A generalization of the relativistic theory of gravitation

Every attempt to establish a unified-field theory must start, in my opinion,from a group of transformations which is no less general than that of the con-tinuous transformations of the four coordinates. For we should hardly be suc-cessful in looking for the subsequent enlargement of the group for a theory basedon a narrower group. It is further reasonable to attempt the establishment ofa unified theory by a generalization of the relativistic theory of gravitation.Such a generalization, which does not seem to have been discovered so far, isdescribed in the following.If we speak about a unified theory we have two possible points of view, whosedistinction is essential for the following:(1) That the field appear as a unified covariant entity. As an example I citethe unification of the electric and the magnetic fields by the special theory ofrelativity. The unification here consists in this that the entire field consideredis described as a skew-symmetric tensor. The basic group of Lorentz trans-formations does not enable us to split this field independently of the system ofcoordinates, into an electric and a magnetic one.(2) Neither the field equations nor the U1amiltonian function can be expressedas the sum of several invariant parts, but are formally unified entities. Alsothis (weaker) criterion of uniformity is satisfied in our example of the specialrelativistic description of Maxwell's equations.The theory we shall describe is unified according to criterion (2), but not ac-cording to criterion (1). Such a theory is to be considered unified only in alimited sense.