Paul Langevin’s contribution to early quantum physics

In 1901 Marcel Brillouin, a broad-minded specialist in statistical mechanics, organized a series of meetings at the Collège de France in Paris on the thermodynamics of radiation. The subject was one that had not yet been taken up in the French physics community, despite numerous advances by physicists in Germany and elsewhere since the late 19th century. Presenters read reports that had been submitted by experts including Ludwig Boltzmann, Wilhelm Wien, and Max Planck, who had just devised his theory of energy quanta. Wien’s personal thoughts on the topic were delivered by the prominent French physicist Paul Langevin, who was born 150 years ago this year.

Langevin, who would join the Collège de France in 1902, came to focus his research on the theory of the electron, and then, during World War I, on developing ultrasound techniques to detect German submarines (see the article by Francis Duck, Physics Today, November 2022, page 42 ). But Langevin returned to the subject of the thermodynamics of radiation several times during his career. By incorporating the latest research on quantum theory into his courses, Langevin took new ideas, shared them with others, and encouraged people to discuss their importance. In doing so, he facilitated the understanding of quantum mechanics in France and helped develop a sound educational foundation for physicists who went on to make influential contributions to the field.

From Lorentz to Langevin

In 1905 Langevin published The Elementary Quantities of Electricity, Ions, Electrons, Corpuscles. In addition to a section on electromagnetic mechanics, it contains contributions by Wien, Joseph Larmor, Henri Poincaré, and Hendrik Lorentz, who had proposed his theory of the electron in 1892.

Invited by Langevin, Lorentz spoke at a conference in April 1905 at the French Physical Society. The conference ended with an evocation of the blackbody radiation problem, in which the theory of electrons and thermodynamics merge. Classical physics theory at the time held that an ideal blackbody at equilibrium would emit more and more energy as the frequency of the emission increased into the UV range.

At the conference, Lorentz mentioned a “very important theory of radiation that we owe to M. Planck.” Planck had offered a solution to the blackbody radiation problem by theorizing that rather than emitting progressively more energy for a given frequency, the blackbody would emit radiation only in fixed amounts called quanta. Langevin took Lorentz’s reflections from the conference, fleshed out by discussions he undoubtedly had with the Dutch physicist, and incorporated Lorentz’s electron theory of metals, which he found to be the most modern understanding of metals’ thermal properties, into a course that he taught in 1905–6.

In the course, Langevin shared the work of Gustav Kirchhoff, Wien, Boltzmann, and Planck, who had demonstrated several theoretical laws to explain the thermodynamics of radiation, including what became known as the Stefan–Boltzmann law and Wien’s displacement law. It appears that in the lessons of his course, Langevin showed and reviewed observations that were consistent with the laws and theory he presented. He was certainly inspired by Lorentz. As for the demonstration of Planck’s law, Langevin had only Planck’s 1900 publication at his disposal. Langevin’s course drew attention to the use of calculating probabilities in physics and helped spread early ideas on quantum theory beyond Boltzmann and other specialists.

New considerations on thermal radiation

In 1908 Langevin began to supervise the doctoral thesis of Edmond Bauer. Defended in 1912, it contains the first in-depth French analysis of quantum theory. Bauer, who frequently traveled abroad, had befriended Paul Ehrenfest, a student of Boltzmann’s in Austria who was interested in the theory of electrons and had reflected on Planck’s application of statistical thermodynamics (see the article by Dirk van Delft, Physics Today, January 2014, page 41 ). Bauer devoted the first part of his work to blackbody radiation. The subject, he felt, was one of the most obscure and therefore one of the most important in physics. “Einstein and especially Planck put us on the path to a solution,” he wrote.

At the time, Albert Einstein, one of only a few specialists in statistical mechanics, was giving a new impetus to the energy elements introduced by Planck. In 1905 he had proposed a physical discontinuity in the radical form of a quantum of light, which he had developed independently of Planck’s theory. Einstein originally disagreed with Planck’s law but changed his mind the following year. He quantified Planck’s thermalized oscillators by demonstrating that their electromagnetic energy could be emitted only in a quantized form. That analysis and other research led Einstein to define the relationship between the specific heat of a solid and the natural frequencies of vibration given by its IR spectrum.

Einstein was not alone in this type of analysis. The English theoretician James Jeans, a specialist in the kinetic theory of gases, also authored several works on the theory of thermal radiation.

Bauer, after analyzing the work of Einstein, Jeans, and Planck, proposed solutions to the blackbody radiation problem in the second part of his thesis. There Bauer affirmed, “M. Planck, by an intuition of genius, discovered a simple hypothesis of probability. However, as this hypothesis is completely contrary to our current habits, and as nothing seems to justify it a priori, we will only introduce it later.” Bauer proposed using a method that had recently been introduced by Ehrenfest to modify the laws of probability and statistical mechanics so that they fit with the new findings on the thermodynamics of radiation. Bauer was one of the first physicists to realize the importance of Ehrenfest’s work in the development of early quantum theory, and he helped spread it within the French academic community.

A meeting on the quanta

As Bauer was finishing his doctoral thesis, his mentor Langevin was taking part in the first-ever Solvay Conference. The subject was radiation and the quanta. Like most of the 20 or so participants who gathered in Brussels from 30 October to 3 November 1911, Langevin was invited because of his visibility on the international scene. At that time, only a small number of specialists were studying the still-primitive field of radiation, including Ehrenfest, Einstein, Lorentz, Planck, and Walther Nernst, the main organizer of the conference. Langevin traveled to Brussels with Maurice de Broglie, his scientific secretary. The following year the two men published the conference report.

Incorporating some of what he’d learned from the conference, Langevin—one of only a few physicists in France who were capable of understanding and teaching Planck’s ideas—gave a course at the Collège de France between December 1912 and March 1913. For this course he brought together a varied audience: young people, students and former students of Parisian schools of higher education, and colleagues, including his close friend the mathematician Émile Borel, a specialist in statistical mechanics. Langevin did not publish his lessons, but some of Borel’s notes are shown in the photo below.

From the notes, it’s clear that Langevin’s calculations are complete and detailed; he did not omit any intermediate stage. He made Lorentz’s theory of the electron one of the pillars of his thought, giving the course a kind of theoretical, intellectual, and conceptual coherence. Langevin’s perspective is in some ways analogous to that of Planck in his Leçons, published in 1906. But unlike Planck, who associated his analyses with James Clerk Maxwell’s electromagnetic theory, Langevin used Lorentz’s electron theory and opened his course to new theoretical content.

The course was a sort of intellectual laboratory where Langevin not only taught the most recent physics research but also developed and tested his own analyses and results. For example, he developed a theory of Brownian motion of the electron—a motion that the electron takes on because of radiation fluctuations. In addition, the course included the first published version of mathematician David Hilbert’s axiomatic theory of thermal radiation, which was based on the method of integral equations. Another one of Langevin’s contributions was his development of new ideas that led to a theorem of geometric optics, which was mentioned by Hilbert in his demonstration of Kirchhoff’s law.

Langevin’s interest in the quantum question continued after the course. In 1913 he gave lectures to the French Physical Society and drew attention to the way in which the notion of discontinuity had just invaded physics: discontinuity of matter, discontinuity of energy, and discontinuity in the definition of probability states of a system. He thought discontinuity was a profound change in physics and a new unifying concept.

Langevin’s focus on discontinuity helped lead to at least one breakthrough in the theory of quantum mechanics. In 1918 Langevin, having resumed teaching at the Collège de France after World War I, began advising the doctoral thesis of Louis de Broglie. Several years prior, Louis had read the report on the Solvay Conference coauthored by his older brother, Maurice. In his 1924 thesis, Louis put forth his now famous postulate that electrons behave as both a particle and a wave.

Martha Cecilia Bustamante de la Ossa is a historian of French theoretical physics at the Laboratory SPHERE-UMR 7219-CNRS and the University of Paris.