Field equations in teleparallel spacetime: Einstein’s Fernparallelismus approach towards unified field theory

A historical account of Einstein’s Fernparallelismus approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a spacetime characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appeared in the period from summer 1928 until spring 1931. In the historical analysis special attention is given to the question of how Einstein tried to find field equations for the tetrads. We claim that it was the failure to find and justify a uniquely determined set of acceptable field equations which eventually led to Einstein’s abandoning of this approach. We comment on some historical and systematic similarities between the Fernparallelismus episode and the Entwurf theory, i.e. the precursor theory of general relativity pursued by Einstein in the years 1912–1915.