In a previous paper a stochastic foundation was proposed for microphysics: the nonrelativistic and relativistic domains were shown to be connected with two different approximations of diffusion theory; the relativistic features (Lorentz contraction for the coordinate standard deviation, covariant diffusion equation) were not derived from the relativistic formalism introduced at the start, but emerged from diffusion theory itself. In the present paper these results are given a new presentation, which aims at elucidating not the foundations of quantum mechanics, but those (...) of relativity. This leads to a discussion of points still controversial in the interpretation of relativity. In particular two problems appear in a new light: the character of time and length alterations, and the privileged role of the velocityc. Besides, the question of a possible limitation of relativity (and more generally of the laws of mechanics) in the domain of particle substructure is raised and supported by exemples drawn from the hydrodynamical model of a spinned particle. Suggestions are presented for the possibility of a deeper conceptual unification of special and general relativity. (shrink)