Approaches to Quantum Gravity

From quantum reference frames to deformed special relativity 517What is the semiclassical limit?To be able to define the semiclassical limit in the context of LQG is the big question.In particular the notion of flat semiclassical spacetime is a key notion tounderstand to make predictions to the forthcoming experiments. The natural flatsemiclassical limit should be a theory of Special Relativity modified in order toaccount for some quantum gravitational fluctuations. In 3d the semiclassical limitis given by the deformed special relativity (DSR) theory. There are good hints nowthat in 4d, DSR is also the QG semiclassical limit [3; 4]. We expect to have somenon-trivial physics happening owing to the modification of the notion of referenceframe, the notion of measurements etc. These modifications should be traced backto an effective description of some gravitational or quantum features.In the qubits universe, 9 the semiclassical limit is just given by taking the QRFsemiclassical as well as the system. After measurements there is still a kick backof the system, due to quantum effects, on the reference frame making the physicsnon- trivial: deformation of the symmetry, modification of the multiparticles states.It is only in a very large limit that these effects disappear. ♦26.3 Semiclassical spacetimesIn the semiclassical limit one has → 0. In 4d, since the Planck scales L P and M Pare proportional to , they both go to zero. Since we are interested in studying theQG fluctuations around a flat spacetime, we can also take the limit G → 0. Sincethe Planck mass is a ratio M 2 P ∼ , to have the limit well defined it is important toGspecify how G goes to zero with respect to . For example we can take G ∼ → 0,so that M P is fixed: this flat semiclassical limit is therefore described by the Planckmass. In this regime gravitational effects are comparable to the quantum effects,this is the DSR regime. M P can be associated to a 3d momentum, to a rest mass,or energy. This regime is then effectively encoded in a modified Casimir, that is amodified dispersion relation (MDR) taking into account M P . The starting point ofthe QG phenomenology is therefore the general MDRE 2 = m 2 + p 2 + F(p,μ,M P ), (26.5)where F is a function of dimension mass two, μ is a possible set of extra massparameters (like Higgs mass), and p =|⃗p|. This MDR can be also interpretedas a manifestation of Lorentz invariance violation (LIV). Using the effective fieldtheory framework, some strong constraints have been set on the first terms whencompared to data (e.g. coming from the Crab nebula) [27]. From the DSR pointof view, it is natural to expect the deformation of the symmetries, to accommodate9 Semiclassical analysis have been done with other constrained toy models [26].