Eur. Phys. J. H 38, 661–702 (2013)
https://doi.org/10.1140/epjh/e2013-40018-4

Reflections on the four facets of symmetry: how physics exemplifies rational thinking

Laboratoire de Mathématiques et de Physique Théorique, Université François Rabelais de Tours – CNRS (UMR 7350), Fédération Denis Poisson, Parc de Grandmont, 37200 Tours, France

^a e-mail: mouchet@phys.univ-tours.fr

Received: 13 May 2013
Received in final form: 8 October 2013
Published online: 28 November 2013

Abstract

In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While their interrelations are examined closely these four facets of symmetry are scrutinised one after the other in great detail. This decomposition allows us to carefully examine the multiple different roles symmetry plays in many places in physics. Furthermore, some connections with other disciplines like neurobiology, epistemology, cognitive sciences and, not least, philosophy are proposed in an attempt to show that symmetry can be an organising principle also in these fields.