Abstract

The introduction of an “elementary length”a representing the ultimate limit for the smallest measurable distance leads to a generalization of Einstein's energy-momentum relation and of the usual Lorentz transformation. The value ofa is left unspecified, but is found to be equal tohc/2E u, whereE u is the total energy content of our universe. Particles of zero rest mass can only move at the velocityc of light in vacuum, while material bodies can move slower or faster than light, whena≠0, without violating the principle of causality. The laws of relativistic mechanics are actually generalized so that they include Mach's principle, since it is found that the universe as a whole can only be in a state of rest for any particular inertial observer