Generalized uncertainty principle and deformed dispersion relation induced by nonconformal metric flutuations

Considering the existence of nonconformal stochastic fluctuations in the metric tensor a generalized uncertainty principle and a deformed dispersion relation (associated to the propagation of photons) are deduced. Matching our model with the so called quantum κ–Poincaré group will allow us to deduce that the fluctuation–dissipation theorem could be fulfilled without needing a restoring mechanism associated with the intrinsic fluctuations of spacetime. In other words, the loss of quantum information is related to the fact that the spacetime symmetries are described by the quantum κ–Poincaré group, and not by the usual Poincaré symmetries. An upper bound for the free parameters of this model will also be obtained.