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Scale Symmetry and Friction

Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
Academic Editor: Flavio Mercati
Symmetry 2021, 13(9), 1639;
Received: 20 July 2021 / Revised: 10 August 2021 / Accepted: 26 August 2021 / Published: 6 September 2021
(This article belongs to the Special Issue Shape Dynamics)
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 to distinguish between different theories and identify those which give rise to identical physical evolutions. These can be reduced into a description that 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–Lemaître–Robertson–Walker cosmology. View Full-Text
Keywords: shape dynamics; scale symmetry; dynamical similarity; contact geometry; Herglotz action; friction shape dynamics; scale symmetry; dynamical similarity; contact geometry; Herglotz action; friction
MDPI and ACS Style

Sloan, D. Scale Symmetry and Friction. Symmetry 2021, 13, 1639.

AMA Style

Sloan D. Scale Symmetry and Friction. Symmetry. 2021; 13(9):1639.

Chicago/Turabian Style

Sloan, David. 2021. "Scale Symmetry and Friction" Symmetry 13, no. 9: 1639.

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