When considering time and space scales such that the description of the trajectories of these bodies is in the shape of non-differentiable curves, one gets fractal curves of fractal dimension 2. Continuity and non-differentiability yield a fractal space and a symmetry breaking of the differential time element which gives a doubling of the velocity fields. An application of these principles on the motion equation of free particles leads to the occurrence of a supplementary TISE (time independent, Schr dinger-type equation). When using a WKBJ method to solve this equation, one gets some interesting results. In other words, scale transformation laws produce, on the motion equation of free particles under some peculiar assumptions, effects which are analogous to those of a "macroscopic quantum mechanics".