# Paul Sophus Epstein

Paul Sophus Epstein (Russian: Павел Зигмундович Эпштейн, romanized: Pavel Zigmundovich Epshteyn; March 20, 1883 – February 8, 1966) was a Russian-American mathematical physicist. He was known for his contributions to fluid dynamics and to the development of quantum mechanics.

## Early life and studies

Paul Epstein's parents, Siegmund Simon Epstein and Sarah Sophia (Lurie) Epstein were of a middle class Jewish family. He said that his mother recognized his potential at the age of four years and predicted that he would be a mathematician.
He went to the Hochschule in Minsk, and from 1901 to 1905 studied mathematics and physics at the Imperial University of Moscow under Pyotr Nikolaevich Lebedev. In 1909 he graduated, and became a Privatdozent at the University of Moscow. In 1910 he went to Munich, Germany, to do research under Arnold Sommerfeld, who was his advisor, and Epstein was granted a Ph.D. on a problem in the theory of diffraction of electromagnetic waves. from the Technische Universität München, in 1914.

## Career

At the outbreak of World War I he was in Munich, and considered an enemy alien. Thanks to Sommerfeld's intervention he was allowed to stay in Munich as a private citizen, and could continue with his research. By that time Epstein became interested in the quantum theory of atomic structure. In 1916, he published a seminal paper explaining the Stark effect using the Bohr–Sommerfeld quantization from old quantum theory. After the war he went to Zurich, where he remained for two years. He moved to Leiden in 1921, to become Hendrik Lorentz' and Paul Ehrenfest's assistant. Shortly afterwards he was recruited by Robert Millikan to come to the California Institute of Technology (Caltech), where he remained for the rest of his career.
In 1930, he was elected a member of the National Academy of Sciences. After World War II, concerned that some young American intellectuals were becoming attracted to communism, he joined the American Committee for Cultural Freedom and in 1951 he served as one of the three US delegates to the seminar the Congress held in Strasbourg.
He retired as emeritus professor at Caltech in 1953 and continued to serve as a consultant for a number of industrial companies. The Epstein Memorial Fund was established through donations from more than fifty of his former students and a bronze bust of Epstein stands in the Physics and Mathematics section of the Millikan library at Caltech.

## Research
### Quantum mechanics

In 1922 he published 3 papers, on the explanations of the Stark effect, Zeeman effect and magnetic dipoles using Bohr's quantum theory.

### Air and fluid drag

As well as quantum theory, Epstein also published papers in other fields. He worked on were the settling of gases in the atmosphere, the theory of vibrations of shells and plates and the absorption of sound in fogs and suspensions.
Epstein calculated in 1924 the drag on a sphere moving in a gas in the rarefied (i.e., high, or at least not small, Knudsen number) flow regime. This calculation was an important ingredient in improved measurements of the charge of the electron in the Millikan's oil drop experiment, as cited and described as "masterly" by Millikan himself in his review paper of 1930. Epstein's important result is now known as Epstein drag in honor of his work.

### Continental drift

Epstein calculated the effect of Polflucht in 1920 as a possible causing force of Alfred Wegener's continental drift. His value was about 10$^{−6}$ of the gravitational force. Some years later other geophysicists could show that the Polflucht force is far too weak to cause plate tectonics. The toughness of the sublayers of the Earth's crust is much more stronger than assumed by Epstein.

## Other interests

Epstein had other interests as well. He was very interested in Freudian psychology and was one of the founding members of a Psychoanalytic Study Group (together with Thomas Libbin) that later merged into the Los Angeles Institute for Psychoanalysis.
In the 1930s he published two articles in the monthly literary and scientific magazine Reflex - "The Frontiers of Science" and "Uses and Abuses of Nationalism". Although he was not an active Zionist, Epstein served as a member of the American National Society of Friends of the Hebrew University and was very friendly with the prominent Israeli mathematician Abraham Fraenkel.

## Personal life

In 1930, Epstein married Alice Emelie Ryckman, and the couple had a daughter Sari (Mittelbach).