Gerald James Whitrow on Willem de Sitter

“It is clear that at best de Sitter's world, like Einstein's, can be regarded only as a limiting form of the real world. In the Einstein world there is the greatest possible concentration of matter without motion. In the de Sitter world there is motion but no matter. However, with... a special hypothesis due to Weyl... a nebula introduced into the de Sitter world will exhibit a red-shift proportional to its distance, similar to Hubble's observational law.”

“In 1932, Einstein and de Sitter, in a joint memoir, argued that the original objections of 1917 to a world model of finite density in Euclidean space no longer applied if space could be regarded as expanding. ...Einstein and de Sitter therefore constructed a homogeneous world-model of finite density, subject to the field equations of General Relativity in expanding Euclidean space. They found... their model predicted a smoothed-out density of... 4 x 10-28 grammes per cubic centimetre. Although... "perhaps on the high side... we must conclude... it is possible to represent the facts without assuming a curvature of three-dimensional space."”

“Shortly after Einstein published his original memoir on cosmology in 1917, de Sitter constructed an alternative static world-model, which satisfied the same laws of world-gravitation. In this model, unlike Einstein's, space-time has an intrinsic structure of its own, independent of the presence of matter. ...there is ...no matter nor radiation. Nebulae... must therefore be considered as 'test particles,' having no influence on the model as a whole. ...whereas a test particle in Einstein's universe will remain at rest if it has no intitial motion, a similar particle... in de Sitter's world will immediately acquire an ever-increasing velocity of recession from the observer. ...in de Sitter's model space-time is 'hyperbolic'. There is no absolute time, and each observer will perceive a horizon at which time will appear to stand still... This phenomenon... is only apparent, like a rainbow. At any point on the (relative) horizon the time-flux experienced by an observer there will be the same as at the original observer. Thus in de Sitter's world there will be an apparent slowing-down of distant atomic vibrations, if these keep standard time. Consequently the radiation from a distant nebula will appear to be shifted toward the red, due to an increase in wave length corresponding to the decrease in vibrational frequency. This effect... will be supplemented by the Doppler effect, due to the relative recession of the nebula regarded as a test particle.”