchon the choice of a compact symmetry group G for labelling states and observables.This choice, although certainly well-motivated and rather convenient, isnot the only possible one, and in fact there exist, for example, spin foam models