Singular extremals in dimensional analysis

Abstract

We suggest an extremality principle for using in classical dimensional analysis; it is stated in the form of a theorem and its corollaries, thanks to which dimensional analysis shapes into a theory substantially extending the possibilities of classical analysis in discovering new laws of nature, predicting new fundamental physical constants, and solving difficult problems. We show by examples that all quantities in nature are connected by hierarchical relations, and the notion of extremality which we introduce makes it possible to obtain new fundamental results in physics.