Paul Ehrenfest Research Articles

More is known about him than about her: Tatiana Ehrenfest-Afanassjewa

Tatiana Afanassjewa and Paul Ehrenfest, her husband, shared their love for physics and mathematics, but their ideal of studying and working together went against the zeitgeist.

Still learning about space dimensionality: From the description of hydrogen atom by a generalized wave equation for dimensions D ≥ 3

A hydrogen atom is supposed to be described by a generalization of the Schrödinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential r−β. Starting from previously obtained solutions for this equation using the 1/N expansion method, it is shown that new light can be shed on the problem of understanding the dimensionality of the world as proposed by Paul Ehrenfest. A surprising new result is obtained. Indeed, for the first time, we can understand that not only the sign of the energy but also the value of the ground state energy of hydrogen atoms is related to the threefold nature of space.

World Physics in Ukraine: A Unique Experience of Consolidation of Scientists at Kharkiv Research Center of Physics (in the 1920s-1930s)

The article examines the development of physics research in Ukraine on the example of the Ukrainian Institute of Physics and Technology (UIPT). Founded on the initiative of the eminent physicist Abram Ioffe, the UIPT has gradually become one of the world’s leading research institutions. During 1928–1938, many important events took place at the institute, which became markers for the development of physics in Ukraine and the USSR as well as in the world. An experiment on the fission of atomic nucleus using artificially accelerated protons confirmed the validity of the intentions to reorient research towards nuclear physics. The involvement of foreign specialists in the work of the UIPT contributed to the informal consolidation of scientific thinking in physics. Outstanding physicists of the world such as Boris Podolskyi, Oleksandr Weisberg, Konrad Weiselberg, Friedrich Houtermans, Laszlo Tisza, Fritz Lange, Victor Weisskopf, George Placzek, Paul Dirac, Georgii Gamov, Niels Bohr, Paul Ehrenfest, and others worked here for longer or shorter periods. Niels Bohr, Ivar Waller, Milton S. Plesset, Evan J. Williams, and Leon Rosenfeld made reports at the theoretical conferences of UIPT. As a result, in the late 1920s and during the 1930s, an informal society of physicists from around the world was formed in Kharkiv. The consolidation of talented scientists has accumulated traditions, centuries of experience, and practical knowledge in the field from many scientific schools around the world.

Did S. P. Timoshenko and P. Ehrenfest Overestimate the Importance of the Fourth-Order Time Derivative in Their Beam Theory?

Abstract In this study, we investigate the importance of the fourth-order time derivative that appears in the equations derived by Jacques Antoine Charles Bresse in 1859, as well as in equations that were derived by Stephen Prokofievich Timoshenko and Paul Ehrenfest during years 1912 and 1913 and reported by Timoshenko in the 1916 book on the theory of elasticity in the Russian language and then in two papers dated 1920 and 1921, in English. The first part of the study demonstrates that Timoshenko and Ehrenfest did not overestimate the importance of the fourth-order derivative term in their equations. The second part deals with the debate on the so-called second spectrum attendant in the original set of equations. It is shown that in the truncated Timoshenko—Ehrenfest equations—which is asymptotically consistent with elasticity theory—“the second spectrum” issue does not arise. Thus, the two parts of this study are intricately interrelated with each other.

The 100th Anniversary of the Timoshenko–Ehrenfest Beam Model

The 100th Anniversary of the Timoshenko–Ehrenfest Beam Model

Лекции С. Л. Франка в голландском Амерсфорте в 1932 г.

Historical and philosophical reconstruction of the visit of Semen Ludwigovich Frank to Amersfoort in the summer of 1932, where the philosopher delivered at the International School for Philosophy (Internationale School voor Wijsbegeerte) a course of lectures entitled “Russian spiritual type in his attitude to the Western one” accompanied by the publication of some materials related to this visit. The organizer and inspirer of the lecture course was the historian and Slavist Bruno Borisovich Becker, a friend of Frank since the pre-emigre period, who moved to Amsterdam after the 1917 revolution. In the summer of 1932 in Amersfoort, fragments of Frank’s lecture course were also recorded on black and white film, recently found at the city archive of Utrecht. This is obviously the only record of Frank that has reached us. Along with the Russian philosopher and numerous course participants, it also captured Albert Schweitzer, Martin Buber, Dietrich Bonhoeffer, Paul Ehrenfest and Bruno Becker. On the 9th of August, 1932, Frank sent from Amersfoort a postcard to his wife, Tatiana Sergeevna Frank, which is stored in the personal archive of Frank’s grandson, Fr Peter Scorer in Great Britain. In the appendix to the publication, this postcard is published, with the permission of the philosopher’s heirs. The publication also includes several photographs from the personal archive of Frank’s grandson, related to his trip to Amersfoort (The Netherlands), in August 1932.

Who developed the so-called Timoshenko beam theory?

The use of the Google Scholar produces about 78,000 hits on the term “Timoshenko beam.” The question of priority is of great importance for this celebrated theory. For the first time in the world literature, this study is devoted to the question of priority. It is that Stephen Prokofievich Timoshenko had a co-author, Paul Ehrenfest. It so happened that the scientific work of Timoshenko dealing with the effect of rotary inertia and shear deformation does not carry the name of Ehrenfest as the co-author. In his 2002 book, Grigolyuk concluded that the theory belonged to both Timoshenko and Ehrenfest. This work confirms Grigolyuk’s discovery, in his little known biographic book about Timoshenko, and provides details, including the newly discovered letter of Timoshenko to Ehrenfest, which is published here for the first time over a century after it was sent. This paper establishes that the beam theory that incorporates both the rotary inertia and shear deformation as is known presently, with shear correction factor included, should be referred to as the Timoshenko-Ehrenfest beam theory.

On social and psychological aspects of a negligible reception of Natanson’s article of 1911 in the early history of quantum statistics

Possible reasons are studied why Ladislas (Władysław) Natanson’s paper on the statistical theory of radiation, published in 1911 both in English and in the German translation, was not cited properly in the early history of quantum statistics by outstanding scientists, such as Arnold Sommerfeld, Paul Ehrenfest, Satyendra Nath Bose and Albert Einstein. The social and psychological aspects are discussed as background to many so far discussions on the academic evaluation of his theory. In order to avoid in the future such Natansonian cases of very limited reception of valuable scientific works, it is proposed to introduce a digital tag in which all the information of relevant papers published so far should be automatically accumulated and updated.

A look back at the Ehrenfest classification

A translation of Paul Ehrenfest's 1933 paper, entitled "Phase transitions in the usual and generalized sense, classified according to the singularities of the thermodynamic potential" is presented. Some historical commentary about the paper's context is also given.

Casimir en Einstein. ‘Hij kan al wat maar heeft nog slaag nodig’

Casimir and Einstein Hendrik Casimir knew Albert Einstein from the presentations he gave at Paul Ehrenfest’s Leiden colloquiums in the late 1920s. As a student he witnessed Einstein’s determined opposition to quantum mechanics, expressed in sharp thought experiments. After Ehrenfest’s suicide they lost touch. Their scientific work, however, still proved to have a connection long after Einstein’s death. Einstein’s last great discovery of the Bose Einstein condensation of 1924 and the Casimir effect due to vacuum fluctuations of 1948 converge in modern physics research.

Afanassjewa en Einstein. Wederzijdse waardering

Afanassjewa and Einstein In 1912 Tatiana Afanassjewa (1876–1964), a Russian mathematician, arrived in Leiden. The university in this city had an amazingly flourishing physics department. Afanassjewa accompanied her husband Paul Ehrenfest (1880–1933), a theoretical physicist from Vienna, who was to become successor to the famous professor Hendrik Antoon Lorentz. Soon the couple’s house became a regular meeting place for Dutch mathematicians and physicists, and a temporary home for many learned guests from all over the world. Among them was Albert Einstein, a close friend of Ehrenfest, with whom he shared a passion for physics and music. This paper recapitulates their friendship and includes new details about Afanassjewa, who was to initiate a fierce debate on the didactics of mathematics in The Netherlands and whose sharp and analytical mind made an impression on Einstein. Both the Ehrenfest-Afanassjewa couple and Einstein had a vivid interest in international relations and, the role of science therein. Afanassjewa and Einstein stayed in touch through letters and cards after Ehrenfest’s untimely death in 1933, the year when Hitler rose to power in Germany and Einstein moved to the United States.

The peaceful atom comes to campus

Youthful idealism, institutional ambition, and Cold War sensibilities all helped shape the Michigan Memorial–Phoenix Project, the University of Michigan’s tribute to fallen World War II soldiers.

Schrödinger’s radial equation

The August 2014 issue of Physics Today contains a letter (page 8) in which M. Y. Amusia comments on the article “Bohr’s molecular model, a century later” by Anatoly Svidzinsky, Marlan Scully, and Dudley Herschbach (Physics Today, January 2014, page 33). Amusia points out that the radial part of the article’s D-dimensional Schrödinger equation in Hartree units isand he criticizes the implication that the Coulomb potential does not depend on D, which it surely does. Half a century ago, following up on the work of Paul Ehrenfest,11. P. Ehrenfest, Proc. Amsterdam Acad. 20, 200 (1917); Ann. Phys. Leipzig 61, 440 (1920). who had studied the hydrogen atom in n spatial dimensions using Bohr orbit theory, I reformulated the problem22. F. R. Tangherlini, Nuovo Cimento 27, 636 (1963). https://doi.org/10.1007/BF02784569 using Schrödinger’s equation extended to n dimensions, in which I had the Coulomb potential for n ≥ 3. I did not include the Coulomb potential for n = 1,2, as discussed by Amusia, as I was only interested in the stability of the higher-dimensional atom for n > 3. (For the dimensionality of space I used “n” rather than “D.”) In that work I gave the radial equation equivalent to the one above: I wrote, “If we now transform to n-dimensional polar coordinates, introduce n-dimensional spherical harmonics, and factor out the angular dependence,33. See, for example, A. Sommerfeld, Partial Differential Equations in Physics, E. G. Straus, trans., Academic Press (1949), app. 4. the resulting radial equation takes the formIn my paper, I did not eliminate the dR/dr term to arrive at a form equivalent to the first equation. However, that is readily done by setting R = r−(n − 1)/2ϕ and generalizing to nuclear charge Z, and setting n → D. The reason I have the D-dependent Coulomb potential for D > 3 and the article authors do not is that they have a different goal—to gain new insight into the real, atomic-molecular 3D world using the limiting behavior of the D-dimensional kinetic energy. In contrast, as indicated above, I was only interested in whether the D-dimensional Schrödinger “hydrogen atom” would have stable bound states for D > 3.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. P. Ehrenfest, Proc. Amsterdam Acad. 20, 200 (1917); Google ScholarAnn. Phys. Leipzig 61, 440 (1920). Google Scholar2. F. R. Tangherlini, Nuovo Cimento 27, 636 (1963). https://doi.org/10.1007/BF02784569, Google ScholarCrossref3. See, for example, A. Sommerfeld, Partial Differential Equations in Physics, E. G. Straus, trans., Academic Press (1949), app. 4. Google Scholar© 2015 American Institute of Physics.

Out of Ehrenfest’s closet

The article by Dirk van Delft on Paul Ehrenfest’s final years (Physics Today, January 2014, page 41) offers fascinating insights into the life of a remarkable man. It also offers a speculation as to why Martin Klein never wrote the second volume he had originally planned for his Ehrenfest biography. As Marty told me many years ago, he took a sabbatical in Leiden, the Netherlands, when he began his research for the biography, and he visited Ehrenfest’s widow, Tatiana, fairly often during that time.At some point—after volume 1 had been written, I believe—Marty visited Tatiana again. During that visit she inadvertently opened a closet, and papers that she had kept hidden came tumbling out. It was my understanding that Marty abandoned the second volume because he did not have access to those papers, which he considered essential and which I assume are the letters acquired by the Boerhaave Museum. The article by van Delft offers abundant clues as to why Tatiana wanted to keep them secret.© 2014 American Institute of Physics.

Paul Ehrenfest’s final years

New access to his correspondence sheds light on the tragic life and death of one of the pioneers of modern physics.

Huygens' principle for the Klein-Gordon equation in the de Sitter spacetime

In this article we prove that the Klein-Gordon equation in the de Sitter spacetime obeys the Huygens' principle only if the physical mass m of the scalar field and the dimension n ⩾ 2 of the spatial variable are tied by the equation m2 = (n2−1)/4. Moreover, we define the incomplete Huygens' principle, which is the Huygens' principle restricted to the vanishing second initial datum, and then reveals that the massless scalar field in the de Sitter spacetime obeys the incomplete Huygens' principle and does not obey the Huygens' principle, for the dimensions n = 1, 3, only. Thus, in the de Sitter spacetime the existence of two different scalar fields (in fact, with m = 0 and m2 = (n2−1)/4), which obey incomplete Huygens' principle, is equivalent to the condition n = 3, the spatial dimension of the physical world. In fact, Paul Ehrenfest in 1917 addressed the question: “Why has our space just three dimensions?”. For n = 3 these two values of the mass are the endpoints of the so-called in quantum field theory the Higuchi bound. The value m2 = (n2−1)/4 of the physical mass allows us also to obtain complete asymptotic expansion of the solution for the large time.

Paul Ehrenfest and the Dilemmas of Modernity

This essay considers the highly ambivalent attitude of the Austrian-Dutch physicist Paul Ehrenfest toward contemporary developments in both science and society. On the one hand, he was in the vanguard of the quantum and relativity revolutions, supported industrialization and economic planning based on mathematical models, and, in general, cherished technocratic ideals. The essay highlights several influences that shaped his attitude in these respects, from his ties with the Philips Physics Laboratory and his sojourns in the United States to the utopian visions of H. G. Wells. On the other hand, he was extremely worried about the harmful consequences of contemporary changes in science and society, such as specialization, the growing pace of city life, and the increasing dependence on modern technologies, be they material or mathematical. In this regard, he agreed with cultural critics such as Max Nordau, Henri Bergson, Ostwald Spengler, and Ludwig Klages. Rather than attempting to solve this paradox, the essay suggests that this kind of ambiguity characterized a great deal of innovative science in the period.

Big Bang paternity in question

Belenkiy replies: As an applied scientist, Alexander Friedmann was keenly interested in testing his theories with available data. An interpretation of the right side of Einstein’s field equations as the “flow of matter” was particularly appealing to him as a meteorologist. Several of his recently discovered letters to Paul Ehrenfest in June 1922 (Physics Today, March 2013, page 9) clearly show Friedmann knew he had made an important discovery.While Friedmann had some a priori estimates of Λ and Λ critical, he was wise enough not to include them in the final draft of his 1922 paper; he remained uncommitted to a particular scenario until the empirical data provided information.11. A. Belenkiy, in Origins of the Expanding Universe: 1912–1932, M. J. Way, D. Hunter, eds., ASP conf. ser. 471, Astronomical Society of the Pacific, San Francisco (2013), p. 71; arXiv:1302.1498. He was unaware of Vesto Slipher’s data on the nebulae’s high radial velocities, publicized by Arthur Eddington in 1923. As the letters to Ehrenfest testify, Russia was so devastated at the time Friedmann was writing his 1922 paper that he was still unable to obtain a copy of Willem de Sitter’s original 1917 paper, which first highlighted Slipher’s data. (Most likely, Friedmann learned of de Sitter’s solution of general relativity equations indirectly from a secondary source.)Furthermore, in his 1923 book, Friedmann discussed the possibility of the universe’s birth from a “singularity.” Thus all components of the Big Bang cosmology were present in Friedmann’s writings long before Georges Lemaître entered the field.As for Peter Hammerling’s comment, Friedmann’s metric, in contrast to the modern one, had the additional factor c–2, thus forcing renormalization of the relevant constants k and λ by the inverse factor c2.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Belenkiy, in Origins of the Expanding Universe: 1912–1932, M. J. Way, D. Hunter, eds., ASP conf. ser. 471, Astronomical Society of the Pacific, San Francisco (2013), p. 71; arXiv:1302.1498. Google Scholar© 2013 American Institute of Physics.

Types of Economic Behavior: The Instrument for Management of Individuals, Institutions, Countries and Humankind

This is short preliminary paper. In next papers the detailed description of all aspects will be published.The typology of economic behavior is constructed. The type of economic behavior is the mathematical (abstract) operator in the information space, which is constructed by a special method from the data about economical problem. It is shown that for description of any human behavior (his/her decision making) it is need only 16 two-component abstract information operators (2AIO), which are constructed by a special manner. It is shown that there are only 16 types of interaction (relationship) between 2AIO. It is shown that typology of 2AIO can to describe wide field of human behavior. Authors carried out the identification of types 2AIO for more than 2 thousand persons from 1998 to 2011. Ex post and ex ante forecast was made for rational behavior for each person. The theoretical prediction for relationships between persons (as between types of 2AIO) was also placed (more than 3 thousands of forecasts). More than one thousand predictions have been done for the level of effectiveness for defined functional responsibilities of a person.As examples there is the description: forecast the individual behavior (the causes for suicide of eminent physicist Paul Ehrenfest in 1933); dangers for the High Level Managers. A few theorems on development of mechanism design for application of game theory in economics are presented. With using of 2AIO typology is an effective tool for solving such problems: the classification of the purposes for the person’s behavior; the forecast of economic behavior for the person; the forecast of constraints for the person’s behavior in a given interior of activity; the development of effective mechanisms and technologies for human resource management (e.g., motivation and incentives); the choice of the most effective trainings for the person, taking into account the interior of his/her behavior; the choice of optimal learning styles for the person.The hierarchical systems for cooperative behavior (pyramids of behavior) from 2AIO were considered. It is shown that there are people who have the ability to introduce new information at a given level of the pyramid of behavior (or to adequately recover the missing it part at this level). These people are called coordinators. The coordinator is often named as “talent” or “genius”. The methods for identification of coordinators are constructed. It is shown that the pyramid of behavior with high-level (for example, at the country level) can be playing a role an institution. It is shown that if at least one player is the coordinator (for this problem), the results of the modern game theory are incorrect.As examples there is the description: elite for the country; modern terrorism and National security (including the terroristic act September 11, 2001 in USA, Russia: 2002 and 2004, Spain: 2003, United Kingdom in 2007 and beyond; these technologies were forecasted in 1998 and presented in Internet in Russian); reasons of the financial crisis at 2008; three levels of loyalty (three-level of goals); democratic mechanisms are not applicable to the coordinators; the P versus NP Problem solving in the frame of 2AIO.Obtained results can to change the life for billions people.

Paul Ehrenfest, Niels Bohr, and Albert Einstein: Colleagues and Friends

In May 1918 Paul Ehrenfest received a monograph from Niels Bohr in which Bohr had used Ehrenfest’s adiabatic principle as an essential assumption for understanding atomic structure. Ehrenfest responded by inviting Bohr, whom he had never met, to give a talk at a meeting in Leiden in late April 1919, which Bohr accepted; he lived with Ehrenfest, his mathematician wife Tatyana, and their young family for two weeks. Albert Einstein was unable to attend this meeting, but in October 1919 he visited his old friend Ehrenfest and his family in Leiden, where Ehrenfest told him how much he had enjoyed and profited from Bohr’s visit. Einstein first met Bohr when Bohr gave a lecture in Berlin at the end of April 1920, and the two immediately proclaimed unbounded admiration for each other as physicists and as human beings. Ehrenfest hoped that he and they would meet at the Third Solvay Conference in Brussels in early April 1921, but his hope was unfulfilled. Einstein, the only physicist from Germany who was invited to it in this bitter postwar atmosphere, decided instead to accompany Chaim Weizmann on a trip to the United States to help raise money for the new Hebrew University in Jerusalem. Bohr became so overworked with the planning and construction of his new Institute for Theoretical Physics in Copenhagen that he could only draft the first part of his Solvay report and ask Ehrenfest to present it, which Ehrenfest agreed to do following the presentation of his own report. After recovering his strength, Bohr invited Ehrenfest to give a lecture in Copenhagen that fall, and Ehrenfest, battling his deep-seated self-doubts, spent three weeks in Copenhagen in December 1921 accompanied by his daughter Tanya and her future husband, the two Ehrenfests staying with the Bohrs in their apartment in Bohr’s new Institute for Theoretical Physics. Immediately after leaving Copenhagen, Ehrenfest wrote to Einstein, telling him once again that Bohr was a prodigious physicist, and again expressing the hope that he soon would see both of them in Leiden.