Paul Ehrenfest Research Articles

Not by discoveries alone: The centennial of Paul Ehrenfest

“It is not by discoveries only, and the registration of them by learned societies, that science is advanced. The true seat of science is not in the volume of Transactions, but in the living mind, and the advancement of science consists in the direction of men’s minds into a scientific channel; whether this is done by the announcement of a discovery, the assertion of a paradox, the invention of a scientific phrase, or the exposition of a system of doctrine.“‘) Th e words are James Clerk Maxwell’s, and they are particularly appropriate in talking about Paul Ehrenfest, who was born a century ago. Ehrenfest did advance science in all the ways that Maxwell mentions. The adiabatic principle -that pillar of the old quantum theory was his discovery, a discovery “found with so much joy”*), as he once wrote. His writings propound and analyze many a most ingenious paradox3). It is hard to imagine a scientific phrase more telling than the one Ehrenfest coined to characterize the devastating implications of the distribution law that classical physics requires for blackbody radiation “the ultraviolet catastrophe”4). There is no exposition of a system of doctrine more incisive, more clarifying than the monograph on the foundations of statistical mechanics written by Paul Ehrenfest and his wife Tatyana for the Encyklopiidie der mathematischen Wissenschaften5). But what makes Maxwell’s words especially relevant to Ehrenfest is their emphasis on science as living in the minds of men. At the Seventh Solvay Conference, held only a few weeks after Ehrenfest’s death in 1933, Paul Langevin described him as having been “at the very heart of the drama of contemporary physics”, and even as having personified that drama in his own life6). For Ehrenfest was passionately committed to his science. His way of being alive involved thinking about physics, talking and arguing about physics, working to his utmost to understand physics, and teaching it to anyone who showed an interest in itstudents, colleagues, laymen, casual acquaintances, children. Others have been as intensely committed to science, but Ehrenfest was unique in his need to have close human contacts as an essential part of doing physics, in the breadth of human experience and the range of emotions that went into his scientific activity. Ehrenfest’s way of being devoted to physics contrasts sharply with that of

On an urn problem of Paul and Tatiana Ehrenfest

A short solution is given for the urn problem proposed by Paul and Tatiana Ehrenfest in 1907.In 1907 P. and T. Ehrenfest(3) proposed an urn model for the resolution of the apparent discrepancy between irreversibility and recurrence in Boltzmann's theory of gases (2). In this model it is assumed that m balls numbered 1, 2, …, m are distributed in two boxes. We perform a series of trials. In each trial we choose a number at random among 1, 2, …, m in such a way that each number has probability 1/m. If we choose j, then we transfer the ball numbered j from one box to the other. Denote by ξn the number of balls in the first box at the end of the nth trial. Initially there are ξ0 balls in the first box. If the trials are independent, then the sequence {ξn;n = 0, 1, 2,…} forms a homogeneous Markov chain with state space I = {0, 1, 2,…, m} and transition probabilities pi,i+1 = (m − i)/m for i = 0, l,…, m − 1, Pi,i−1 = i/m for i = 1, 2,…, m, and pi,k = 0 otherwise. The problem is to determine the transition probabilitiesfor i∈I, k∈I and n = 0,1, 2,….

Paul Ehrenfest. Volume I: The Making of a Theoretical Physicist. Martin J. Klein

<i>Paul Ehrenfest. Volume I: The Making of a Theoretical Physicist</i>. Martin J. Klein

Letter Writing

We want to make a strong plea for an improvement in the composition of Letters. Most Letters seem to have been written for a small group of insiders only. Physicists interested in a different research field often question the importance and urgency of Letters of which the meaning escapes them completely. In spite of the growing specialization it is still possible to communicate the significance of notable new discoveries and theories to all colleagues without having to resort to popularization. A change in the style of Letters can help in approaching this desirable goal.There must be several ways in which a Letter can be written so that it is understandable to more physicists than just the specialists. As an example we recommend a study of the way in which that eminent teacher Paul Ehrenfest wrote his own articles. When reading a paper Ehrenfest looked for what he called its "patent claim." It is that statement in the paper which marks its essential distinction from past knowledge; it is thus its main contribution. He also tried to locate "the moment when the frog jumps into the pond," which means the place where the author introduces a new argument or an experimental modification essential for the proof or justification of his "patent claim." In many papers this crucial "moment" is so obscured that it seems that the author did not clearly realize which new assumptions he used to reach his conclusions.Ehrenfest believed that each section of a paper should begin with a concise statement of its aim and its assumptions so that the reader's attention is focussed on the relevant arguments in that section. Secondary arguments, such as mathematical derivations, should be omitted or put in an appendix so as not to interrupt the discussion. The result can be a very clear paper appealing to many readers and moreover it can be kept short. It is for these reasons that we would like to see more Letters following this style. Reading such a Letter or Article is like visiting a museum with a guide who points out its treasures. It is true that an expert does not need a guide and prefers to decide for himself which among the many objects are the real treasures, but not only experts should enjoy an exhibit.In the traditional way of writing physics papers the author takes the reader along his own path of reasoning expecting him in the end to arrive, as if independently, at the same conclusion as the author. Though the printed reasoning may have been rationalized, this method is a most excellent and convincing way to present the work to those readers who are thoroughly familiar with the subject. For the uninitiated, however, reading the paper is like visiting, without a catalog, an overfilled museum of unfamiliar art; he does not appreciate the exhibit and gets tired instead.It is not easy to compose a Letter that is both clear and short since this requires that the author himself decide which are the most relevant aspects of his work. Some authors are reluctant to omit anything at all, believing that every detail is needed to convince the reader. Moreover, whereas most authors are willing to consider criticism regarding the physics in their papers, very few are favorably disposed towards a suggestion that presentation could be improved. We often envy the editors of commercial magazines who place the interest of their readers before that of the authors.

The Works of Paul Ehrenfest

Collected Scientific Papers By Paul Ehrenfest. Edited by Martin J. Klein. Pp. xii + 632. (Amsterdam: North-Holland Publishing Company, 1959.) 90s.

On the Use of the Notion “Probability” in Physics

An analysis of the meanings of such terms as “at random,” “equal chances,” “probability calculus,” “laws of probability” as used in physics. The author treated this subject for the first time in a lecture at St. Petersburg in 1911, after which it was published in Russian in the Journal of the Physical-Chemical Association of St. Petersburg. Later, Paul Ehrenfest made it the topic of several lectures.

Reproductions of Prints, Drawings, and Paintings of Interest in the History of Physics. 53. Photograph of H. A. Lorentz, H. Kamerlingh Onnes, Niels Bohr, and Paul Ehrenfest

The year 1953 marks the hundredth anniversary of the birth of two remarkable Dutch physicists, Hendrik Antoon Lorentz and Heiche Kamerlingh Onnes. The purpose of this article is to commemorate this anniversary by reproducing an interesting photograph of these two men, together with their great friends and fellow physicists, Niels Bohr and Paul Ehrenfest.

Prof. P. Ehrenfest

THEORETICAL physics has lost one of its ablest and most enthusiastic exponents through the death on September 25 last of Paul Ehrenfest, professor of theoretical physics in the University of Leyden. Born in Vienna in 1880, he studied first under Boltzmann. From Vienna he went to Gottingen; there he made the acquaintance of his future wife (Mrs. T. Ehrenfest-Afanashewa). In collaboration with Mrs. Ehrenfest, he undertook a thorough critical investigation of the principles underlying the kinetic theory of matter, a problem which had fascinated him ever since his Vienna days. The elucidation of certain paradoxes in Boltzmann's theorem (1907) and the extensive article on statistical mechanics in the “Enzyklopadie der mathematischen Wissenschaften” (1912) testify to the fertility of their combined activity. The latter work was written in Russia, where the Ehrenfests lived for several years.