  A threshold anomaly refers to a theoretically expected energy threshold that
is not observed experimentally. Here we offer an explanation of the threshold
anomalies encountered in the ultra-high energy cosmic ray events and the
TeV-gamma ray events, by arguing that energy-momentum uncertainties due to
quantum gravity, too small to be detected in low-energy regime, can affect
particle kinematics so as to raise or even eliminate the energy thresholds. A
possible modification of the energy-momentum dispersion relation, giving rise
to time-of-flight differences between photons of different energies from gamma
ray bursts, is also discussed.
