1 1 2 D O C . 9 2 E L E C T R O N A N D G E N E R A L R E L A T I V I T Y 2) One could consider not permitting all transformations, but only those with a positive substitution determinant. For only the latter can be composed from infini- tesimal transformations yet the transformations considered above had a negative substitution determinant. One recognizes that this is not essential, though, because in each of the interpre- tations of the electric density considered, the latter changes its sign under the sub- stitution This substitution, however, has a positive determinant.[6] Postscript to the Proofs. Further pondering about this difficulty has led me to a possible path of solving it or, at any rate, to deeper insight into the essence of this problem. The difference between the positive and negative elementary particles, which we know through experience, cannot be derived from a theory that merely uses the and as field variables. This is connected to the fact that the electric density scalar ρ cannot be represented unambiguously by the and . For it is the case that , where . The square root occurring here makes it impossible to express the positive and negative electric density separately. As long as this indeterminacy remains, one cannot set up laws in which the sign of ρ plays a role. Rather, there must be a way to determine the electric density ρ and its sign from the field tensors. This is achieved in the following way. For the light cone at every worldpoint, let us take the backward light- cone and the forward lightcone as distinguishable from the outset. This comes down to defining a direction of time a priori, i. e., assigning an arrow to each time- like line element (past → future). x1 x –= y1 y = z1 z = t1 t –= [p. 333] gμν fμν gμν fμν ρ gμνiμiν = iμ ∂xν ∂f μν = ds2 0=