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.

中文翻译：

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卡坦（E. Cartan）尝试在爱因斯坦（Einstein）和科塞拉特（Cosserats）之间架起桥梁，或平移曲率如何被称为扭转

埃莉·卡丹（ÉlieCartan）的“概念化设计”（généralisationde la courbure）（1922年）源自对爱因斯坦的重力理论和Cosserat兄弟广义弹性理论两者基础的几何结构的创造性评估。在这两种理论中，以无穷小操作的组都起着至关重要的作用。从1922–24年的出版物中判断，Cartan在考虑广义相对论和非标准弹性的双重语境的基础上发展了广义空间的概念。在这种情况下，用旋转量表达新空间的平移曲率是很自然的（通过一种格拉斯曼对偶）。因此，Cartan称其平移曲率为“扭转”，并将其与假设的物质旋转动量耦合，然后在量子力学中遇到自旋。