  A complete geometric unification of gravity and electromagnetism is proposed
by considering two aspects of torsion: its relation to spin established in
Einstein--Cartan theory and the possible interpretation of the torsion trace as
the electromagnetic potential. Starting with a Lagrangian built of Dirac
spinors, orthonormal tetrads, and a complex rather than a real linear
connection we define an extended spinor derivative by which we obtain not only
a very natural unification, but can also fully clarify the nontrivial
underlying fibre bundle structure. Thereby a new type of contact interaction
between spinors emerges, which differs from the usual one in Einstein--Cartan
theory. The splitting of the linear connection into a metric and an
electromagnetic part together with a characteristic length scale in the theory
strongly suggest that gravity and electromagnetism have the same geometrical
origin.
