Approaches to Quantum Gravity

560 L. Smolinare identified by their transforming under emergent symmetries that commute withthe interactions of the subsystem with an environment. In this way they protect thesubsystems from decoherence. In the application of this idea to Quantum Gravityproposed in [55], the environment is the quantum fluctuations of geometry and theemergent particle states are to be identified as noiseless subsystems [60].28.5 Possible new generic consequencesGiven that there is progress on this key issue, we can go on to discuss three moregeneric consequences which might be associated with the low energy behavior ofquantum theories of gravity.28.5.1 Deformed Special RelativityA new physical theory should not just reproduce the old physics, it should leadto new predictions for doable experiments. The problem of the classical limit isimportant not just to show that General Relativity is reproduced, but to go beyondthat and derive observable Quantum Gravity effects. It turns out that such effectsare observable in Quantum Gravity, from experiments that probe the symmetry ofspacetime.A big difference between a background independent and background dependenttheory is that only in the former is the symmetry of the ground state a predictionof the theory. In a theory based on a fixed background, the background, and henceits symmetry, are inputs. But a background independent theory must predict thesymmetry of the background.There are generally three possibilities for the outcome.(1) Unbroken Poincaré invariance.(2) Broken Poincaré invariance, so there is a preferred frame [61].(3) Deformed Poincaré invariance or, as it is sometimes known, Deformed or DoubleSpecial Relativity (DSR) [62].There is a general argument why the third outcome is to be expected from abackground independent theory, so long as it has a classical limit. As the theoryhas no background structure it is unlikely to have a low energy limit with a preferredframe of reference. This is even more unlikely if the dynamics is institutedby a Hamiltonian constraint, which is essentially the statement that there is nopreferred frame of reference. Thus, we would expect the symmetry of the groundstate to be Poincaré invariance. But at the same time, there is as we have describedabove, a discreteness scale, which is expected to be the minimal length at which acontinuous geometry makes sense. This conflicts with the Lorentz transformations,according to which there cannot be a minimal length.