I have a question about the nomenclature of the "spin connection". To me "spin" implies quantum mechanics. However, as I understand it, the spin connection is just a part of the covariant derivative of a vector that is written in tetrad (i.e., local frame) components. So isn't the "spin connection" a perfectly valid general relativistic concept that has nothing to do with quantum mechanics? When I go to Wikipiedia and type in "spin connection", I get: "In differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle." which seems to imply quantum mechanics (spinor). Also, what use are tetrads in general relativity? Why can't general relativity be done using a basis induced by the coordinate chart of the spacetime manifold (i.e., the partial derivatives), instead of choosing a new "moving frame" at each point in spacetime?