The Struggles of Paul Ehrenfest

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Elegant Connections in Physics

The Struggles of Paul Ehrenfest

A biography of Paul Ehrenfest


Dwight E. Neuenschwander, Professor of Physics at Southern Nazarene University in Bethany, OK

During the founding years of quantum mechanics, the Niels Bohr Institute in Copenhagen, Denmark, hosted an annual spring meeting where the hottest topics in physics were discussed. It became traditional to close the meeting with a skit that parodied the state of physics at the time. The 1932 conference coincided with the tenth anniversary of the institute’s founding and needed to end on a special note.

A few years earlier, Wolfgang Pauli had suggested the existence of a particle carrying zero mass and zero electric charge that could explain the missing energy and momentum in beta decay, a type of radioactive decay of the nucleus. He called this hypothetical particle the “neutron.” When in 1932 James Chadwick discovered the massive neutral particle we now call the neutron, Enrico Fermi suggested that the name of Pauli’s particle be changed to neutrino, the “little neutral one.”

At the Bohr Institute’s 1932 meeting, Pauli’s neutrino was still a speculative teaser, with many doubters. This offered the perfect theme for the 1932 closing skit, modeled on Goethe’s Faust, in which Faust, who has attempted to master all knowledge and remains frustrated, makes a pact with the devil (Mephistopheles), who will do Faust’s bidding in this life. With Mephistopheles’ help, Faust seduces the beautiful Gretchen, but their relationship leads to tragedy. Of the brilliant Copenhagen parody, which portrayed Pauli and Paul Ehrenfest, George Gamow wrote, “The theme of this dramatic masterpiece has Pauli (Mephistopheles) trying to sell to the unbelieving Ehrenfest (Faust) the idea of a weightless neutrino (Gretchen).”[1]

 Museum Boerhaave, Leiden,  courtesy of the Emilio Segrè Visual ArchivesEhrenfest (1880–1933) was born in Austria and earned his PhD under Ludwig Boltzmann. During his career Ehrenfest made fundamental contributions to statistical mechanics and quantum theory, and was held in the highest esteem by his students and colleagues. In September 1912, on the recommendation of Arnold Sommerfeld, he was offered the prestigious chair at the University of Leiden in the Netherlands, held by the departing H.A. Lorentz.

Paul Ehrenfest always insisted on honesty in thought and action. In the preface to Ehrenfest’s collected papers, H.B.G. Casimir wrote that Ehrenfest’s lectures were brilliant in an unconventional way:[2]

He emphasized salient points rather than continuity of argumentation; the essential formulae appeared on the blackboard almost as aesthetical entities and not only as links in a chain of deductions. . . . One had very little inclination to go to sleep during Ehrenfest’s lectures, but if one ever showed any tendency in that direction one was immediately and ruthlessly called to order.

In his 1934 memorial essay for Ehrenfest, Albert Einstein recalled when they first met 22 years earlier: “We also discussed the theory of relativity, to which he responded with a certain skepticism but with the critical judgment peculiar to him. Within a few hours we were true friends—as though our dreams and aspirations were meant for each other. We remained joined in close friendship until he departed this life.”[13] Whenever Einstein visited Leiden, he stayed in the Ehrenfest home.

The authors of the Faust parody no doubt chose Ehrenfest as Faust because of his inherent skepticism, his brilliance, his mastery of a comprehensive range of subjects, and his sterling standards of truth. Casimir recalled that “To Ehrenfest . . . discussions and arguments were an essential part of his scientific activity and the best way to clarify an obscure point.”[2] Ehrenfest’s skepticism of Gretchen was genuine.

But whether or not it was consciously recognized by the Faust parody playwrights, Ehrenfest’s personality also fit the gloominess of the original Faust. In the 1932 skit, the opening scene begins with Faust (Ehrenfest) brooding with dissatisfaction over the vast knowledge he has mastered:

I have–alas–learned Valence Chemistry,
Theory of Groups, and the Electric Field,
And Transformation Theory as revealed
by Sophus Lie in eighteen-ninety-three.
Yet here I stand, for all my lore,
No wiser than I was before.

From the factual notes about his career mentioned above, we might assume that life for Ehrenfest was always a forward-looking adventure. Far from it. From a young age he was a melancholy figure who struggled with chronic depression. Paul was the youngest of five brothers and suffered from poor health as a child. He was often the target of anti-Semitism. His mother died when he was 10. He loathed school, and his academic performance suffered. His school experiences were sufficiently negative that, years later, he insisted that his own children be educated at home.[4]

His biographer, Martin Klein, wrote, “He was often miserable, deeply depressed, and at odds with himself and the world.” When Paul was 16 his father died. Older brother Arthur convinced Paul to remain in school, and his outlook seemed to improve. Klein continues, “Paul was apparently able to work himself out of depression, which had sometimes been deep enough to make him contemplate suicide. His intellectual interests grew stronger, perhaps as a form of self-protection.”[4]

In 1899 Paul enrolled in the Technische Hochschule in Vienna and attended lectures by Boltzmann on the new subject of statistical mechanics. It was under Boltzmann’s influence that Paul’s loathing of school was replaced by a passion for physics and mathematics. European students in those days typically migrated from one university to another to study under a variety of mentors. Starting in 1901, Ehrenfest took courses at the University of Göttingen under David Hilbert, Walther Nernst, Felix Klein, Johannes Stark, and Karl Schwarzschild. At Göttingen he met a young Russian mathematics student, Tatyana Alexeyevna Afanasyeva. At that time women were not allowed to attend meetings of the mathematics club, a rule that Ehrenfest successfully challenged after “quite a battle.”[4] (His tenacity would resurface after Hitler came to power, when he found jobs for German Jews fleeing the Nazis.[5]) He returned to Vienna in 1904 and completed his doctorate that June under Boltzmann’s direction, writing a dissertation on the motion of rigid bodies in fluids. His advisors respected this work, but, as was the pattern throughout his life, Ehrenfest felt it to be inadequate. He did not publish his dissertation. However, Tatyana soon joined him and they were married in Vienna that December.[4]

After finishing his PhD, Dr. Ehrenfest had difficulty securing a permanent position. Despite repeated residences in Vienna, Göttingen, and St. Petersburg, his letters of application to numerous institutions in Europe and North America proved fruitless. He published several important papers between 1904 and 1912, but his situation did not stabilize until he was offered the Leiden position in 1912. Even then, Ehrenfest continued suffering from unrealistic self-doubt...

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