Albert Einstein and the fifth dimension. A new interpretation of the papers published in 1927
In 1927 Einstein sent two brief communications to the Prussian Academy of Sciences on Kaluza's five-dimensional theory. In his Einstein biography, Abraham Pais asserted that he could not understand the reasons that pushed Einstein to communicate his work. Indeed, Einstein's paper seems to be very close to Oskar Klein's approach, published in 1926. The question seems to be yet unanswered, also in recent works. We analysed the differences between Einstein's and Klein's work and we propose a new interpretation of Einstein's approach. In 1927, he tried to use Weyl's scale invariance in order to construct a theory covering macroscopic as well as microscopic phenomena. In constructing a five-dimensional action, Einstein used in a modern way the idea of ``gauge invariance''. Furthermore, we propose an additional motivation for the fact that he did not mention Klein's and Vladimir Fock's contributions in his first communication and we show further evidences which would confirm also Paul Halpern's recent proposal. As a consequence of our interpretation of the role of conformal transformations, we suggest that in 1927 Einstein did not consider the fifth dimension as real and that his approach, unlike Klein's attempt, cannot be considered inconsistent.