ANALOGY BETWEEN SCALE SYMMETRY AND RELATIVISTIC-MECHANICS - I - LAGRANGIAN-FORMALISM

Using only the logarithm of physical quantities, we show that the equi valence of all systems of units is deeply analogous to symmetry by tra nslation in mechanics. Similarly, the equivalence of all systems of un its and subunits helps to generalize usual dimensional analysis, in a curious analogy with speed relativity in mechanics. This analogy leads to nontrivial practical applications when applied to random fields, w hose moments combine measurements at different scales.