E. Cartan’s attempt at bridge-building between Einstein and the Cosserats – or how translational curvature became to be known as torsion★
Faculty of Mathematics/Natural Sciences, Interdisciplinary Centre for History and Philosophy of Science, University of Wuppertal,
42097 Wuppertal, Germany
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Published online: 19 February 2019
Élie Cartan’s “généralisation de la notion de courbure” (1922) arose from a creative evaluation of the geometrical structures underlying both, Einstein’s theory of gravity and the Cosserat brothers generalized theory of elasticity. In both theories groups operating in the infinitesimal played a crucial role. To judge from his publications in 1922–24, Cartan developed his concept of generalized spaces with the dual context of general relativity and non-standard elasticity in mind. In this context it seemed natural to express the translational curvature of his new spaces by a rotational quantity (via a kind of Grassmann dualization). So Cartan called his translational curvature “torsion” and coupled it to a hypothetical rotational momentum of matter several years before spin was encountered in quantum mechanics.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019