max})| \sim |\rho_{12}(0)| \left({M_P \over M_{\rm
BH}}\right)^{2 \over 3}.$$

For astrophysical sized black holes, where $M_{\rm BH}$ is of the order of the mass of the Sun, this indicates that the off diagonal elements are suppressed by the time of evaporation by $10^{-28}$, rendering the information puzzle effectively unobservable. What happens for smaller black holes? The effect is smaller. So can one claim that there still is an information puzzle for smaller black holes? This is debatable. After all, we do expect decoherence from other environmental effects to be considerably larger than the one we are considering here. If one makes the holes too small, then none of these calculations apply, and in fact the traditional Hawking evaporation is not an adequate description, since one has to take into account full quantum gravity effects. So we can say that the paradox is effectively eliminated for large black holes and we cannot say for sure for smaller ones using this simplified analysis.

The measurement problem in quantum mechanics
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A potential conceptual application of the fundamental decoherence that we discussed that has not been exploited up to now is in connection with the measurement problem in quantum mechanics. The latter is 