Lazare Carnot’s Mechanics: The Beginning of Group Theory in Science

Present paper quickly reviews the main characteristic features of Lazare Carnot’s formulation of mechanics according to the results of the research of the last four decades. Three basic features of its theoretical development are illustrated: 1) Its starting point as declared by Carnot himself, i.e. the principle of virtual works modified in a suitable version for the case of the impact of bodies; the theoretical treatment of this phenomenon avoids the use of the main basic notion of Newton’s theory of mechanics, i.e. the force-cause; 2) The recognition of two basic choices on two dichotomies concerning the entire theoretical physics; his choices are the alternatives ones to Newton’s; 3) The introduction of the group theory in theoretical physics; Carnot was proud to have given birth to “an intermediate science between geometry and mechanics”. The latter novelty is compared with i) René-Just Haüy’s introduction (occurred one year later) of symmetries into crystallography; ii) Evariste Galois’ introduction (occurred fifty years later) of group theory into mathematics; iii) Pierre Curie’s introduction (occurred a century later) of symmetry breaking into theoretical physics; iv) Albert Einstein’s 1905 paper introducing Lorenz group into mechanics. The open problems of a rational re-construction of L. Carnot’s formulation according to two alternative basic choices are suggested.