Willem de Sitter: The Architect of Relativistic Universes

Youth and Mathematical Education

Willem de Sitter was born on May 6, 1872 in Sneek, Netherlands. His father, Lambertus de Sitter, was a judge at the Court of Appeal in Leeuwarden. After secondary education in Arnhem, he entered the University of Groningen in 1889 to study mathematics.

In 1897, he earned his doctorate under the supervision of Jacobus Cornelius Kapteyn (1851-1922) with a thesis on solutions of differential equations in astronomy. He then spent two years at the Cape Observatory in South Africa, where he specialized in the study of binary stars and stellar photometry.

Academic Career and Contributions at Leiden

In 1908, de Sitter was appointed professor of astronomy at Leiden University and director of Leiden Observatory, a position he held until his death. He thus succeeded Hendrik Lorentz (1853-1928), another giant of Dutch theoretical physics.

His main achievements at Leiden included:

• Modernization of the observatory with the acquisition of new instruments
• Development of a theoretical astrophysics research program
• Training of a new generation of astronomers, including Jan Oort (1900-1992)

Cosmological Solutions of General Relativity

De Sitter's most important contributions concern relativistic cosmology. In 1916-1917, he found two exact solutions to Einstein's equations for a universe empty of matter (except possibly a cosmological constant):

De Sitter Universe (1917)

This solution describes an empty universe in exponential expansion, where the scale factor \( a(t) \) grows as \( e^{Ht} \), with \( H \) proportional to the square root of the cosmological constant \( \Lambda \). This solution shows that:

• A vacuum universe can be dynamic (unlike Einstein's static universe)
• The cosmological constant can cause accelerated expansion
• Test particles follow trajectories that move away from each other

Einstein-de Sitter Static Universe (1932)

In collaboration with Einstein, de Sitter proposed a static universe model with a uniform distribution of matter and zero cosmological constant. The metric of this universe is given by:

\( ds^2 = c^2 dt^2 - R^2 \left( \frac{dr^2}{1-r^2} + r^2 d\Omega^2 \right) \)

where \( R \) is the curvature radius of the universe.

The Debate with Einstein on the Cosmological Constant

De Sitter maintained a famous correspondence with Einstein about the interpretation of the cosmological constant \( \Lambda \). Their exchanges revealed fundamental differences:

Contributions to Celestial Mechanics

Before his work in cosmology, de Sitter made significant contributions to celestial mechanics:

• Study of perturbations of planetary orbits by Jupiter
• Development of methods to calculate the masses of Jupiter's satellites
• Improvement of lunar motion theories

His book On the Motion of the Moon's Node (1900) remains a reference in celestial mechanics.

De Sitter's Scientific Legacy

De Sitter's work had a profound impact on modern cosmology:

Scientific Collaborations and Correspondences

De Sitter maintained scientific exchanges with many physicists of his time:

• Regular correspondence with Albert Einstein (1916-1933) on general relativity
• Collaboration with Arthur Eddington (1882-1944) on observational tests of relativity
• Exchanges with Georges Lemaître (1894-1966) on expanding universe models
• Correspondence with Karl Schwarzschild (1873-1916) on exact solutions to Einstein's equations

Chronology of Willem de Sitter's Life

Honors and Recognition

De Sitter's contributions were recognized by:

• Foreign Member of the Royal Society (1922)
• Gold Medal of the Royal Astronomical Society (1931)
• A lunar crater named after him (de Sitter)
• An asteroid (1686) De Sitter
• The Institute for Theoretical Physics at Leiden University bears his name

Posthumous Quotes and Tributes

Several scientists paid tribute to de Sitter:

• Albert Einstein (1879-1955): "De Sitter was the first to fully understand the cosmological implications of my equations."
• Arthur Eddington (1882-1944): "His solutions paved the way for modern cosmology as an exact science."
• George Gamow (1904-1968): "Without de Sitter's work, we would not have understood the expansion of the universe so quickly."