4 2 6 D O C . 4 4 3 G E N E R A L R E L A T I V I T Y A N D M O T I O N electrons are present at the same time and at a finite distance from each other, and if they move just as assumed above, then they determine the field , which likewise satisfies the field equations. The latter follows from the linearity of the field equations. From this it follows, however, that the law of motion is logically independent of the field equations.[2] This circumstance of the heterogeneous basis of electrodynamics is especially disturbing because the motion of electrically charged particles is determined by to- tal differential equations, whereas the behavior of the field is determined by partial differential equations. Mie tried to get rid of this blemish by attempting to formu- late a continuum theory of electrically charged particles. In that theory, the compo- nents of the current density are viewed as continuous functions that belong to the “field” just like the electromagnetic field components do and additional field equations were supposed to completely causally constrain the behavior of the cur- rent density as well. Although this attempt has not yet led to any success, it has re- mained a dominant program beyond the domain of pure electrodynamics (Weyl, Eddington). The underlying general thought is to be understood as follows: physi- cal reality as a whole is described by a singularity-free field that describes not only “empty space” but also the material particles. The corresponding law of nature is completely governed by partial differential equations. In this way, Mie sought to overcome the above described dualism, which disturbs any systematic mind. What does the general theory of relativity look like when considered from this point of view? Is the dualism (field law)–(law of motion) present here, too? The situation is not so simple here. Let us distinguish various perspectives.[3] The first perspective is modeled after Newton’s theory. In its gravitational theory it also yields 1. the field law of empty space ( ), 2. the law of motion of a material point (the geodesic equation).[4] The second perspective amends the field law by introducing the energy tensor of matter (and of the electromagnetic field):[5] . If one assumes that no singularities should exist, then this equation gives a theory that is analogous to Mie’s. The theory requires an amendment that cannot be ob- tained by the relativity principle alone: the ’s must be expressed by some sort of (continuous) field quantities, and the differential equations determining them must be given. Only then would we have a complete theory.[6] f1 f2) + ( [p. 3] R i k 0= Tik R i k 1 2 -- - δikR¹ – © § · Tik + 0 = Tik