1927/01/01 by E. T. Whittaker · 2 citations
Physics and Astronomy · #Relativity and Gravitational Theory #Quantum Mechanics and Applications
paper · doi:10.1098/rspa.1927.0003
openalex publication_date 1927/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21
Abstract The well-known theorem that the motion of any conservative dynamical system can be determined from the “Principle of Least Action” or “Hamilton’s Principle” was carried over into General Relativity-Theory in 1915 by Hilbert, who showed that the field-equations of gravitation can be deduced very simply from a minimum-principle. Hilbert generalised his ideas into the assertion that all physical happenings (gravitational electrical, etc.) in the universe are determined by a scalar “world-function” H, being, in fact, such as to annul the variation of the integral ∫∫∫∫H√(−g)dx0dx1dx2dx3 where (x0, x1, x2, x3) are the generalised co-ordinates which specify place and time, and g is (in the usual notation of the relativity-theory) the determinant of the gravitational potentials gvq, which specify the metric by means of the equation dx2 = ∑p, q gvq dxv dxq. In Hilbert’s work, the variation of the above integral was supposed to be due to small changes in the gvq's and in the electromagnetic potentials, regarded as functions of x0, x1, x2, x3.