  In this paper, we explore the quantum spacetimes that are potentially
connected with the generalized uncertainty principles. By analyzing the
gravity-induced quantum interference pattern and the Gedanken for weighting
photon, we find that the generalized uncertainty principles inspire the
effective Newton constant as same as our previous proposal. A characteristic
momentum associated with the tidal effect is suggested, which incorporates the
quantum effect with the geometric nature of gravity. When the simplest
generalized uncertainty principle is considered, the minimal model of the
regular black holes is reproduced by the effective Newton constant. The black
hole's tunneling probability, accurate to the second order correction, is
carefully analyzed. We find that the tunneling probability is regularized by
the size of the black hole remnant. Moreover, the black hole remnant is the
final state of a tunneling process that the probability is minimized. A theory
of modified gravity is suggested, by substituting the effective Newton constant
into the Hilbert-Einstein action.
