In this paper we show that the formalism of O. Klein's version of the five-dimensional relativity can be interpreted as a four-dimensional theory based on projective instead of affine geometry. The most natural field equations for the empty space-time case are a combination into a single invariant set of the gravitational and electromagnetic field equations of the classical relativity without modification. This seems to be the simplest possible solution of the unification problem.

When we drop a restriction on the fundamental projective tensor which was imposed in order to reduce our theory to that of Klein a new set of field equations is obtained which includes a wave equation of the type already studied by various authors. The use of projective tensors and projective geometry in relativity theory therefore seems to make it possible to bring wave mechanics into the relativity scheme.

• Received 16 June 1930

DOI:https://doi.org/10.1103/PhysRev.36.810