General Relativity Theory

Abstract

In Appendix III of the fifth edition of his book Space, Time, Matter [15] henceforth cited as W (which has not been translated into English), Hermann Weyl derived for the first time, motivated by cosmological considerations, the general frequency shift formula for sources and observers moving arbitrarily in a general spacetime. In his discussion of cosmology (W, 39) he argued for a non-stationary model. In support of this he cited astrophysical considerations (stellar ages and motions), used essentially Olbers’ argument against Einstein’s static model of 1917 [3], emphasized the significance of initial rather than (spatial) boundary conditions in GRT in relation to the difference between past and future, and asserted (in 1922!): “The present state of the system of stars on the sky does not resemble a final statistical state. The small stellar velocities are due to a common origin rather than to an adjustment, and it appears that the velocities between distant celestial objects on average increase with their mutual separations.” (My translation and underlining.) Weyl then constructed a corresponding model, an isotropically expanding substratum which occupies an initially small, but monotonically growing part of de Sitter’s hyperboloidal, globally non-stationary spacetime [7] depicted in Fig. 1, and applied to it his frequency shift formula. Using Slipher’s red shift data and Lundmark’s estimate of the distance of the Andromeda nebula, he obtained a ‘world radius’ (Hubble radius) of about 109 light years corresponding to a ‘Hubble constant’ of about 103 km/s/Mpc—6 years ahead of