Einstein’s Further Considerations on the Generalized Kaluza Theory

We identify Einstein’s sketches on projective geometry with his program of finding particle solutions for the Einstein–Bergmann approach. In order to find particle solutions, Einstein considered a special ansatz for the metric components of the five-dimensional theory and plugged them either into the field equations or into the respective Noether identities. He also introduced power series expansions for the various metric coefficients and recast the differential equations into algebraic equations. Einstein then searched for solutions for the coefficients in terms of particle solutions. Therefore, he required spherical spatial symmetry, periodicity, and quantum conditions for the 5th dimension, time-like stationarity, regularity at the origin, a certain fall-off at spatial infinity, and integrability. As Einstein did not publish on these ideas, the details can only be found by a meticulous analysis of Einstein’s working sheets. In addition, we also take into account contemporary correspondence between Einstein and his assistants.