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E. Cartan’s attempt at bridge-building between Einstein and the Cosserats – or how translational curvature became to be known as torsion

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Abstract

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.

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  • 05 May 2020

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A French version of this article appears in E. Haffner, D. Rabouin, eds. 2019. L’épistémologie du dedans. Mélange en l’honneur d’Hourya Benis-Sinaceur. Paris: Garnier.

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Scholz, E. E. Cartan’s attempt at bridge-building between Einstein and the Cosserats – or how translational curvature became to be known as torsion. EPJ H 44, 47–75 (2019). https://doi.org/10.1140/epjh/e2018-90059-x

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