Hendrik Casimir

A son of The Hague

Hendrik Brugt Gerhard Casimir was born on 15 July 1909 in The Hague, the son of a Dutch educational reformer who ran a progressive school and a mother who had studied classical philology. The household was bookish, lively, and trilingual: Dutch at the kitchen table, German for science, French for literature. Hendrik was an unhurried child who liked maps, sailing on the inland waterways, and the kind of arithmetic puzzles that ask how many ways one can arrange the dominos on a table. He would later say that he had grown up assuming, without quite noticing it, that every problem had a solution if you sat with it long enough.

He entered the University of Leiden in 1926, intending to read mathematics and ended up reading physics because the lectures of Paul Ehrenfest, who had inherited Hendrik Lorentz’s chair, were the most fun on campus. Ehrenfest was a Viennese-born Jewish physicist whose Tuesday-evening colloquia were the closest thing the European continent had to a quantum salon. Einstein dropped in when he could. Bohr came down from Copenhagen. The students were expected to disagree, in writing, on the blackboard, in front of everyone, and to keep disagreeing until the question dissolved. Casimir thrived in that climate.

Apprentice to two giants

In 1929, on Ehrenfest’s recommendation, Casimir went to Copenhagen to spend a year with Niels Bohr. It was the high noon of the new quantum mechanics. Heisenberg’s matrices and Schrödinger’s waves had been reconciled only four years earlier. Dirac had just published the relativistic electron equation. Bohr’s Institute was producing complementarity, the Copenhagen interpretation, and the first attempts at a quantum theory of fields, all at once, often in the same afternoon. Casimir, twenty years old and fluent in mathematics he had taught himself in school, served as Bohr’s assistant: drafting letters, polishing arguments, walking with Bohr at midnight while the master dictated paragraphs that would be re-dictated in the morning and again at noon. He came home with a doctoral thesis on the rotation of rigid bodies in quantum mechanics, supervised jointly by Ehrenfest and Bohr, defended at Leiden in 1931.

Ehrenfest’s suicide in September 1933 hit Casimir hard. Ehrenfest had been the first adult who treated him as an equal, and the loss closed a door in Leiden that never quite reopened. Casimir stayed on as a lecturer through the rest of the 1930s and married Josina Jonker, a former student of his, in 1933. By the time the German army crossed the border in May 1940, he had two children, a permanent position, and a growing reputation in the spectroscopy of group representations. The university was steadily emptied of its Jewish staff over the next eighteen months. Casimir signed protests, taught the courses he could, and in 1942, with the academic world closing around him, took an offer that would surprise his colleagues: he left the university to join the research laboratory of N. V. Philips in Eindhoven.

The long Philips career

For the next forty years, Casimir was a company physicist. Philips Research Laboratories, the Natuurkundig Laboratorium or Nat Lab, was at the time one of the strangest places in industrial science. Its founding director, Gilles Holst, had built it as a small academic colony inside a giant electronics firm: hire excellent researchers, give them room to ask their own questions, trust that the patents would come. Casimir flourished there. He rose to director of research by 1946, joined the board of management in 1956, and stayed until his retirement in 1972, by which point Philips employed over four hundred Ph.D. physicists in Eindhoven alone. He used to say that he had never published a paper because he had to: he had always published because he had something he wanted to say, and that this was the only honest reason to write.

His best-known papers from the Philips years were not on any product. The company let him keep one foot in fundamental research, and the foot he kept in was sensitive. In 1947, in conversation with his colleague Dirk Polder, Casimir worked out the retarded van der Waals force between two atoms or between an atom and a metal wall, a calculation that brought relativistic delay into a problem that had previously assumed instantaneous Coulomb interaction. The result, the Casimir-Polder force, was a small correction at long range but it implied something stranger. If retardation mattered between two atoms, it ought to matter between two whole conducting plates. And when Casimir tried that calculation, he found that the answer was not zero.

Dutch physicists Hendrik Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947; this special form is called the Casimir–Polder force. After a conversation with Niels Bohr, who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948. This latter phenomenon is called the Casimir effect. Predictions of the…

Force out of nothing

The paper that bears his name was four pages long and appeared in the Proceedings of the Royal Netherlands Academy of Arts and Sciences in 1948. Two parallel, perfectly conducting, uncharged plates in a perfect vacuum should, Casimir showed, attract each other. The size of the attraction depended on Planck’s constant, the speed of light, and the fourth power of the distance between them. Nothing else. There were no atoms involved, no charges, no fields one could draw with arrows. The force came entirely from the way the plates restricted which standing waves the quantum electromagnetic field was allowed to support between them. The vacuum on the inside contained fewer modes than the vacuum on the outside, the energies on either side did not quite cancel, and the imbalance pushed the plates together.

The result was so clean it looked wrong. Casimir himself had a hard time believing his own arithmetic. He showed the calculation to Bohr on a visit to Copenhagen and Bohr, after his usual long pacing silence, said something like yes, that is right, and it has to do with zero-point energy. That sentence, repeated by Casimir for the rest of his life, became the framing the textbooks adopted. The Casimir force was not a force between things. It was a force the vacuum exerted on the things that interrupted it.

It took half a century for the laboratory to catch up with the prediction. Marcus Sparnaay, working in the Philips Nat Lab in 1958, tried to measure the force directly and obtained results that were merely consistent with the theory, the experimental error bars being almost as large as the predicted attraction. Sparnaay’s apparatus was a marvel of patience, but the signal was tiny and the dust between plates was enormous. The definitive measurement waited until 1997, when Steve Lamoreaux at Los Alamos used a sphere against a plate, a torsion pendulum, and electronics that had not existed in Casimir’s lifetime to pin the force to within five percent of the predicted value. By then Casimir was eighty-eight and living quietly in Heeze, near Eindhoven, and the news reached him in time. He outlived the validation by three years, dying on 4 May 2000.

Two cultures, one career

What is remarkable about Casimir is not just the discovery but the platform from which he made it. He spent most of his working life inside a corporate research lab, a setting which, in most countries and in most decades, has steered physicists toward problems with a customer attached. Philips needed better cathode-ray tubes and better gas-discharge lamps, and Casimir oversaw the work that gave them. But the same management that funded the lamp engineering let him publish, year after year, on the magnetic properties of paramagnetic salts at millikelvin temperatures, on the thermodynamics of irreversible processes, on superconductors, and on the strange new effect that the vacuum could push. He liked to remark that the best industrial research, like the best academic research, was driven by curiosity that happened to land on something useful, and that the wisdom of an institution was measured by how patiently it tolerated the wait.

He wrote, in addition to physics, a memoir titled Haphazard Reality in 1983 and a long sequence of essays for Philips Technical Review in which he reflected on the relation between fundamental science and the technologies that fund it. The thesis that gave the book its title was characteristic: that breakthroughs do not arrive on schedules, that you cannot extract them by planning, and that the only management strategy that works in the long run is to hire excellent people and leave them alone. He was not nostalgic about the academy. He thought industrial labs of the Holst type, properly run, were the equal of any university physics department he had known, and that the historians of science had underrated them.

What he left

Casimir’s effect is now one of the canonical predictions of quantum field theory, taught in every advanced electrodynamics course and measured in laboratories on three continents. It shows up as an unwanted attractive force in micro-electromechanical systems, where it can stick parts together and ruin a fabrication run, and it shows up as a desired tool in the design of certain nano-scale sensors. There is a dynamical version, in which a mirror oscillating fast enough should radiate photons out of the vacuum, first observed in 2011 with superconducting circuits. There is a Casimir-Polder version, the original calculation that started everything in 1947, that matters in the physics of cold atoms near surfaces. And there is the wider intuition the effect has given physics: that the vacuum is not nothing, that boundary conditions on quantum fields have measurable mechanical consequences, that the zero-point energy of the world is not a bookkeeping fiction but something the world can be made to push against.

Hendrik Casimir was the bridge between two physics generations. He apprenticed under the founders, worked through the worst of the European twentieth century, ran a major industrial laboratory through the rise of the transistor, and lived long enough to see his calmest piece of arithmetic become an experimental science of its own. The lesson of his career is the one his old teacher Ehrenfest had given him on the blackboard in Leiden: sit with a problem long enough, and it answers.

Casimir is the quiet figure at the back of the quantum century who showed that emptiness has a shape, and that the shape pushes back.