Physical, metaphysical and logical thoughts about the wave equation and the symmetry of space-time

D’Alembert’s and similar wave equations are not fundamental relations, but result from a continuity equation and internal dynamics. The continuity equation is considered to be an elementary persistent element in a ’permanently changing world’ (Heraclitus). Generalizing a reasoning by Euler, the principle of sufficient reason implies inertial motion in a homogeneous and isotropic space-time to be straight and uniform. For an empty as well as an homogeneously and isotropically filled universe, the principle of sufficient reason implies the universe to be spatially and temporarily homogeneous and isotropic (in agreement with Cusanus’ metaphysical arguing). With Euclidian metric, the coordinate transformation which leads ds invariant is not the Galileo, but the ’Cusanus transformation’, a rotation in R. The wave equation, however, corresponds to Minkowski’s metric. For physical (there is no Galileo space-time) and logical reasons (asymmetry of space and time coordinates), the Galileo transformation is at most a useful approximation in problems, where Galileo invariant equations are useful.