Phenomenological consequences of a geometrical model with limited proper acceleration

It is discussed the possibility of testing the hypothesis that the proper acceleration of a massive particle cannot exceed a natural limit, determined by its rest mass. To this aim the phenomenological consequences of a geometric scheme in which the space-time, at a microscopic level, is to be regarded as a four-dimensional hypersurface locally embedded in a higher-dimensional phase space have been considered. As a first consequence it is found that the energy of a uniformly and linearly accelerated particle should be quantized. Moreover, in this context the universality of the gravitational interaction is violated, but no contradiction is found with the upper bounds deduced from the present tests of the equivalence principle