Background
Willem de Sitter was born on May 6, 1872 in Sneek, Netherlands.
(Kosmos : six lectures on development of structure of the ...)
Kosmos : six lectures on development of structure of the universe : Lowell Institute Boston 1931i ; H. A. Baldwin
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Astronomer mathematician physicist
Willem de Sitter was born on May 6, 1872 in Sneek, Netherlands.
De Sitter studied mathematics at the University of Groningen and then joined the Groningen astronomical laboratory. At the University of Groningen, he worked with Jacobus C. Kapteyn, head of the astronomical laboratory.
De Sitter had an interest in alternatives to Newton’s theory of gravitation even before Einstein’s theory of general relativity.
In 1905 Henri Poincaré had suggested a special-relativistic (and non-Einsteinian) theory of gravitation that five years later was formulated in a different way by H. A. Lorentz.
In a paper of 1911 de Sitter examined in detail this kind of theory and its astronomical consequences, concluding that Poincaré’s theory predicted an additional perihelion advance, which in the case of Mercury amounted to 7’15” per century. These articles introduced Einstein’s theory to the English-speaking world, and it was on the basis of them that Eddington wrote his important Report on the Relativity Theory of Gravitation in 1918. In the fall of 1916 de Sitter discussed the theory with Einstein, and the discussions led Einstein to attempt to apply his theory to the universe at large. The result was Einstein’s closed or spherical model of 1917, incorporating the cosmological constant (Λ). Einstein originally believed that his static, matter-filled model was the only solution to the cosmological field equations. However, in his third report to the Royal Astronomical Society of 1917, de Sitter showed that there exists another solution, corresponding to an empty universe with Λ = 3/R2 and spatially closed in spite of its lack of matter (R denotes the radius of curvature). Although the de Sitter model would eventually be seen as representing an expanding universe, to de Sitter and his contemporaries it represented a static space-time. When Einstein was confronted with de Sitter’s alternative, he was forced to accept it as a mathematical solution to the field equations, but he considered it a toy model with no physical significance. In his third paper to the Monthly Notices, de Sitter showed that if a particle was introduced at some distance from the origin of a system of coordinates, it would appear as moving away from the observer. Moreover, he showed that clocks would appear to run more slowly the farther away they were from the observer. Because frequencies are inverse time-intervals, light would therefore be more redshifted the larger the distance between source and observer. De Sitter was careful to point out that although the redshift corresponded to a Doppler shift, it was not caused by a recession but by the particular space-time metric he used. In spite of the red-shift built into de Sitter’s model, it was thought of as static. Keeping abreast of recent astronomical observations in spite of the war, de Sitter suggested that the predicted effect might be related to the measurements of (apparent) radial nebular velocities reported by Vesto Slipher at the Lowell Observatory. This was the first suggestion that Einstein’s theory might have connections to the observations of nebular redshifts. With a mean radial velocity of 600 km/s and an average distance of 10 parsecs, he found R = 3×1011 astronomical units. At the end of his 1917 paper de Sitter compared the two rival world models with available astronomical data. It was seen as particularly interesting because of its connection with the redshift observations of spiral nebulae, which by the early 1920s left little doubt that there was a systematic recession.
In an examination in 1925 of de Sitter’s line element, Georges Lemaître transformed it in such a way that the space part increased with time, yet without concluding that the model described an expanding universe. When, in spring 1929, Edwin Hubble published the celebrated paper in which he demonstrated the linear red-shift-distance relationship, he suggested that the relation might represent “the de Sitter effect. ” However, at that time Hubble did not interpret the redshifts as Doppler shifts caused by the recession of the galaxies.
At a meeting of the Royal Astronomical Society on 10 January 1930, Eddington and de Sitter reached the conclusion that because neither of the solutions A and B had proved adequate, interest should focus on nonstatic solutions. Shortly thereafter the two astronomers “rediscovered” a paper Lemaître had published in 1927 and in which he had derived a model for an expanding universe. In the light of Hubble’s new measurements, Lemaître’s theory appeared as convincing evidence that the universe is indeed in a state of expansion. De Sitter now abandoned his solution B and immediately began to develop expanding models of the type suggested by Lemaître. In June 1930 he presented his own version of the expanding universe, including a derivation of the Hubble law (v = Hr) and a recession constant of H = 490 km/s/Mpc, not far from Hubble’s value. One month later he presented a full investigation of Lemaître’s theory which he extended to cover also dynamical solutions that had not been considered by Lemaître. Interestingly, he included among his models big-bang solutions corresponding to R(t = 0) = 0, the same kind of model that Lemaître would propose in 1931. However, whereas Lemaître considered it a model of the real universe, to de Sitter it was just a mathematical solution of no particular physical importance. In his work on Lemaître-like expanding models, de Sitter kept to the cosmological constant, which he found to be a useful quantity, although one whose physical meaning was admittedly unclear. Back in 1917 he had shared Einstein’s opinion that it was “somewhat artificial, ” but he had no strong feelings about the constant and tended to consider it as no stranger than other constants of nature. It is also worth recalling that de Sitter was the first to estimate the value of the cosmological constant: in a letter to Einstein of 18 April 1917 he stated that the constant was certainly smaller than 10-45 cm-2 and probably smaller than 10-50 cm-2. Although de Sitter was an enthusiastic advocate of the expanding universe, his advocacy did not extend to cosmological models of a finite age. Given his doubts with respect to such models it is noteworthy that he contributed significantly to the early history of big-bang theory, namely in a brief paper of 1932 written jointly with Einstein. The Einstein-de Sitter model made no use of the cosmological constant and assumed space curvature to be zero. It follows that the matter density is given by ρc = 3H2/8πG, what in later literature became known as the critical density (corresponding to Ω ≡ p/pc = 1). The expansion of the Einstein-de Sitter universe follows R(t) ~ t2/3, which means that the age is finite and given by 2/3H. However, Einstein and de Sitter did not write down the variation of R(t), and neither did they note that it implies an abrupt beginning of the world. The Einstein-de Sitter model came to be seen as a typical big-bang model, but in 1932 neither Einstein nor de Sitter seems to have considered it important. With the value of the Hubble constant accepted at the time, the age of their model universe would be 1. 2 billion years, which was much less than the age of the stars (and even less than the age of the Earth). Worried about the age paradox, de Sitter never felt at home with the big-bang theory. At a meeting of the British Association for the Advancement of Science in the fall of 1931 he emphasized that the age paradox was a genuine dilemma that somehow might mean that the expansion of the universe and the evolutionary changes of stars were unconnected processes, to be understood in different ways. He apparently preferred two kinds of models at the time, neither of them being the Einstein-de Sitter model. The other possibility was a model in which the universe had contracted during an infinite time and then, after having passed a minimum, started to expand and would continue to do so indefinitely. These views were decidedly empiricist and inductivist in the sense that he stressed that physical theory must begin and end in observation.
If a theory was based on a priori principles or went outside the observational realm it was metaphysical, and de Sitter strongly disliked metaphysics. Now cosmology is concerned with the universe as a whole, something which is not observable, and it relies on tremendous extrapolations. He believed Einstein’s general theory of relativity belonged to the first class, that it was essentially an empirical theory, uncontaminated by metaphysics. At the same time, he found Eddington’s ambitious attempt to connect cosmology with micro-physics to be objectionable because it rested on speculations and unverifiable hypotheses. It was also for philosophical reasons that he rejected Edward Arthur Milne’s alternative world model without examining it closely. For example, the steady-state universe of the 1950s was geometrically described by de Sitter’s metric, which was also used in the inflation theories of the very early universe that were developed in the 1980s.
(Kosmos : six lectures on development of structure of the ...)
Member of the Royal Netherlands Academy of Arts and Sciences (1912), foreign member of the Royal Astronomical Society