D O C U M E N T 3 0 2 J U L Y 1 9 2 2 2 3 5 should be set, as you did. (Comp[are], however, what is said under 6.) 2) It agrees with this if in the static case you regard as the expression for the inertia of the test mass.[5] For your solution this expression disappears into infinity. The velocity of light measured in the coordinate scale also extends into infinity in all directions toward the value ∞. 3) Even so, I cannot view your consideration as a satisfactory solution to the cos- mological problem at all, because the limiting condition has to be retained otherwise one could not speak of a degeneration of the metric continuum at an infinite distance from the matter.[6] A clock at infinity would simply have to run infinitely rapidly, because the clock is slowed by neighboring matter and its running speed should be determined solely by the matter.[7] A spring with a mass attached is a clock that must operate faster the farther away it is from the bodies. For, what should a finite limiting velocity be determined by, if inertia is ultimately a kind of interaction? The incompatibility between this condition and the fact of small stellar velocities that demand a constant at the limit constitutes one of my arguments for the necessity of spatial closure for the universe.[8] 4) You will also be able to persuade yourself of the inadmissibility of your way out in that you can move from the matter-free space [9] by mere singularity-free transformations to an expression that behaves in infinity like yours. For that, in your argument you need [10] only to be as continuously dependent on [ ] so that it vanishes for small ’s and continuously reaches the value ε for increasing ’s. One thus does not need any masses to make the space behave as you prescribe. So you certainly cannot view this behavior as an expression of the relativity of inertia. 5) The relativity of inertia, or a linkage between the (quasi-static) metric field and the existence of matter can only be achieved for a spatially finite, closed world.[11] 6) I don’t want to uphold the remark I made in my earlier letter about the inertial mass for the reasons mentioned.[12] One could do so, however, in that the equation for the geodetic line be interpreted in the Newtonian manner on the justification that the concept of inertial mass actually only makes clear sense from the stand- point of the Newtonian approach and that for this approach there would therefore be little justification for defining inertial mass from the momentum concept of the general theory of relativity.[13] miκ m γ g44 dx ds 2 -------------------------------κi0 = g44 = g44 gμν const. = ds2 dt2 dx1 2 dx2 2 dx3 2) = ( xi xiBr–ε = r r r
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