Willem de Sitter

"The outstanding feature... is the possibility that the velocity-distance relation may represent the de Sitter effect, and hence that numerical data may be introduced into discussions of the general curvature of space. In the de Sitter cosmology, displacement of the spectra arises from two sources, an apparent slowing down of atomic vibrations and a general tendency of material particles to scatter. The latter involves an acceleration and hence introduces the element of time. The relative importance of these two effects should determine the form of the relation between distances and velocities; and in this connection it may be emphasized that the linear relation found in the present discussion is a first approximation representing a restricted range in distance."

"If anything, de Sitter disliked Milne's program even more than Eddington's. In this dislike, he was soon joined by Herbert Dingle. ...de Sitter came to good knowledge of the genuine, actual, empirical basis of astronomical science. Secondly, reducing the observational data from the Jovian satellites practiced the young astronomer's mathematical skills in thorough and useful ways. Such a powerful combination of two skills—empirical, observational skill plus theoretical, mathematical skill—was lacking in the colleagues with whom de Sitter would later practice cosmology—with the interesting exception of Dingle."

"In "Kosmos", de Sitter shows how steps forward in the development of science can be associated with scientists, who considered the Universe from a non-static, dynamic point of view. Charles Darwin is cited as one of the examples. ...From early on, de Sitter was actively engaged in the debate between Einstein, LeMaître, Eddington and others in the significance of the General Theory of Relativity for cosmology. De Sitter found in his preferred solutions of Einstein's field equations that the Universe was expanding and the relative velocity V of recession was expected to be in proportion to the distance r. De Sitter was searching for observational evidence of such a relative recession and turned to Kapteyn for advice on the feasibility..."

"In 1917 de Sitter showed that Einstein's field equations could be solved by a model that was completely empty apart from the cosmological constant—i.e. a model with no matter whatsoever, just dark energy. This was the first model of an expanding universe. although this was unclear at the time. The whole principle of general relativity was to write equations for physics that were valid for all observers, independently of the coordinates used. But this means that the same solution can be written in various different ways... Thus de Sitter viewed his solution as static, but with a tendency for the rate of ticking clocks to depend on position. This phenomenon was already familiar in the form of gravitational time dilation... so it is understandable that the de Sitter effect was viewed in the same way. It took a while before it was proved (by Weyl, in 1923) that the prediction was of a redshifting of spectral lines that increased linearly with distance (i.e. Hubble's law). ..."

"The theorists of the time were still debating whether the universe obeyed Einstein's static model, in which no red-shift is seen, or a model by Willem de Sitter in which the universe is expanding, and distant objects are red-shifted, but the universe contains no matter. ...Few astronomers were aware of the more general expanding universe solutions found by Georges Lemaître, and, especially, Alexander Friedmann, who had found in 1922-24 a complete set of solutions for Einstein's equations for the cosmological problem. Following Hubble's paper it was quickly realized that the expanding universe solutions were the ones that were needed to understand his observations."

"De Sitter made observations in 1913 of double-star systems and became the first astronomer to prove that the velocity of light had nothing to do with the velocity of its source. ...De Sitter ...published three papers entitled "On Einstein's Theory of Gravitation and Its Astronomical Consequences. The first two... explained Einstein's theories, and the third proposed his own interpretation of the astronomical consequences... de Sitter and Einstein published a joint paper in which they proposed there may be in the universe large amounts of matter that does not emit light and consequently has not been detected. This became known as "dark matter"..."

"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."

"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.""

"He [de Sitter] reminds us that in Einstein's paper of November 1915 the Λ term did not appear at all. Hence, Λ had obviously the value zero. Cosmologically speaking, this implies that the curvature of the Universe is proportional to Λ. In 1917, two solutions of Einstein's field equations for a homogeneous, isotropic universe were offered. ...in A the universe has a finite density, whereas in B, the average density is zero ...We are confronted with a static unverse containing matter and having no expansion on the one hand, and on the other an empty universe void of matter and expanding... when these two solutions were constructed, the expansion of the universe had not yet been discovered."

"De Sitter proposed three types of nonstatic universes: the oscillating universes and the expanding universes of the first or second kiind. The main characteristic of the expanding "family" of the first kiind is that the radius is continually increasing from a definite initial time when it had the value zero. The universe becomes infinitely large after an infinite time. In the second kind... the radius possesses at the initial time a definite minimum value... in the Einstein model... the cosmological constant is supposed to be equal to the reciprocal of R2, whereas de Sitter computed for his interpretation the constant to be equal to 3/R2. Whitrow correctly points out the significant fact that in special relativity the cosmological constant is omitted..."