In this paper the squared mass of the hadron is defined as a random variable, whose average is the measured quantity. This leads to a mass formula, of a unique type for mesons and baryons, with a general law for the spin variation of the coefficients. The central squared masses form an overall geometrical scheme; in the baryon case it contains trajectories which are a fine structure of the Regge trajectories. For the accurately measured masses the difference between the computed (...) and experimental value lies within 5 MeV for mesons and baryons. The geometrical scheme will be the basis for the computation of the decay rates, to be developed in the next paper. (shrink)

The guiding idea of this work is that classical diffusion theory, being nonrelativistic, should be associated with nonrelativistic quantum mechanics. A study of classical diffusion leads to a generalization which should correspond to the relativistic domain. Actually, with a convenient choice of the basic constants, one sees the relativistic features (Lorentz contraction and covariant diffusion equation) emerge in the generalized process. This leads first to a derivation of the nonrelativistic and relativistic wave equations (and to a model of the Dirac (...) fluid); then to a better understanding of several relativistic aspects of quantum mechanics (spin connection with relativity and link of relativity with nonlocalization). No quantum mechanical forces are postulated: they arise as pseudo-forces in the course of the calculations. The physical significance of the stochastic model is examined and shown to give a pictorial description only in certain ideal situations, but to remove several conceptual difficulties. Remarks are presented on the role of idealization in microphysics. (shrink)