Paul Halpern

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Professor of Physics and Fellow in the Humanities at the University of the Sciences in Philadelphia, Paul Halpern has written a number of popular science books on subjects ranging from space, time and higher dimensions to the history and the cultural aspects of science. The most recent one is Einstein’s Dice and Schrödinger’s Cat. Also worth checking out: The Cyclical Serpent, Cosmic Wormholes and The Great Beyond. His What’s Science Ever Done for Us was based on the series The Simpsons, which led to his special appearance in the documentary special The Simpsons 20th Anniversary Special – In 3-D! On Ice! The German-language version of that book, Schule ist was für Versager, was reviewed in Spektrum.  If you check YouTube, you will find him starring (among others) on the PBS series Future Quest, on the History Channel and the Discovery Channel. His blog: Cosmic Quest. Not to mention that he received a Guggenheim Fellowship, a Fulbright Scholarship, and an Athenaeum Literary Award.

For Vienna Quantum Café, Paul has written a very special contribution on the name-giver of our new Paul Ehrenfest Best Paper Award for Quantum Foundations. In a delicate balancing act between Paul Ehrenfest’s genius and his darker side, he gives us a glimpse into the life and work of this great scientist, brilliant teacher and troubled individual in the setting of his time. Those of you based in Vienna or within traveling distance will have the opportunity to hear Paul Halpern speak on that same subject and meet him in person at the occasion of the Inaugural Award Ceremony of the Award on 2 December 2016. We are particularly pleased to be able to welcome him in Vienna in person then.

The Book Too Painful To Complete:  Interpreting the Life of Paul Ehrenfest

By Paul Halpern

Sometimes, if the fate of its subject is tragic enough, a scientific biography is too painful to complete.  Historian of science Martin J. Klein, a professor at Yale University, was widely recognized as the world’s foremost expert on the life and work of physicist Paul Ehrenfest.  He wrote the quintessential biography of the first half of Ehrenfest’s life, calling it “Volume One.”  He collected material for a second volume, but never completed it.  The reason, as he related to many who asked him, is that he found the latter part of Ehrenfest’s life too depressing.

“For years Klein had immersed himself in his subject’s work and life, and he found it increasingly difficult to come to terms with the way that it ended.”

After Klein died in 2009, only a segment of his planned “Volume Two” saw publication, in the form of a short article published in the journal “Physics in Perspective.”  Klein’s former students and colleagues appreciated the dilemma he had faced:  dealing with the ethical dilemmas associated with the tragic, violent demise of an influential physicist.

Ehrenfest was an expert in statistical mechanics, the study of the connections between the microscopic motions of particles—as characterized by their momenta, kinetic energies, and so forth—and the macroscopic behavior of systems that include them.  He trained at the University of Vienna under the groundbreaking physicist Ludwig Boltzmann, and took classes at the University of Göttingen taught by legendary mathematicians David Hilbert and Felix Klein.  It was in one of Klein’s classes that he met Russian mathematician Tatyana Afanasyeva, whom he would marry.

One of Boltzmann’s key contributions to statistical mechanics was developing methods for understanding why, if Newtonian mechanics is fully time-reversible, thermodynamics possesses an unmistakable arrow of time, pointing in the direction of non-decreasing entropy.  Closed systems tend over time to maintain or increase—but never spontaneously decrease—their overall entropy.  Boltzmann developed a definition of entropy based on the number of possible distinct microstate configurations associated with a given macrostate.  By further assuming that the universe began in an unlikely configuration, he showed how its microscopic state  would pass through increasingly indistinct sectors of a phase space of possibilities, leading naturally to the entropic arrow of time.

Ehrenfest’s life story was markedly asymmetric in time.  Start at the beginning—with his birth in Vienna in 1880—and we see a clever youth, accruing knowledge, developing a wide range of mathematical tools, becoming a masterful teacher, assuming Hendrik Lorentz’s former position at Leiden, developing there an impressive colloquium series,  befriending noted physicists such as Albert Einstein and Niels Bohr, and mentoring numerous impressive graduate students such as Hans Kramers,  George Uhlenbeck and Samuel Goudsmit.   As Arnold Sommerfeld once wrote:

“He lectures like a master. I have hardly ever heard a man speak with such fascination and brilliance.  Significant phrases, witty points and dialectic are all at his disposal in an extraordinary manner… He knows how to make the most difficult things concrete and intuitively clear. Mathematical arguments are translated by him into easily comprehensible pictures.”

However, if you play Ehrenfest’s life chronicle backward in time—from his death in 1933—you are confronted with a far different picture—a story capped with depression, the murder of his disabled son, and suicide.  How might we reconcile the forward story with the backward story—the promising start with the tragic finale?  That dilemma, faced by Martin Klein, remains a conundrum for anyone trying to reckon with the stark contradictions of Ehrenfest’s life.

A life of great promise was cut short when Ehrenfest plunged into depression and met his end.  In contrast, his early years at the University of Leiden were exuberant.  At the colloquium series he organized, which attracted luminaries such as Einstein, he was known for challenging the speakers in a friendly way to elucidate key principles.  As Klein remarked, he was “the world’s champion questioner in physics,” pointing out with great candor any flaws in their lines of reasoning.  The wall each speaker signed after his talk has been carefully preserved by the university.

Sometimes the speakers would visit Ehrenfest at his spacious house of yellow stucco, just across the river from the university and city centre.  If the weather permitted, often he would entertain them in his garden and engage them in further discussions. Einstein stayed there several times, and greatly enjoyed the visits.  As scientific historian John Stachel has remarked, Ehrenfest was like Einstein’s brother, and served as a kind  “uncle” to his children.

Paul and Tatyana Ehrenfest had four children: two boys and two girls.  One of their sons, Wassik, had Down Syndrome and attended a special residential school in Jena, Germany.  They home-schooled the other children and encouraged them to be young scholars.  The children pretended to run their own colloquium where they gave lectures about various subjects.   The eldest daughter used a cardboard model of a hyperboloid as a dollhouse.

Paul Ehrenfest kept extensive notebooks that recorded the numerous questions about nature that guided his research.  For example, in May 1917, his notebooks record his growing interest in role of dimensionality in science.  The line of reasoning led to  a remarkable paper entitled “In what way does it become manifest in the fundamental laws of physics that space has three dimensions?”

The article lists many examples of how nature would be different if it weren’t three-dimensional.  For instance, he demonstrates that closed, stable planetary orbits are possible only in three dimensions.  In four or more dimensions, he shows, planets would either spiral toward or away from their suns.  Similarly, the Bohr model of the atom is stable only in three dimensions.  Thus life as we know it can exist only in three dimensions.   (In Ehrenfest’s time, the concept of extra dimensions in unified field theory emerged, but these were thought to be unobservable.)

One of Ehrenfest’s key contributions to physics was the development of the Ehrenfest Theorem in quantum mechanics.  It brilliantly connects Hamilton’s equations of classical mechanics with the notion in quantum mechanics of expectation values.  In the form Ehrenfest proposed, it relates the time derivative of the position expectation value, multiplied by the mass, to the expectation value of momentum (essentially the first Hamilton equation), as well as the time derivative of the momentum operator to the expectation value of the force (essentially the second Hamilton equation).  This can be generalized to a broader spectrum of relationships between conjugate operators.  It cleverly offers a natural way to demonstrate the correspondence principle relating quantum mechanics to classical physics for large systems.  Hence it proves an important “glue” to cement the behavior of the very large and very small.

At the ‘Bohrfest” of 1921, held in Göttingen in honor of Niels Bohr, Ehrenfest met another eminent Vienna-born physicist Wolfgang Pauli.  They had each recently finished articles that appeared in a encyclopedia edited by Arnold Sommerfeld.  Ehrenfest’s piece was a summary of advances in statistical mechanics, co-authored with his wife.  Pauli’s article was a compendium of advances in relativity.  When Ehrenfest and Pauli met, their respective articles were much on their minds.  As Swedish physicist Oskar Klein reported:

“On that occasion Ehrenfest stood a little away from Pauli, looked at him mockingly and said: ‘Herr Pauli, I like your article better than I like you!  To which Pauli very calmly replied:  ‘That is funny, with me it is just the opposite!’”

In 1925, Pauli proposed his famous exclusion principle precluding two fermions (such as electrons) from being in the same quantum state.  To help address this and other dilemmas in quantum physics, two of Ehrenfest’s students, George Uhlenbeck and Samuel Goudsmit, proposed a new quantum number called spin, which allowed for two electrons of opposite spin state to occupy the lowest energy level for hydrogen. Ehrenfest, to his credit, submitted his students’ then-radical proposal for publication.  It was radical because there was no classical explanation:  electrons couldn’t really rotate at the required rates.  When Uhlenbeck worried about the physics community’s reaction, Ehrenfest told him, “You don’t yet have a reputation, so you have nothing to lose.”

Later, Ehrenfest suggested to Pauli that the exclusion principle was responsible for the stability of matter, making stone and metal solid.  That was yet another of his intuitive leaps that proved important.

At the famous Solvay conference of 1927, Ehrenfest played a pivotal role in trying to bridge the gap between Einstein’s opposition to the concept of probability in quantum mechanics, and the embrace of probability by Werner Heisenberg and others, which Bohr endorsed.  The disagreement had led to debates, mostly conducted during meals, rather than the seminars themselves.  Ehrenfest tried to convince Einstein to become more open-minded about the chance aspects of quantum transitions.

As Heisenberg reported, “After the [debates] continued for a few days … Ehrenfest said: ‘Einstein, I am ashamed of you; you are arguing against the new quantum theory just as your opponents argue about relativity theory.’ But even this friendly admonition went unheard.”

In the years thereafter, however, Ehrenfest began to feel that newer developments in theoretical physics had become too difficult for him to understand.   He became trapped in cycles of self-criticism that hindered his ability to conduct research and led to even more self-criticism.  In 1930, he wrote to some of his former students:   “Every new issue of the Zeitschrift für Physik or the Physical Review immerses me in blind panic.  My boys, I know absolutely nothing.”

Ehrenfest’s personal life was in shambles as well.  He had become estranged from his dear wife Tatyana, and engaged in a romantic liaison with a noted art historian Nelly Posthumus Meyjes.  The separation was uncomfortable for him, and he tried ardently to reconcile with his wife.

To make matters even worse, the economic and political situation in Europe was deteriorating.  Ehrenfest had great financial worries due to the downturn.  He tried, without success, to obtain a more lucrative position in America, where his brother Hugo was a successful physician.  He pleaded with Hugo for help.  Hugo was unsympathetic, blaming him for his “annoying inferiority complex.”  Ehrenfest also looked unsuccessfully for positions in the Soviet Union, where Tatyana had family connections.

As a cosmopolitan man of Jewish background, he was horrified when Hitler came to power in Germany.  Conditions in Europe seemed increasingly unbearable.  Focusing on those bleak developments, Ehrenfest saw little hope of economic and political improvement.

Hitler’s rise had direct impact on the situation of Wassik’s education.  Ehrenfest felt compelled to remove him from his school in Germany and bring him to Holland, where he was placed in the Waterink Institute for Afflicted Children in Amsterdam.   Waterink was very expensive, which led to further worry.

As Martin Klein related, “During the last year or more of Ehrenfest’s life he was struggling to find a way out of all these what seemed to be totally impossible situations.  He looked very hard to find a position that would pay him very well.  Finally he saw no way out.  He thought he would make his position available and remove the burden to his family.”

By the middle of 1933, Ehrenfest had already made up his mind to commit suicide.  He wrote a note to Einstein, Bohr and several other close friends, which he never sent.  He revealed his plans to take the life of Wassik, to spare his family of the financial burden, and then to kill himself.  The letter read, in part:

“In recent years it has become ever more difficult for me to follow the developments in physics with understanding. After trying, ever more enervated and torn, I have finally given up in desperation. This made me completely weary of life … I did feel condemned to live on mainly because of the economic cares for the children. I tried other things but that helps only briefly. Therefore I concentrate more and more on the precise details of suicide.  I have no other practical possibility than suicide, and that after having first killed Wassik. Forgive me …”

On September 25, 1933, Ehrenfest brought a pistol with him as he entered the waiting room of the Waterink Institute.   He shot Wassik and then himself.  Wassik survived only a few hours.  Promising lives had come to a tragic end.

In a moving obituary, Einstein praised his late friend’s extraordinary teaching style and contributions to the field. He speculated that Ehrenfest had difficulties handling the ardors of middle age.  (They were both in their mid-fifties.) As Einstein wrote:

“He was not merely the best teacher in our profession whom I have ever known; he was also passionately preoccupied with the development and destiny of men, especially his students. To understand others, to gain their friendship and trust, to aid anyone embroiled in outer or inner struggles, to encourage youthful talent — all this was his real element, almost more than his immersion in scientific problems.”

In reviewing the life of Paul Ehrenfest, we remember his pedagogical brilliance along with his personal and emotional shortcomings.  Many of his students went on to great careers, furthering the impact of his work.  While lamenting the black hole of despair into which he was trapped in the end, we salute the supernova brilliance of his life that preceded those dark final days.

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