3 0 0 D O C . 3 1 3 O N C U R R E N T S T A T E O F F I E L D T H E O R Y Apart from the riddle of quanta, from whose solution we are, in my opinion, still very far in spite of very promising beginnings, the field theory can only become satisfactory when it has combined the entities of the electric and the gravitational fields in such a way that they appear as the unified structure of the four-dimensional space-time continuum. For the solution of this problem, our experience— apparently—gives us no clues however, we may hope to find some among the re- sults of a completed theory obtained speculatively, results that may be tested by ex- perience. For the solution of this problem, there is a theoretical idea initiated by H. Weyl that has been generalized by Eddington, as well as a second idea that has occurred to me in recent times.[6] In the following, I will attempt only to expound the metri- cal structures of the four-dimensional continuum upon which the essentials of these theories are built, and then to consider my own idea in somewhat more detail. All the theories have the following in common: The world is taken to consist of a four-dimensional continuum whose individual points P are associated with the spatio-temporally not extended physical point events. Each such point is assigned a quadruplet of coordinates (x 1 , x 2 , x 3 , x 4 ) in such a way that “spatio-temporally neighboring” events correspond to neighboring values of the coordinates. At every point, there is an infinitesimal cone (the “light cone”) whose envelope points P ' are characterized by the property that light signals emitted at the point P can reach them. This cone is described—referred to an infinitesimal local coordinate sys- tem—by the equation1 , (1) or, in the arbitrary coordinate system (x 1 … x 4 ), by the equation . (2) In this sense, the spatial functions g μν , which are defined, according to what has thus far been said, only up to a factor λ, express a physically real quality of space that is, the law of propagation of light pulses. According to Weyl’s theory, all physical entities, such as the gravitational field, the electromagnetic field, the behavior of rulers and clocks (the metric field), etc. are to be attributed solely to this structure. Indeed, this theory encompasses along with gravitation also the electromagnetic field, insofar as it leads naturally to the existence of four quantities φ μ , whose antisymmetric derivatives have the character of a tensor. Its weakness was recognized from the beginning to lie in the fact that it does not describe the elementary facts of the metric i.e., that the behavior of rul- ers or clocks is independent of their previous history.[8] 1 The negative sign of the last term can be considered to be converted to a positive quantity by Minkowski’s procedure of appropriate application of imaginary quantities.[7] [p. 128] dx 1 2 dx 2 2 dx 3 2 dx 4 2 – + + 0 = g  dx  dx  0 = [p. 129]