Friedrich Kottler

“ Infinitely thin spacetime-threads as an image of a pointlike charge. pointlike charges in the mathematical sense of this word do not exist; potentials and fields would indeed become infinitely large within them. The employment of pointlike sources in potential theory is only legitimate in the integral representation of the potential, or otherwise as approximation at distances which are not infinitely small. The same also holds in our case. Therefore we have to imagine the pointlike charge as physically very small. However, the individual points of this charge will exert forces upon each other. ”

“ It also cannot act upon a later position of itself; because this would require superluminal speed. Outside of the world line there should by now charges though. If we therefore extend the integral
over a piece of which does not contain the world line , it will (being extended over a charge-free space) vanish. This is indeed a known property of the ponderomotive force of the electron theory of Lorentz. ”

“ Now, it cannot be done without making assumptions on the shape of the infinitely thin spacetime-thread. Since we do not want to make them, we have to confine ourselves with an approximation. So let the world line of the charge be given, for instance as a function of the arc. The pointlike charge cannot act on itself ”