TY - JOUR

T1 - Scale Symmetry and Friction

AU - Sloan, David

PY - 2021/9/6

Y1 - 2021/9/6

N2 - 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.

AB - 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.

KW - shape dynamics

KW - scale symmetry

KW - dynamical similarity

KW - contact geometry

KW - Herglotz action

KW - friction

U2 - 10.3390/sym13091639

DO - 10.3390/sym13091639

M3 - Journal article

VL - 13

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 9

M1 - 1639

ER -