{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T00:50:30Z","timestamp":1781743830030,"version":"3.54.5"},"reference-count":47,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T00:00:00Z","timestamp":1630886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2019s principle and generally exhibit friction. Here, we will demonstrate this through three example systems: the Kepler problem, the N-body system and Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker cosmology.<\/jats:p>","DOI":"10.3390\/sym13091639","type":"journal-article","created":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T23:55:22Z","timestamp":1630972522000},"page":"1639","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Scale Symmetry and Friction"],"prefix":"10.3390","volume":"13","author":[{"given":"David","family":"Sloan","sequence":"first","affiliation":[{"name":"Department of Physics, Lancaster University, Lancaster LA1 4YB, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,6]]},"reference":[{"key":"ref_1","unstructured":"Poincar\u00e9, H. (1914). Science and Method, Dover Publications."},{"key":"ref_2","unstructured":"Delboeuf, M. (Popular Science Monthly, 1883). 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