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Cosmology at the Turning Point of Relativity Revolution. the Debates During the 1920’S on the “De Sitter Effect”

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Cosmology at the Turning Point of Relativity Revolution. the Debates During the 1920’S on the “De Sitter Effect” UNIVERSITA` DEGLI STUDI DI PADOVA Dipartimento di Astronomia Scuola di Dottorato di Ricerca in Astronomia XXI Ciclo (2006 - 2008) Tesi di Dottorato Cosmology at the turning point of relativity revolution. The debates during the 1920's on the \de Sitter E®ect" Direttore della Scuola: Prof. Giampaolo PIOTTO Dipartimento di Astronomia - Universit`adi Padova Supervisore: Prof. Giulio PERUZZI Dipartimento di Fisica - Universit`adi Padova Co-supervisore: Prof. Luigi SECCO Dipartimento di Astronomia - Universit`adi Padova Dottorando: Matteo REALDI UNIVERSITY OF PADOVA Department of Astronomy Ph.D. in Astronomy XXI Cycle (2006 - 2008) Dissertation Thesis Cosmology at the turning point of relativity revolution. The debates during the 1920's on the \de Sitter E®ect" Ph.D. Coordinator: Prof. Giampaolo PIOTTO Department of Astronomy - University of Padova Supervisor: Prof. Giulio PERUZZI Department of Physics - University of Padova Co-supervisor: Prof. Luigi SECCO Department of Astronomy - University of Padova Candidate: Matteo REALDI A mia mamma e mio pap`a. A Gi¶o,Anna, Luca, Vale, Albe, Matteino, Bettax. Alla zia Gisa e alla nonna Laura. A Giuliano e Marinella. Soprattutto, a Michela. La chair est triste, h¶elas!Et j'ai lu tous les livres. (Mallarm¶e,Brise marine) Abstract This thesis is devoted to a critical analysis of the cosmological debates which took place during the 1920's about the so-called \de Sitter e®ect", which represents the linking thread between the 1917 beginning of the- oretical relativistic cosmology and the 1930 ¯rst di®usion and general acceptance of the model of the expanding universe. The de Sitter e®ect is a theoretical redshift-distance relation which can be derived from the cosmological solution of ¯eld equations proposed by de Sitter. This solution and the solution proposed by Einstein repre- sent the ¯rst theoretical relativistic cosmological models. They appeared in 1917, when stars, not yet galaxies, where considered the fundamental pieces ¯lling the universe, and the expanding universe still had to enter modern cosmology. During the 1920's it was just the de Sitter e®ect which played a fundamental role in the ¯rst pioneering attempts to re- late the theoretical relativistic description of the universe to astronomical observations. The models of the universe proposed by Einstein and de Sitter, both based on general relativity, soon appeared as revolutionary tools in order to investigate the properties of the universe as a whole and the connec- tion among space, time and gravitation. In his own spherical model, Einstein proposed a static, ¯nite and unbounded universe. In this uni- verse, according to Machian inspiration, inertia was fully determined by all masses. Dealing with the universe as a whole and its properties, Einstein took into account a hypothetical density of matter which was uniformly and homogeneously distributed through space, foreshadowing VII VIII Abstract what became later known as the Cosmological Principle. Einstein modi- ¯ed his ¯eld equations and introduced a new term with the cosmological constant ¸, which in Einstein's intentions acted like an anti-gravity, in order to express in general relativity his model of a static universe. On the contrary, de Sitter found a suitable solution of ¯eld equations which corresponded to a completely empty and static world. In de Sit- ter's static universe, a spectral displacement was expected from a mass test for the form of the metric and the geodesic equations. This property of de Sitter's universe became known as the de Sitter e®ect. Already in 1917 de Sitter related spectral shifts to velocity and distance of as- tronomical objects through his own relativistic solution. He proposed that spectral displacements which were observed in some stars and neb- ul½ could be interpreted in his static and empty world as an apparent (spurious) velocity of test particles due to the peculiar line element, su- perimposed to a relative (Doppler) velocity which resulted from geodesic equations. The ¯rst contribution led to a quadratic redshift-distance (or equivalently velocity-distance) relation, while the latter involved a linear dependence. This ¯rst suggestion did not pass unnoticed, and during the 1920's several scientists dealt with the properties of de Sitter's universe and pro- posed di®erent formulations of the redshift-distance e®ect which resulted by the metric of such a model. Despite its lack of matter, de Sitter's universe attracted the attention of scientists because it o®ered more ad- vantages than Einstein's one with regard to astronomical consequences and observations. According to Eddington, a general cosmic recession was expected in de Sitter's universe just because of the presence of the cosmological con- stant. Such a tendency of particles to scatter, which Eddington pro- posed in 1923, could roughly account for the astonishing radial velocities measured by Slipher in spiral nebul½, the most part of which revealed receding motions from the observer. Moreover, the geometry of de Sitter's world-model was not uniquely Abstract IX determined, and non-static pictures emerged by appropriate coordinate changes, as done in the 1920's by Weyl, Lanczos, Lema^³treand Robert- son. Their contributions marked the actual departure from the metric of a static universe, by using a stationary frame of de Sitter's model. All of them took into account the empirical evidence of relevant veloci- ties in spiral nebul½, and each of them proposed an own version of the redshift-distance relation in de Sitter's world. In 1924 Wirtz realized that the universe of de Sitter represented a suitable model accounting for redshift and apparent diameter measured in spiral nebul½. In the same year, on the contrary, Silberstein criticized the possibility of a general cosmic recession, and considered the distances of globular clusters in order to verify the de Sitter e®ect. However, the correctness of the method and the results proposed by Silberstein were shortly after denied by Lundmark and StrÄomberg. The de Sitter e®ect could o®er an answer to the question of relevant redshift measurements in nebul½, however there was an ambiguous for- mulation of such a theoretical relation between velocities and distances. Nevertheless, up to 1930 such an e®ect was the only possible, however puzzling, explanation of the redshift problem. A suitable test of redshift relations was possible only with reliable determinations of distance of spiral nebul½. In this controversial picture, the contributions of Hubble marked a turning point in the comprehension of the structure of the universe. Thanks to the revolutionary observations which Hubble furnished dur- ing the 1920's, spiral nebul½ were ¯nally accepted in 1925 as `island universes', i.e. as true extra-galactic stellar systems. In 1929 Hubble con¯rmed that such systems receded relatively to one another, and that their radial velocities linearly increased with distances. The puzzling question of the interpretation of the de Sitter e®ect and the meaning of redshift was solved in 1930, when the cosmology of Lema^³trewas reconsidered in order to explain the cosmic recession of galaxies revealed by Hubble. The model of a non-empty expanding uni- X Abstract verse which Lema^³trehad already proposed in 1927 provided the proper cosmological interpretation of redshift: the displacement of spectral lines was due to the expansion of the universe. The cosmological solution of Lema^³trecorresponded to a \third way" between the Einstein's model, which had matter but not motion, and the de Sitter's model, which had motion but not matter. Since 1930, also the cosmological consequences of similar solutions proposed by Friedmann in 1922 and 1924 were fully acknowledged. In their analysis, Friedmann and Lema^³tre took into account dynamical models of the universe, i.e. they considered the possibility of a not empty, homogeneous and isotropic universe which world-radius increased in time. Static and stationary models were eventually seen as limiting cases of solutions of ¯eld equations describing an expanding universe. As from 1930, the de Sitter e®ect, which during the 1920's represented the ¯rst hint in the intersection between the new theory of gravitation and observed facts, was seen as an e®ect of minor importance, and the expanding universe inaugurated another chapter of modern cosmology. The historical analysis which is below proposed is useful to highlight the richness of contributions, attempts and controversies which appeared in the early connections between astronomical observations and predic- tions o®ered by relativistic cosmology. In particular, scientists involved in the 1920's debates about the de Sitter e®ect approached and thoroughly analyzed some fundamental questions in the framework of relativistic cosmology, such as the nature of redshift measurements, the geometry of space, the assumption of a homogeneous and isotropic universe. Several passages from primary literature, original manuscripts, un- published sources and correspondence among scientists have often been quoted, in order to highlight the very contributions by actors involved in those debates. From the present thesis it emerges the fundamental role played by the de Sitter e®ect in the 1920's debates. It was a very fruitful phase for the introduction of new ideas, discoveries and changes, and the history Abstract XI of that period permits to understand how cosmology developed passing from a sphere of theoretical speculations to a truly empirical science. Riassunto Ci si riferisce alla cosmologia moderna, o scienti¯ca, come alla scienza che studia l'origine e l'evoluzione dell'universo, interpretando il quadro che ne risulta sulla base delle leggi della ¯sica. In questa tesi viene proposta una ricostruzione storica del ruolo svolto dal cosiddetto \e®etto de Sitter" durante le prime fasi della cosmologia moderna. Vengono ricostruiti in particolare i dibattiti cosmologici cen- trati su tale e®etto che ebbero luogo negli anni Venti, prima cio`eche il concetto di universo in espansione facesse la sua comparsa u±ciale nella storia della cosmologia moderna.
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