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

摘要

Elie Cartan's generalisation 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.