D O C U M E N T 3 2 8 D E C E M B E R 1 9 2 8 3 1 5 I sent the enclosed manuscript “On the Axiomatics of the Five-Dimensional Theory of Relativity”[3] some time ago in a somewhat different version for publi- cation to the Naturwissenschaften (J. Springer, Berlin), and it was rejected. In the hope that it will perhaps be of interest to you, esteemed professor, I take the liberty of sending you my work. If you are of the opinion that this small article should in fact be published, I would humbly request that you submit one of the en- closed copies to whatever journal you feel to be appropriate.[4] I should like to add a few words here concerning an objection that was raised by Mr. R. Zaykoff (Sofia) in opposition to five-dimensional electrodynamics (in the sense of Kaluza-Klein-Einstein).[5] He wrote that the electromagnetic equations that I obtained are nonlinear and therefore “are complete nonsense.” However, the geometric treatment of the field equations employed in my recent works yields pre- cisely and without making use of any new hypotheses—merely from the cylindri- cal condition—the most general form of the well-known Maxwell equations that is, equations that are linear through and through.[6] How can it then be that they can be linear when they stand immediately beside the nonlinear equations of gravita- tion? This is a result of 1) the principle of projection (perpendicular to the direction of the fifth dimension), and 2) the cylindrical symmetry. An example: Mr. Zajkov points out my form of the vacuum equations written in five-dimensional, covariant form, they are: . Now the projection (in the special “Z-coor- dinate system”): for , thus gives, once again, the well-known vacuum equations . The[7] article “On the Axiomatics of the Five-Dimensional Theory of Relativi- ty” leads, just like the whole of Riemannian field theory, precisely to classical elec- trodynamics, and thus evidently refers only to macroscopic physics. In spite of all the problems that are posed by microscopic physics, I remain con- vinced that the space-time concepts are fundamental there also they need only be refined. This has been the goal of my efforts in recent years. I hope soon to be able to publish an article in which I can explicate this refine- ment, in the sense of introducing the complex quantities and matrices that play such an important role in quantum mechanics—as purely geometric concepts. It is indeed a fact that the treatment of time is complex! As a special case, one obtains macroscopic electrodynamics, whereby one is led quite naturally to a five- dimensional approach. Respectfully yours, H. Mandel M i 1 2 -- M 2i = i 0 = i 14 = Mi 0 =