Abstract
The author shows that the Planck-scale black holes of quantum gravity must obey a consistency condition relating Planck's constant to the integral of the mass of the black holes over time, if the usual path integral formulation of quantum mechanics is to make sense on physical spacetime. The author also shows, using time-dependent perturbation theory in ordinary quantum mechanics, that a massless particle will not propagate on physical spacetime with the black holes present, unless the same condition is met.
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