Abstract

The manifold of space and time in which physical events evolve permits a subdivision of laws dependent or independent of a universal metric in the form of a metric tensor. Dimensional analysis and geometric transformation theory shed light on this aspect if the mass unit is replaced by an action unit. One so obtains a systematic separation between geometric and physical units of reference. These criteria permit the delineation of a subdivision of metric-free laws, especially a category of metric-free global relations culminating in a set of 1,2 and 3-dimensional residue integrals; the residues of which can be assessed as counting elementary flux, charge and action quanta. The charge counter is simply the Amp?re-Gauss law of Maxwell theory. The flux and action counters have traditionally been viewed as asymptotic byproducts of Schroedinger's equation. Since, the Amp?re-Gauss law is taken to have universal macro-micro validity, it is now reasonable to extend similar basic exactness also to the flux and action counters. The Schroedinger equation now emerges as a derived entity, applicable to ensembles of phase and orientation randomized identical systems. Schroedinger's own recipe for obtaining his wave equation then graduates to the level of a derivation; thus establishing its position as a tool for primeval ensembles while excluding single system applications.