Scale Symmetry and Friction

TL;DR

This paper explores how dynamical scale symmetries in physical systems can be extended to the space of couplings, enabling the reduction of systems to scale-invariant descriptions and revealing friction-like behavior.

Contribution

It demonstrates that scale symmetry extends to coupling space and can be used to derive frictional systems from scale-invariant principles, with applications to celestial mechanics and cosmology.

Findings

Scale symmetry extends to the space of couplings.

Systems can be reduced to scale-invariant descriptions.

Derived systems exhibit friction-like behavior.

Abstract

Dynamical similarities are non-standard symmetries found in a wide range of physical systems that identify solutions related by a change of scale. In this paper we will show through a series of examples how this symmetry extends to the space of couplings, as measured through observations of a system. This can be exploited to focus on observations that can be used distinguish between different theories, and identify those which give rise to identical physical evolutions. These can be reduced into a description which makes no reference to scale. The resultant systems can be derived from Herglotz's principle and generally exhibit friction. Here we will demonstrate this through three example systems: The Kepler problem, the N-body system and Friedmann-Lema\^itre-Robertson-Walker cosmology.