mixed states. (For further discussion and references on the paradox see [@paradox]).

On the other hand, we have argued that due to the lack of perfectly classical clocks, quantum mechanics really implies that pure states do evolve into mixed states. The question is: could the effect be fast enough to render the black hole information paradox effectively unobservable? On one hand we have argued that our effect is small. But it is also true that black holes usually take a very long time to evaporate. Of course, a full calculation of the evaporation of a black hole would require a detailed modelling including quantum effects of gravity that no one is in a position of carrying out yet. We have done a naive estimate [@prl; @piombino] of how our effect would take place in the case of an evaporating black hole. To this aim we have assumed the black hole is a system with energy levels (this is a common assumption in many quantum gravity scenarios), and that most of the Hawking radiation is coming from a transition between two dominant energy levels separated by a characteristic frequency dependent on the temperature as $$\omega_{12}(t) = {1 \over \left(8 \pi\right)^2
t_P 