  Beginning from the standard Arnowitt-Deser-Misner (ADM) formulation of
general relativity we construct a tentative model of quantum gravity from the
point of view of an observer with constant proper acceleration, just outside of
a horizon of spacetime. In addition of producing the standard results of
black-hole thermodynamics, our model makes an entirely new prediction that
there is a certain upper bound for the energies of massive particles. For
protons, for instance, this upper bound is around $1.1\times 10^{21}eV$. The
result is interesting, because this energy is roughly of the same order of
magnitude as are the highest energies ever measured for protons in cosmic rays.
