## Willem de Sitter

**-**

## Sitter, Willem De

# SITTER, WILLEM DE

(*b*. Sneek, Netherlands, 6 May 1872; *d*. Leiden, Netherlands, 20 November 1934), *astronomy, cosmology*. For the original article on de Sitter see *DSB*, vol. 12.

This supplement to Adriaan Blaauw’s article in the *Dictionary of Scientific Biography* focuses on de Sitter’s important contributions to relativistic cosmology and also calls attention to his views on the methods and nature of science. The bibliography includes only works not mentioned in Blaauw’s article.

**Theories of Gravitation** About 1910, after he had become professor of astronomy in Leiden, de Sitter’s main occupation was with celestial mechanics, but this was only one of his research fields. He 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. He showed that although the special-relativistic force law could be brought to agree with observations, because of its flexibility (it contained several free parameters) it could not be refuted. At any rate, with the advent of general relativity the Mercury anomaly was fully explained without special hypotheses, and de Sitter immediately turned his interest to the new theory.

As a foreign member of the Royal Astronomical Society, he was invited by Arthur Stanley Eddington (who then served as the society’s secretary) to produce an account of the new theory, which he did in three articles in the *Monthly Notices*. 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/*R*^{2} and spatially closed in spite of its lack of matter (*R* denotes the radius of curvature). De Sitter termed his new model solution B, to distinguish it from Einstein’s solution A. Compared with Einstein’s model, de Sitter’s was complex and difficult to conceptualize, in particular because it was unclear how to distinguish the properties of the model itself from those properties that merely reflected a particular coordinate representation of it. 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* = 3×10^{11} astronomical units. At the end of his 1917 paper de Sitter compared the two rival world models with available astronomical data. Adopting Jacobus Kapteyn’s estimate of a density of about 80 stars per 1000 cubic parsecs, he found that on Einstein’s model the radius *R* would be about 10^{12} astronomical units and the total mass of the universe about 10^{12} sun masses.

Although de Sitter’s model, being devoid of matter, may seem a very artificial candidate for the real world, it soon became a foundation for further theoretical work, both among astronomers and mathematicians. 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.

** Willem de Sitter. AP IMAGES** .

**The Expanding Universe** 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 *ρ*_{c} = 3*H*^{2}/8π*G*, what in later literature became known as the critical density (corresponding to Ω ≡ *p/p*_{c} = 1. The expansion of the Einstein–de Sitter universe follows *R*(*t*) ~ *t*^{2/3}, which means that the age is finite and given by 2/3*H*. 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. He briefly considered the idea in a 1931 paper in the Italian journal *Scientia*, but only to conclude that it was implausible. 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. As one possibility he considered a universe of the Lemaître-Eddington type, that is, a model slowly starting its expansion from a stationary state. 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. In a paper of 1933 he discussed the contraction-expansion scenario, which, he argued, might provide a solution to the paradox of stars being much older than the universe.

**An Empiricist Astronomer** De Sitter’s mind was not of the philosophical kind, but on several occasions, especially in connection with cosmology, he nevertheless expressed his views about the methods and philosophical foundation of science. 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. De Sitter realized that this was a problem, but of course without drawing the conclusion that cosmology is therefore non-scientific or metaphysical. He always emphasized the danger of extrapolating beyond the observable part of the universe, yet he found it to be acceptable so long as it was understood that models of the entire universe inevitably depend on “our philosophical taste.” In *Kosmos*, a book published 1932, he stated that the concept of the universe was after all a hypothesis, and he suggested that it might have properties that would be contradictory and impossible for a finite material structure.

In agreement with his preference for the inductive-empirical method, de Sitter tended to reject theories based on hypotheses and deductions. 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. Not only was this model deduced from a priori assumption, it also had no observable consequences— hence from de Sitter’s point of view it was hardly a scientific theory. Willem de Sitter died in the fall of 1934 and was thus spared the experience of seeing how popular (and controversial) Milne’s system of kinematic relativity became in British cosmological circles.

De Sitter’s greatest contribution to cosmology was probably his theory of 1917 which in modernized versions continued to play a role many years after his death, understood in the early twenty-first century as a model of an exponentially expanding universe. 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. In the inflationary model, de Sitter’s solution relates to a universe dominated by vacuum energy or, equivalently, the cosmological constant.

## SUPPLEMENTARY BIBLIOGRAPHY

*De Sitter’s unpublished papers and correspondence are in the Collectie-De Sitter, Archive of the Leiden Observatory, Huygens Laboratory*.

### WORKS BY DE SITTER

“On the Bearing of the Principle of Relativity on Gravitational Astronomy.” *Monthly Notices of the Royal Astronomical Society*71 (1911): 388–415.

“On Einstein’s Theory of Gravitation and Its Astronomical Consequences: Third Paper.” *Monthly Notices of the Royal Astronomical Society*78 (1917): 3–28.

“The Expanding Universe: Discussion of Lemaître’s Solution of the Inertial Field.” *Bulletin of the Astronomical Institutes of the Netherlands* 5 (1930): 211–218.”

The Expanding Universe.” *Scientia* 49 (1931): 1–10.

With Albert Einstein. “On the Relation between the Expansion and the Mean Density of the Universe.” *Proceedings of the National Academy of Sciences* 18 (1932): 213–214.

“On the Expanding Universe and the Time-Scale.” *Monthly Notices of the Royal Astronomical Society*93 (1933): 628–634.

### OTHER SOURCES

Eddington, Arthur S. “Obituary: Prof. Willem de Sitter.” *Nature 134* (1934): 924–925.

Gale, George. “Dingle and de Sitter against the Metaphysicians; or, Two Ways to Keep Modern Cosmology Physical.” In *The Universe of General Relativity*, edited by A. J. Kox and Jean Eisenstaedt. Boston: Birkhäuser, 2005.

Kerzberg, Pierre. *The Invented Universe: The Einstein–de Sitter Controversy (1916–17) and the Rise of Relativistic Cosmology*. Oxford: Clarendon Press, 1992.

Kragh, Helge. *Cosmology and Controversy: The Historical Development of Two Theories of the Universe*. Princeton, NJ: Princeton University Press, 1996.

Schulmann, Robert, et al., eds. *The Collected Papers of Albert Einstein*. Vol. 8, part A. Princeton, NJ: Princeton University Press, 1998.

*Helge Kragh*

## Sitter, Willem De

# SITTER, WILLEM DE

(*b*. Sneek, Netherlands, 6 May 1872; *d.* Leiden, Netherlands, 20 November 1934)

*astronomy*.

De Sitter was the son of L. U. De sitter, a judge, who became president of the court at Arnhem, and T. W. S. Bertling. After preparatory education at Arnhem he entered the University of Groningen, where he studied mathematics and physics. Later he became interested in astronomy while participating (under Kapteyn’s guidance) in the work of the astronomical laboratory. From 1897 to 1899 he worked under David Gill at the Royal Observatory in Cape Town, South Africa, and next served as an assistant to Kapteyn at Groningen until 1908, when he was appointed professor of astronomy at the University of Leiden. From 1919 until his death he also was director of the Leiden observatory.

De Sitter’s main contributions to astronomy lie in the fields of celestial mechanics (particularly his research into the intricate problem of the dynamics of the satellites of Jupiter), the determination of the fundamental astronomical constants, and the theory of relativity applied to cosmology. He also contributed significantly, during his early years, to stellar photometry and to the measurement of stellar parallaxes in the context of Kapteyn’s general program of researches on the structure of the Milky Way. Throughout his career De Sitter often acknowledged that his scientific approach was strongly influenced by Kapteyn and Gill.

Of the twelve satellites of Jupiter, four (Io, Europa, Ganymede, and Callisto) are of the fifth and sixth stellar magnitude, whereas the remaining ones are of thirteenth magnitude and fainter. These four, discovered by Römer in 1675 to determine the velocity of light. Their brightness enabled accurate determinations to be made of their projected positions on the sky with respect to Jupiter and to each other, first by heliometer observations and then photographically. De Sitter first participated at the Cape Observatory in the heliometer observations started by Gill and W. H. Finaly and then undertook their reduction and discussion, which led to his doctoral thesis at Groningen, “Discussion of Heliometer Observations of Jupiter’s Satellites” (1901).

Satellites of a planet slightly disturb the motions of each other by their mutual attractions, and a study of these perturbations enables the mass of a satellite to be determined with its orbital elements. This problem was one of high mathematical complexity, requiring critical appreciation of both the value and limitations of the observations. De Sitter was particularly well prepared for the task. The satellites of Jupiter continued to interest him for the next thirty years. At his instigation a series of photographic observations were obtained at observatories in Cape Town, Greenwich, Johannesburg, Leiden, and Pulkovo. Their analysis, and a discussion of old observations of the eclipses of these satellites (by Jupiter) dating from 1668, led to an extensive series of publications by De Sitter in various journals and observatory publications, culminating in his “New Mathematical Theory of Jupiter’s Satellites” (1925).

Shortly after Einstein’s first publication on the restricted principle of relativity, De Sitter discussed its consequences for the small deviations in the motions of the moon and the planets: and after Enstein’s paper on the generalized theory of relativity, De Sitter published (1916–19617) a series of three papers on “Einstein’s Theory of Gravitation and Its Astronomical Consequences” in Monthly Notices of the Royal Astronomical Society. In the third of these papers he introduced what soon became known as the “De Sitter universe” as an alternative to the “Einstein universe” as an alternative to the “Einstein universe.” Because De Sitter was able to discus fully the astronomical consequences of the theory of relativity, and he was among the first to appreciate its significance for astronomy. Apparently De Sitter’s papers contributed uniquely to the introduction into the English-speaking countries of Einstein’s theory during and shortly after World War I, and, for instance, led to Eddington’s solar eclipse eclipse expeditions of 1919 to measure the gravitational deflection of light rays passing near the sun. De Sitter showed that in addition to the solution given by Einstein himself for the Einstein field equation (representing a static universe) a second model was possible with systematic motions—particularly the “expanding universe”-provided the density of matter could be considered negligible. Subsequent work by Georges Lemaitre, Eddington, and De Sitter led to solutions satisfying more accurately both theory and observations, from which modern cosmology has emerged.

Closely related to De Sitter’s work on the satellites of Jupiter were of investigations of the rotation of the earth and of the fundamental astronomical constants. Starting in 1915 with a discussion of the figure and composition of the earth, he tried to combine in a coherent system results from geodetic and gravity measurements with those from astronomical observations. In his paper “Secular Accelerations and Fluctuations of the Longitude of the Moon, the Sun, Mercury and Venus” (1927), De Sitter showed that these phenomena can be understood by assuming that varying tidal friction influences the rotation of the earth as well as the motion of the moon and by assuming internal changes in the moment of inertia of the earth. A comprehensive discussion of the earth. A comprehensive discussion of the fundamental, but observationally interrelated, astronomical constants-for example, the parallax of the sun, the constant of aberration, and the constant of nutation-appeared in “The Most Probable Values of Some Astronomical Constants; 1st Paper; Constants Connected With the Earth” (1927). An unfinished manuscript extending this work was edited and commented upon by D. Brouwer and was published posthumously in 1938 as “On the System of Astronomical Constants.”

As director of the Leiden observatory. De Sitter successfully reorganized the institute, adding an astrophysical department and modern observing facilities. The latter included an arrangement with the Union Observatory in Johannesburg for the use of the telescopes there. This arrangement later led to the establishment of a Leiden station in Johannesburg that was equipped with a twin astrograph donated by the Rockefeller Foundation. These organizational efforts and nearly uninterrupted research were carried out by De Sitter despite repeated periods of illness. In 1933 he published a *Short History of the Observatory of the University at Leiden*, 1633–1933 to commemorate its third centennial. In 1921 he created the *Bulletin of the Astronomical Institutes of the Netherlands*.

De Sitter was president of the International Astronomical Union from 1925 to 1928 and in that capacity did much to reestablish relations between scientists of formerly hostile countries. He received many honors, including the Gold Medal of the Royal Astronomical Society of London (1931), the Bruce Medal of the Astronomical Society of the Pacific, and honorary degrees from Cambridge, Cape Town, Oxford, and Wesleyan universities.

## BIBLIOGRAPHY

I. Original Works. A list of principal publications is given in C. H. Hins’s obituary (seebelow). De Sitter’s works include “Secular Accelerations and Fluctuations of the Longitude of the Moon, the Sun, Mercury and Venus,” in *Bulletin of the Astronomical Institutes of the Netherlands*, **4** no. 124 (1927), 21–38: “The Most Probable Values of Some Astronomical Constants: 1st Paper: Constants Connected With the Earth,” *ibid*., 57– 61: “New Mathematical Theory of Jupiter’s Satellites,” in *Annalen van de Sterrewacht te Leiden***12** , pt. 3 (1925), 1–83, and in his George Darwin lecture “Jupiter’s Galilean Satellites,” which appeared in *Monthly Notices of the Royal Astronomical Society*, **91** (1931), 706–738; *Kosmos, a Course of Six Lectures on the Development of Our Insight Into the Structure of the Universe* (Cambridge, Mass., 1932); *The Astronomical Aspect of the Theory of Relativity* (Berkeley, Calif., 1933); and “On the System of Astronomical Constants.,” D. Brouwer, ed., in *Bulletin of the Astronomical Institutes of the Netherlands*, **8** (19378), 213–231.

II. Secondary Literature. Extensive obituaries are given by C. H. Hins, in *Hemel en Dampkring*, **33** (1935), 3–18, with bibliography; H. Spencer Jones, in *Monthly Notices of the Royal Astronomical Society*, **95** (1935), 343–347; and J. H. Oort, in *Observatory*, **58** (1935), 22–27. De Sitter’s wife, Eleonora De Sitter Suermondt, wrote *Willem de Sitter, een Memsenleven* (Haarlem, 1948), a memoir.

A. Blaauw

## Sitter, Willem de

Willem de Sitter (vĬl´əm də sĬt´ər), 1872–1934, Dutch astronomer and mathematician. He was professor from 1908 at the Univ. of Leiden and in 1919 became director of its observatory. His early work on the motions of Jupiter and its satellites contributed to the downfall of the pre-Einstein celestial mechanics. Using Einstein's formulation of relativity, he theorized that space cannot be in a stable equilibrium, and he concluded that the universe is expanding. He suggested a dynamic universe in which there is motion but no matter, in contrast to Einstein's static universe containing matter but no motion. In the combined Einstein–de Sitter model, the universe is expanding at a decreasing rate that approaches zero. De Sitter's works in English include *Kosmos* (1932) and *The Astronomical Aspect of the Theory of Relativity* (1933).