Casimir, Hendrik Brugt Gerhard

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(b. The Hague, Netherlands, 15 July 1909;

d. Heeze, Netherlands, 4 May 2000), physicist, quantum physics, statistical physics.

Casimir’s major achievements in physics lie in the field of quantum physics (theory of nuclear and electron spins, intermolecular forces, “Casimir effect”) and statistical physics (superconductivity, Onsager relations). He also introduced what became known as the “Casimir operator” in the theory of groups, and played an important role in the international world of industrial research.

Early Life . The son of Rommert Casimir and Teunsina Dina Borgman, Hendrik (Henk) Casimir grew up and went to school in The Hague. Casimir’s early environment was that of an intellectual milieu: His father was an important educational reformer and pedagogue who combined his work as the head of a progressive secondary school in The Hague with an extraordinary professorship in pedagogy at the University of Leiden. Already at a young age Casimir showed extraordinary abilities, both in the sciences and in languages. He combined these talents with an extraordinary memory, which allowed him to recite favorite texts throughout his life. Starting in 1926, he studied physics at the University of Leiden in the Netherlands. After finishing the first phase of his studies in record time, ending with the candidaatsexamen in 1928, he began his specialization, theoretical physics, under Paul Ehrenfest. As was the case with so many of his fellow students, Casimir became deeply influenced by Ehrenfest’s personality and his unique style of doing physics.

At the initiative of Ehrenfest, Casimir spent much time with Niels Bohr in Copenhagen, Denmark, in the period from 1929 to 1931. In his autobiography, Haphazard Reality (1983), Casimir tells how Ehrenfest introduced him to Bohr: “I bring you this boy. He has already some ability, but he still needs thrashing” (p. 91). The Copenhagen years were formative ones for young Casimir. He witnessed firsthand how the new and still rudimentary quantum mechanics was developed into a mature theory. Working with Bohr, he made the acquaintance of all the major physicists of the time. From the stories and anecdotes related in the autobiography, a picture emerges of a close-knit group of young people having a wonderful time, not just doing physics but engaging in all sorts of social activities in Copenhagen as well.

In November 1931, Casimir obtained his doctorate with a dissertation on the rotation of rigid bodies in quantum mechanics. It contains, among other things, the introduction of what became known as the Casimir operator in the theory of representations of groups. After completing his doctoral work, Casimir first remained in Leiden as Ehrenfest’s assistant, but in the fall of 1932, he left for Zürich, Switzerland, to become Wolfgang Pauli’s assistant at the Swiss Federal Institute of Technology. He enjoyed his new position and was planning to stay in Zürich for at least two years, but in the spring of 1933, Ehrenfest implored him to return to Leiden in the fall, saying “Please, Caasje, put your broad shoulders under the wagon of Leiden physics” (Haphazard Reality, p. 147). The reason for this request became obvious when Ehrenfest committed suicide on 25 September of that year, an act that he had been planning for quite some time. Casimir took on Ehrenfest’s duties until the fall of 1934, when Hendrik Anthony Kramers was appointed as Ehrenfest’s successor.

The Leiden Laboratory . In the meantime, Casimir had developed an interest in experimental physics. He assisted his wife, an experimental physicist, with her work in the Kamerlingh Onnes Laboratory of the University of Leiden. Casimir’s experimental activities eventually led to his appointment, in 1936, as conservator(managing director) of the laboratory. He worked in the section that was led by Wander J. de Haas, who codirected the laboratory with Willem Keesom. Notable in this period is his work with Cornelis Jacobus Gorter on superconductivity, reported in

their paper, “On Supraconductivity I” (1934), in which they introduced a two-fluid model for this phenomenon, and his paper (with Frits K. du Pré) on a thermodynamic theory of paramagnetic relaxation, “Note on the Thermodynamic Interpretation of Paramagnetic Relaxation Phenomena” (1938). In this work a magnetic crystal is treated as a combination of two systems with two different temperatures: the lattice with its phonons and electrons, on the one hand, and the spins, on the other. These two systems have different relaxation times, with the spin lattice relaxation time determining the time in which the two temperatures become equal. Finally, a paper with de Haas and Gerard J. van den Berg, “The Electrical Resistance of Gold Below 1°K” (1938), described a newly discovered effect: a temperature dependent residual electrical resistance in metals that seemed to diverge as the temperature approached absolute zero. Only many years later was this phenomenon explained by Jun Kondo as the result of an interaction between the conducting electrons and magnetic impurities; it became known as the Kondo effect.

Not related to experimental work in the Kamerlingh Onnes Laboratory was Casimir’s book, On the Interaction between Atomic Nuclei and Electrons (1936), in which he summarized earlier work on electron and nuclear spins and their interactions. It was his contribution to an essay contest by Teyler’s Foundation in Haarlem, the Netherlands, and it earned him a gold medal.

Philips Company . Not long after the German invasion and occupation of the Netherlands in May 1940, the University of Leiden was closed down by the occupiers. Work in the Kamerlingh Onnes Laboratory continued, however, though under increasingly difficult circumstances. Casimir’s decision in 1942 to accept the offer of a position at the Physics Laboratory of the Philips Company in Eindhoven, in the south of the Netherlands, was undoubtedly influenced by these difficulties. A deteriorating relationship with his director, de Haas, may have played a role as well.

In the Philips Laboratory, which from its creation in 1914 provided a stimulating atmosphere in which fundamental as well as applied research flourished, Casimir clearly found his place. After only four years he became one of its three directors and ten years after that, in 1956, he became a member of the top executive committee of the Philips Company. In that capacity he was in charge of all Philips laboratories worldwide. By appointing him a member of the executive committee, the leaders of Philips showed their dedication to fundamental as well as applied research. Especially at the central laboratory in Eindhoven, much fundamental research was being done, and so it became an attractive place for new PhDs to start their professional careers. Casimir supervised, stimulated, and where necessary gave direction to the research, always considering both the company’s interests and the scientific merit of the work.

Casimir’s move from the academic world to the world of industry was not received favorably by all of his colleagues. A prominent example is Pauli, who began addressing him facetiously as “Herr Direktor.” There was concern that the industrial environment would put an end to Casimir’s research in theoretical physics, a concern that would prove to be largely unfounded. In fact, some of his most important work in theoretical physics dates from the Philips days; most famous is the discovery, in 1948, of the Casimir effect: the attractive force between two perfectly conducting uncharged plates in vacuum.

Intermolecular Forces and the Casimir Effect . In the Philips laboratory, experiments had been done on the stability of colloids, with results that seemed to contradict theoretical predictions, in particular those concerning the long-range behavior of the attractive intermolecular forces acting between the colloidal particles. One of the experimenters, the physical chemist Jan Theodoor Gerard Over-beek, suggested to Casimir that the problem might be solved by modifying the London-van der Waals electromagnetic theory of molecular forces between electrically neutral particles by taking into account the finite propagation speed of electromagnetic interactions. For this, Casimir quickly realized, one needed a quantum-electro-dynamical theory for the interaction energy between polarizable particles. Together with his collaborator, Dirk Polder, he succeeded in creating such a theory, using the still-rudimentary formalism of quantum electrodynamics. Their final result was deceptively simple. They found an attractive force that for large distances R decreases as R-7instead of the usual R-6 of the London-Van der Waals forces. It did not take long before Casimir had the insight that these forces could also be calculated by looking at the vacuum energy fluctuations of the electromagnetic field. Although the zero-point energy of the vacuum is infinite, the presence of, for instance, two metal plates will create a finite disturbance that will manifest itself as a force on the plates. A short calculation led Casimir to a very simple expression for the attractive force per unit area between two perfectly conducting parallel plates in a vacuum, now known as the Casimir effect:

There is a simple way to grasp the mechanism behind this effect, namely by considering the space between the plates as a resonance cavity. Only the radiation modes that “fit” between the two plates will be present in this cavity; the other ones will be damped out. Thus, there are fewer modes between the plates than outside of them, so that the radiation pressure on the outside will exceed that on the inside, leading to an effective attraction. An amusing analogous phenomenon will appear when two ships are reasonably close together under the right weather conditions, which are little wind and strong waves: the ships will then drift towards each other. The Casimir effect, which is extremely difficult to test (the effect becomes measurable only for distances of the order of one hundred atom diameters), became a widely discussed phenomenon, especially since its experimental verification in the 1990s.

Onsager Relations . Another important contribution by Casimir from the Philips period is his generalization of Lars Onsager’s theory of irreversible phenomena, in particular the so-called Onsager reciprocal relations. In irreversible thermodynamics, one distinguishes between “forces” (for instance, gradients) and the “fluxes” caused by those forces. In a very general way one may write Ii =∑kLikXk,with Ii the fluxes and Xk the forces.

Onsager had found the general relations Lik = L ki,, a result based on time reversal invariance of the underlying microscopic processes. Casimir succeeded in generalizing this to situations where effects that are not time-reversal invariant play a role. In the presence of a magnetic field, for instance, one has Lik (B) = L ki(-B).

Other Activities . As part of his work at the Philips Company, Casimir traveled a great deal, visiting the various Philips laboratories and also attending scientific meetings. He developed a large network and became widely respected, not only for his work in physics, but also as a mediator between industry and the world of science in academia (as opposed to industrial science). In 1966, he became the first president of the European Industrial Research Management Association (EIRMA), which was cofounded by him. After his retirement from Philips in 1972, Casimir began spending more time on organizational and other nonscientific matters. He served as president of the Royal Netherlands Academy of Arts and Sciences from 1973 to 1978 and was one of the founding members of the European Physical Society, as well as its president from 1972 to 1975. He was also frequently asked to be the chairman or keynote speaker at conferences and other gatherings. His after-dinner speeches were famous for their wit and erudition. His sense of humor was also evident in one of his most widely read nonscientific papers: a pseudo-linguistic essay on Broken English as the international language of science. (It was reprinted in Casimir’s autobiography.)

Casimir was a man of power and influence, but he was also a kind and even somewhat shy person, with a genuine interest in other people. His interests ranged far and wide, as is witnessed by his many articles on cultural topics and by his co-editorship of De Gids, one of the oldest Dutch literary journals. In the Netherlands, he became the grand old man of physics, one of the last of the generation that helped to shape modern physics in the heroic years of the 1920s and 1930s. He was a member of several scientific organizations and academies and received many honors, including eight honorary doctorates and two of the highest Dutch Royal decorations.


Casimir’s papers are in Rijksarchief in Noord-Holland, Haarlem, the Netherlands. Bibliographies of Casimir’s work are on pp. 193–217 of Sarlemijn and in the Hargreaves article, both cited below.


Rotation of a Rigid Body in Quantum Mechanics. Groningen, Netherlands: Wolters, 1931.

With Cornelis J. Gorter. “On Supraconductivity I.” Physica 1(1934): 306–320.

On the Interaction between Atomic Nuclei and Electrons. Haarlem,Netherlands: Bohn, 1936.

With Wander J. de Haas and Gerard J. van den Berg. “The Electrical Resistance of Gold Below 1°K.” Physica 5 (1938): 225–229.

With Frits K. du Pré. “Note on the Thermodynamic Interpretation of Paramagnetic Relaxation Phenomena.” Physica 5 (1938): 507–511.

“On Onsager’s Principle of Microscopic Reversibility.” Reviews of Modern Physics 17 (1945): 343–350.

With Dirk Polder. “The Influence of Retardation on the London-van der Waals Forces.” Physical Review 73 (1948): 360–372.“On the Attraction between Two Perfectly Conducting Plates.” Proceedings of the Koninklijke Akademie van Wetenschappen B51 (1948): 793–795.

Haphazard Reality: Half a Century of Science. New York: Harper and Row, 1983. This autobiography appeared first in English and then in a slightly rewritten Dutch version, Het toeval van de werkelijkheid: Een halve eeuw natuurkunde (Amsterdam, Netherlands: Meulenhoff Informatief, 1983).

Waarneming en visie, over wetenschap en maatschappij. Amsterdam, Netherlands: Meulenhoff Informatief, 1987.

Mens en Kosmos: Essays. Amsterdam, Netherlands: Meulenhoff,1993.


Hargreaves, C. M. “Casimir, Hendrik Brugt Gerhard.” Biographical Memoirs of Fellows of the Royal Society 50 (2004): 39–45.

Lamoreaux, Steve K. “Hendrik Brugt Gerhard Casimir.”Proceedings of the American Philosophical Society 146 (2002): 285–290.

Polder, Dirk. “Hendrik Brugt Gerhard Casimir: 15 juli 1909–4 mei 2000. Levensbericht door D. Polder.” In Koninklijke Nederlandse Akademie van Wetenschappen: Levensberichten en herdenkingen 2001. Amsterdam: Koninklijke Nederlandse Akademie van Wetenschappen, 2001.

Rechenberg, Helmut. “Hendrik Brugt Gerhard Casimir(1909–2000): The Physicist in Research, Industry and Society.” European Journal of Physics 22 (2001): 441–446.

Sarlemijn, A., ed. Tussen academie en industrie: Casimirs visie op wetenschap en researchmanagement. Amsterdam: Meulenhoff Informatief, 1984.

A. J. Kox