Unified Field Theory with Fifteen Field Variables

Abstract

In the spring of 1946, Professor W. Pauli turned over to the author of this paper galleys of a paper by P. Jordan entitled Gravitationstheorie mit veriinderlicher Gravitationszahl, which was to have appeared in the Physikalische Zeitschrift sometime in 1945, but which was, of course, never published because the Phys. Zeitschrift in the meantime ceased publication. In this paper, Jordan attempted to generalize Kaluza's five dimensional unified field theory by retaining gqs as a fifteenth field variable. Professor Einstein and the present author had worked on that same idea several years earlier, but had finally rejected it and not published that abortive attempt. The fact that another worker in this field has proposed the same idea, and independently, is an indication of its inherent plausibility. Therefore, it seemed worthwhile to review these attempts to ''vary the constant of gravitation and to discuss the possibilities inherent in geometries of this kind. It should be mentioned that the manuscript of Jordan's was entitled I and that the contents of part II had to be surmised by the author. While this report attempts to reproduce the essentials of Jordan's geometrical concepts, the formalism employed is that of the author, which was first presented in the book Introduction to the Theory of Relativity (New York, Prentice-Hall, 1942) and which permits greater clarity of presentation. The critical discussion of this geometry and its physical implications are, of course, solely the author's responsibility.