Willem de Sitter

Born: 6 May 1872 in Sneek, Netherlands
Died: 20 November 1934 in Leiden, Netherlands

Willem de Sitter's parents were Lamoraal Ulbo de Sitter and Catharine Theodore Wilhelmine Bertling. Lamoraal Ulbo de Sitter was a judge and firmly in the de Sitter family tradition of becoming lawyers. His son Willem was expected to follow the family tradition, but he took a different career path with his love of mathematics and science. Willem attended secondary school in Arnhem, studying at the Arnhem Gymnasium. After graduating from the school, he entered the University of Groningen with the intention of taking a mathematics degree. In addition to his love for mathematics, his enjoyment of physics and carrying out physical experiments grew during his undergraduate years. He obtained permission to assist with experiments being carried out by Hermanus Haga, the professor of physics at the University of Groningen, and as a consequence began to work in the Astronomical Laboratory at Groningen. In the Laboratory Jacobus Kapteyn, the Professor of Astronomy and Theoretical Mechanics, was measuring photographic plates which had been taken by the astronomer David Gill as part of a photographic survey of the southern sky taken at the Cape Town Observatory. Although Kapteyn was the Groningen Professor of Astronomy, he had volunteered to assist in the Astronomical Laboratory since he had no observatory in which to conduct his own observations.

The turning point in de Sitter's life came in 1896 when David Gill visited Kapteyn to discuss progress on the southern sky survey. Entering the Laboratory, Gill saw de Sitter at a measuring machine and the two talked briefly [15]. On :-

... the following morning de Sitter, while having breakfast in his rooms, received a message that Gill wished to speak with him in the laboratory. De Sitter did not possess at that time the fluent command of the English language which he afterwards acquired; Kapteyn was lecturing at the time and Mrs Kapteyn acted as interpreter at the interview. Gill invited de Sitter to come to the Cape as a computer and, as de Sitter afterwards stated in a letter to Gill, "thereby complete my astronomical education - or rather begin it, for up to that time I had never made a speciality of astronomy and intended to become a mathematician."

De Sitter consulted his parents, and decided to take their advice and complete his examinations at Groningen before taking up Gill's offer. He received a Bachelor's Degree in 1897 and left for Cape Town in the summer of that year arriving in August. He worked at the Cape Observatory in South Africa for two years taking part in photometric and heliometer programmes. It was at Gill's suggestion that de Sitter also worked towards his doctorate studying heliometer observations of Jupiter's moons which had been made by Gill in 1891. After de Sitter returned to Groningen in 1899 he was appointed as an assistant in the Astronomical Laboratory and also continued to work towards his doctorate, advised by Kapteyn. He submitted his thesis Discussion of Heliometer Observations of Jupiter's Satellites to the University of Groningen in 1901. Jan Hendrik Oort writes in [13]:-

With the discussion of Gill's heliometer observations of Jupiter's satellites, de Sitter had entered upon the field which seemed so completely to suit his versatile mind: the talent, on one hand, for seeing clearly through the most intricate mathematical problems and dealing practically with them; on the other hand, the critical insight into the value and limitations of observations - an insight which sprang from a very active interest in observations as well as instruments.

On 6 December 1898 de Sitter had married Eleonora Suermondt in Cape Town, South Africa. Eleonora was born in Surabaya, the second largest city in the Dutch East Indies, and she had met de Sitter in the Cape where she was working as a school teacher. Their first child Lamoraal Ulbo was born in Cape Town in September 1899 but sadly died on 10 January 1901 after the family had returned to Groningen. Their other children were: Theodora born on 28 September 1900 in Groningen; Lamoraal Ulbo born on 6 March 1902 in 's-Gravenhage; Aernout born on 5 April 1905 in Groningen; and Agnes born 14 May 1908 in Groningen. Let us record a few details of the lives of two of these children at this point. Lamoraal Ulbo de Sitter became well-known as a structural geologist and died in Nistelrode in 1980. Aernout de Sitter served as director of the Bosscha Observatory in Lembang, Dutch East Indies. After the Japanese invasion of the Dutch East Indies he was arrested and put into a detention camp where he died on 5 September 1944.

Hendricus Gerardus van de Sande Bakhuyzen had been Professor of Astronomy and Director of the University Observatory at the University of Leiden from his appointment in 1872. He retired in 1908 and his duties were split into two, with the chair of astronomy being separated from the directorship of the Observatory. De Sitter was appointed to the chair of astronomy while Ernest-Frederich van de Sande Bakhuyzen, H G van de Sande Bakhuyzen's brother, was appointed as Director of the Observatory. On taking up the chair, de Sitter gave his inaugural lecture on The New Methods in Celestial Mechanics. E F van de Sande Bakhuyzen died in 1918 and in the following year de Sitter was appointed Director of the Leiden Observatory in addition to his professorship. He undertook a complete reorganisation of astronomy at Leiden dividing it into three divisions: Fundamental Astronomy of position or astrometry; Astrophysics; and Celestial Mechanics or theoretical astronomy. Under his leadership it was one of the leading astronomical centres in the world. Oort writes [13]:-

Throughout the years at Groningen, as well as later, de Sitter showed an almost unbelievable activity. In looking through a number of his more important publications, one is struck with the rapidity with which discussions on different topics follow each other and by the amount of thorough critical thinking of which each of these brings evidence. Neither a serious illness from which he suffered during some years, nor the directorship of an observatory which he undertook to reorganise almost entirely, nor his constant activities in many matters connected with the University could slow up the flow of his scientific investigations.

In 1913 de Sitter produced an argument based on observations of double star systems which proved that the velocity of light was independent of the velocity of the source. It put to rest attempts which had been made up until this time to find emission theories of light which depended on the velocity of the source but were not in conflict with experimental evidence.

De Sitter corresponded with Paul Ehrenfest in 1916, and he proposed that a four-dimensional space-time would fit in with cosmological models based on general relativity. He published a series of papers (1916-17) on the astronomical consequences of Einstein's general theory of relativity. He found solutions to Einstein's field equations in the absence of matter. This was significant since Mach had stated a principle that local inertial frames of reference were determined by the large-scale distribution of mass in the universe. De Sitter asked:-

If no matter exists other than the test body, does it have inertia.

De Sitter's work led directly to Arthur Eddington's 1919 expedition to measure the gravitational deflection of light rays passing near the Sun, results which, at that time, could only be obtained during an eclipse. De Sitter, unlike Einstein, maintained that relativity actually implied that the universe was expanding, theoretical results which were later verified observationally and only then accepted by Einstein.

In fact Einstein had introduced the cosmological constant in 1917 to solve a significant problem concerning the universe, which had also troubled Newton before him, namely why does the universe not collapse under gravitational attraction. This rather arbitrary constant of integration which Einstein introduced, admitting it was not justified by our actual knowledge of gravitation, was later said by him to be "the greatest blunder of my life." However de Sitter wrote in 1919 that the term:-

... detracts from the symmetry and elegance of Einstein's original theory, one of whose chief attractions was that it explained so much without introducing any new hypothesis or empirical constant.

In the 1990s observational evidence suggested that the expansion of the universe is accelerating. One way to incorporate this into the relativistic model is to reintroduce the cosmological constant. This remains an extremely active area of research.

In 1932 Einstein and de Sitter published a joint paper in which they proposed the Einstein-de Sitter model of the universe. This is a particularly simple solution of the field equations of general relativity for an expanding universe. They argued in this paper that there might be large amounts of matter which does not emit light and has not been detected. This matter, now called 'dark matter', has since been shown to exist by observing is gravitational effects. However the dark matter postulated by Einstein and de Sitter in 1932 still remains a mystery in that its nature is still unknown but is the subject of major research efforts today.

Although de Sitter is best known for this work on relativity, he made many other contributions of great significance. His doctorate had been on the satellites of Jupiter and he maintained an interest in this topic throughout his life. He used data on eclipses of the satellites dating back to 1668 to produce definitive data on the orbital elements and masses of the four satellites. He published theoretical discussion in three papers of 1918, 1919 and 1925. Finally in 1929 he produced his definitive results, but he was still working on tables of the motions of the satellites when he died in 1934. During his investigations of the timings of the eclipses of Jupiter's moons, he realised that his data was being affected by variations in the speed of rotation of the earth. Immediately de Sitter had another topic for which he had precisely the right skills to make a breakthrough. His study showed that there is varying tidal friction which affects both the earth and the moon and, in addition, sudden changes which occur in the moment of inertia of the earth.

Another study which de Sitter undertook was to refine the data for the fundamental constants of astronomy. Simon Newcomb had published values for these constants in 1895 and in a rather remarkable international agreement in Paris in 1896, it had been decided that the ephemerides of every country in the world should use Newcomb's values for these constants. In 1915 de Sitter published his first paper on improving the values, this one being concerned almost entirely with the figure and composition of the earth. He wrote in the introduction:-

On various occasions I have found myself confronted with the question which would be the best value to adopt for one of the fundamental astronomical constants. We have, of course, the set of constants officially adopted in the national ephemerides ... Some of the adopted constants are inconsistent with each other. This the adopted length of the year and the constant of precession are contradictory, and similarly the mass of the earth and the solar parallax. Newcomb's great work is now more than thirty years old, but it still stands unsurpassed as an example of sound critical discussion. ... I have only been led by the considerations that on the one hand my results may perhaps be useful to others in similar circumstances, and on the other hand that a critical survey like the present may be helpful to guide the efforts of astronomers to those points where they are most needed.

His second paper on the fundamental constants was published in 1927 and dealt with the constants associated with precession, nutation, solar parallax, lunar parallax and the mass of the moon. At the time of his death, de Sitter had almost completed a new updating of these constants.

Many honours were given to de Sitter for his outstanding contributions. He received the Watson Gold Medal from the National Academy of Sciences in 1929. The Medal was presented to him in Washington, USA, by Armin Otto Leuschner, Professor of Astronomy of the University of California and Chairman of the Trustees of the Watson Fund. Leuschner said:-

The privilege accorded me involves a task of unusual difficulty, for the major part of de Sitter's work is in intricate, speculative, and mathematical fields dealing with the perturbations of the motions of bodies of the solar system according to classical celestial mechanics, and with the theory of relativity from a purely speculative point of view as well as in relation to perturbations observed, but not explained, and relativistic theoretical perturbations not perceived or as yet perceivable by observation. I, therefore, beg your indulgence if I fail in a clear presentation of the significance of some of his contributions to science. His intellectual abilities cover so wide a range and penetrate so deeply and so minutely into practical astronomy and the mathematical theories to explain what is observed, that only an intensive study of his brilliant work could do justice to the greatness of the man.

In 1931 de Sitter received the Bruce Medal from the Astronomical Society of the Pacific. Also in 1931 he received the Gold Medal of the Royal Astronomical Society:-

... for his theoretical investigations on the orbits of the satellites of Jupiter, and for his contribution to the Theory of Relativity.

He was elected as President of the International Astronomical Union and served in this capacity from 1925 to 1928.

De Sitter suffered from chest complaints for several years but seemed to overcome them. However he died from pneumonia at the young age of sixty-two years. The following is part of a tribute to him which appeared in the New York Times on 25 November 1934; it is also reproduced in [8]:-

In [de Sitter's] work we see the creative mathematician at his best. He is not a cold, dispassionate juggler of Greek letters, a balancer of equations, but rather an artist in whom wild flights of the imagination are restrained by the formalism of a symbolic language and the evidence of observation. Only the musician can fully grasp what it must have meant to de Sitter to see the cosmos shaping itself in new ways in his formulas. Like musical notes, strange symbols, standing for forces and masses that were divined rather than known, arranged themselves into a coherent message. And when the message came to be read a totally new universe was revealed. Here we have something of the direct personal experience of the outer world, of the significance of nature's wonders, that comes only to a Beethoven or a Milton. The expanding universe of de Sitter must be regarded as something more than an inexorable conclusion drawn from the strictest kind of logic with which the human mind is familiar. It is poetry of a new sort - the scientist's way of writing an epic.

Article by: J J O'Connor and E F Robertson

April 2009

MacTutor History of Mathematics