Different Pathways to the Generalization of Kaluza’s Theory

We recapitulate Einstein and Bergmann’s theory on the generalization of Kaluza’s theory by a detailed derivation of the field equations of the five-dimensional Einstein–Bergmann theory. In this process, we learn about further documents that were written in the same context. For example, a largely unknown manuscript on the five-dimensional approach exists that Einstein referred to as “Washington Manuscript.” This manuscript has never been published and was composed without Bergmann being co-author. There are different versions of this manuscript extant that slightly differ. It is interesting to see that Einstein chose a different structure to discuss substantially the same theory in his Washington manuscript compared with the publication. In fact, the Washington manuscript is based on a more axiomatic formulation that can be connected to earlier statements of Einstein’s on the role of axioms in theoretical physics. We also found several manuscript pages that were written in the context of Einstein and Bergmann’s theory. By our analysis of these research notes, we gain a better understanding of Einstein’s way of thinking and calculating.