Space-time quantization and Cerenkov emission at velocities v>c

The value /b a/ of the ultimate limit for the smallest measurable distance should be considered as an unknown quantity, instead of assuming that /b a/=0. The corresponding generalization of physical laws implies the use of finite-difference equations and a modification of Einstein's energy-momentum relation, with the conclusion that a material body can move at a velocity /b v/>/b c/, when /b a/ ne 0. The theory developed so far, which applies only to free particles, is extended to the case of interacting particles, to account for the Cerenkov radiation emitted by any charged particle, moving at a velocity /b v/>/b c/. It is found that the quantum-mechanical selection rules for the energy and momentum variables are still valid when /b a/ ne 0, and that the spectral distribution of the emitted light can be predicted by means of a generalization of the usual classical theory of the Cerenkov effect. Some implications with respect to the principle of relativity are also discussed.Anglai