E. Cartan's attempt at bridge-building between Einstein and the Cosserats -- or how translational curvature became to be known as {\em torsion}

Erhard Scholz

doi:10.1140/epjh/e2018-90059-x

paper

E. Cartan's attempt at bridge-building between Einstein and the Cosserats -- or how translational curvature became to be known as {\em torsion}

arXiv:1810.03872 · doi:10.1140/epjh/e2018-90059-x

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.

arXiv comment36 pp

E. Cartan's attempt at bridge-building between Einstein and the Cosserats -- or how translational curvature became to be known as {\em torsion}

Abstract

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