„Die Schönste Leistung der Allgemeinen Relativitätstheorie“: The Genesis of the Tensor-Geometrical Conception of Gravitation

Abstract

One of the most effective ways in which physics and mathematics can influence each other in modern science, especially in developing fundamental theories, is such a use of abstract mathematical theories where all the relevant mathematical quantities and relations are identified with all the basic physical quantities and relations describing a certain class of physical phenomena. Two most fundamental physical theories which appeared in the first quarter of the XX century — the general theory of relativity (GTR) and quantum mechanics — have precisely this mathematical structure. From the mathematical viewpoint, the GTR is the Riemannian geometry and quantum mechanics is a theory of linear self-conjugated operators in the Hilbert space.