Dimensional Analysis and Scaling

This group gathers theorems that use the units and dimensions of physical quantities to constrain what a law can look like, without solving the underlying equations. The central result is the Buckingham pi theorem, a key theorem in dimensional analysis which says that a physically meaningful equation among a set of variables can be rewritten in terms of dimensionless combinations of them, so that the validity of a law does not depend on the choice of unit system. Related results about similarity and the scaling of physical systems belong here as well. Theorems that derive a specific conservation law or response relation from a symmetry or a dynamical equation belong in the other mathematical physics groups.