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.     

How Einstein Did Not Discover

What powered Einstein’s discoveries? Was it asking naïve questions, stubbornly? Was it a mischievous urge to break rules? Was it the destructive power of operational thinking? It was none of these. Rather, Einstein made his discoveries through lengthy, mundane investigations, pursued with tenacity and discipline. We have been led to think otherwise in part through Einstein’s brilliance at recounting in beguilingly simple terms a few brief moments of transcendent insight, and in part through our need to find a simple trick underlying his achievements. These ideas are illustrated with the examples of Einstein’s 1905 discoveries of special relativity and the light quantum.     

Paul Ehrenfest’s Rough Road to Leiden: A Physicist’s Search for a Position, 1904–1912

Paul Ehrenfest (1880–1933) received his Ph.D. degree at the University of Vienna in 1904 and moved with his wife and young daughter to St. Petersburg in 1907, where he remained until he succeeded Hendrik Antoon Lorentz (1853–1928) in the chair of theoretical physics at the University of Leiden in 1912. Drawing upon Ehrenfest’s correspondence of the period, we first examine Ehrenfest’s difficult and insecure years in St. Petersburg and then discuss his unsuccessful attempts to obtain a position elsewhere before he was appointed as Lorentz’s successor in Leiden. Pim Huijnen is writing a doctoral dissertation in history; the present paper is based upon his Master’s Thesis, “‘Die Grenze des Pathologischen’: Het leven van fysicus Paul Ehrenfest, 1904–1912,” University of Groningen, 2003. A.J.Kox is Pieter Zeeman Professor of History of Physics at the University of Amsterdam.     

爱因斯坦坚持场纲领的原因

探讨了爱因斯坦坚持场纲领的物理学认识基础和思想发展过程，分析了其坚持场纲领的目的及未获成功的原因。     

Klein,Einstein, and Five-Dimensional Unification

I examine the changing attitudes of Oskar Klein (1894–1977) and Albert Einstein (1879–1955) toward the notion of extending general relativity by an extra dimension with the aim of encompassing electromagnetism and gravitation in a unified field theory. I show how Klein developed his model of five-dimensional unification with the goal of explaining the discreteness of atomic energy levels, and how Einstein later embraced that goal. By examining the correspondence between Klein and Einstein, some of which was relayed through Paul Ehrenfest (1880–1933), I speculate that Klein’s work helped motivate Einstein to explore deterministic five-dimensional theories as a potential alternative to probabilistic quantum mechanics. Finally, I consider the contributions of Wolfgang Pauli (1900–1958) to the subject and elucidate his role in convincing Klein and Einstein that their models were not viable. Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. He currently is a member of the Executive Committee of the Forum on the History of Physics of the American Physical Society.     

Relativity and indeterminism

It is well known that Albert Einstein adhered to a deterministic world view throughout his career. Nevertheless, his developments of the special and general theories of relativity prove to be incompatible with that world view. Two different forms of determinism—classical Laplacian determinism and the determinism of isolated systems—are considered. Through careful considerations of what concretely is involved in predicting future states of the entire universe, or of isolated systems, it is shown that the demands of the theories of relativity make these deterministic positions untenable.     

Einstein as Engineer:The Case of the Little Machine

I first discuss Albert Einstein’s practical and educational background in engineering and then his invention of his “little machine,” an electrostatic induction machine, while working in the Patent Office in Bern, Switzerland, between 1902 and 1909. He believed that it could be used as a voltage or potential multiplier in experiments to test his new theory of Brownian motion of 1905. I then discuss Einstein’s search for collaborators to produce it and the work that his friends Conrad and Paul Habicht, in particular, did in designing and testing it. Although the initial response to it was promising, it never became a success after Paul Habicht manufactured a few specimens of it beginning in 1912.Today only three specimens are known to exist; these are preserved at the Zürcher Hochschule Winterthur, Switzerland, in the Physics Institute of the University of Tübingen, Germany, and in the Museum Boerhaave in Leiden,The Netherlands.     

On the Appeal to a Pre-Established Harmony Between Pure Mathematics and Relativity Physics

Soon after its appearance in 1905, the Einsteinian relativity with its relativistically admissible 3-velocities was recognized by Vladimir Variak in 1908 as the realization in physics of the hyperbolic geometry of Bolyai and Lobachevski. At the same time, however, during the years 1907–1909 Minkowski reformulated the Einsteinian relativity in terms of a space of 4-velocities that now bears his name. As a result, the special theory of relativity that we find in the mainstream literature is not the one originally formulated by Einstein but, rather, the one reformulated by Minkowski. Thus, in particular, one of the most powerful ideas of Einstein in 1905, the Einstein addition of relativistically admissible 3-velocities that need not be parallel, is unheard of in most texts on relativity physics. Following our recently published book, Beyond the Einstein Addition, Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces [1], the aim of this article is to employ the principle of pre-established harmony between mathematics and physics to demonstrate that the original Einsteinian relativity, as opposed to the Minkowskian relativity, is the legitimate formulation of special relativity whose time has returned.     

Einstein's First Steps Toward General Relativity: Gedanken Experiments and Axiomatics

Jahrbuch paper is an extraordinary document because it contains his first steps toward generalizing the 1905 relativity theory to include gravitation. Ignoring the apparent experimental disconfirmation of the 1905 relativity theory and his unsuccessful attempts to generalize the mass-energy equivalence, Einstein boldly raises the mass-energy equivalence to an axiom, invokes equality between gravitational and inertial masses, and then postulates the equivalence between a uniform gravitational field and an oppositely directed constant acceleration, the equivalence principle. How did this come about? What is at issue is scientific creativity. This necessitates broadening historical analysis to include aspects of cognitive science such as the role of visual imagery in Einstein's thinking, and the relation between conscious and unconscious modes of thought in problem solving. This method reveals the catalysts that sparked a Gedanken experiment that occurred to Einstein while working on the Jahrbuch paper. A mental model is presented to further explore Einstein's profound scientific discovery.     

There Is No Spooky Action at a Distance in Quantum Mechanics

Einstein became bothered by quantum mechanical action at a distance within two years of Schrödinger’s introduction of his eponymous wave equation. If the wave function represents the “real” physical state of a particle, then the measurement of the particle’s position would result in the instantaneous collapse of the wave function to the single, measured position. Such a process seemingly violates not only the Schrödinger equation but also special relativity. Einstein was not alone in this vexation; however, the dilemma eventually faded as physicists concentrated on using the Schrödinger equation to solve a plethora of pressing problems. For the next 30 years, wave function collapse, while occasionally discussed by physicists, was primarily a topic of interest for philosophers. That is, until 1964, when Bell introduced his famous inequality and maintained that its violation proved that quantum mechanics and, by implication, nature herself are nonlocal. Unfortunately, this brought the topic back to mainstream physics, where it has remained and continues to muddy the waters. To be sure, not all physicists are bothered by the apparent nonlocality of quantum mechanics. So where have those who embrace quantum nonlocality gone wrong? I argue that the answer is a gratuitous belief in the ontic nature of the quantum state.     

On integrability of the Szekeres system. I

The Szekeres system is a four-dimensional system of ?rst-order ordinary differential equations with nonlinear but polynomial (quadratic) right-hand side. It can be derived as a special case of the Einstein equations, related to inhomogeneous and nonsymmetrical evolving spacetime. The paper shows how to solve it and ?nd its three global independent ?rst integrals via Darboux polynomials and Jacobi’s last multiplier method. Thus the Szekeres system is completely integrable. Its two-dimensional subsystem is also investigated: we present its solutions explicitly and discuss its behaviour at in?nity.     

Z?llner’s Universe

The idea that space is not Euclidean by necessity, and that there are other kinds of “curved” spaces, diffused slowly to the physical and astronomical sciences. Until Einstein’s general theory of relativity, only a handful of astronomers contemplated a connection between non-Euclidean geometry and real space. One of them, the German astrophysicist Johann Carl Friedrich Z?llner (1834–1882), suggested in 1872 a remarkable cosmological model describing a finite universe in closed space. I examine Z?llner’s little-known contribution to cosmology and also his even more unorthodox speculations of a four-dimensional space including both physical and spiritual phenomena. I provide an overview of Z?llner’s scientific work, of his status in the German scientific community, and of the controversies caused by his polemical style of science. Z?llner’s cosmology was effectively forgotten, but there is no reason why it should remain an unwritten chapter in the history of science.     

Einstein,Incompleteness, and the Epistemic View of Quantum States

Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein’s preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein’s attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927.     

Interrogating the Legend of Einstein's “Biggest Blunder”

It is well known that, following the emergence of the first evidence for an expanding universe, Albert Einstein banished the cosmological constant term from his cosmology. Indeed, he is reputed to have labelled the term, originally introduced to the field equations of general relativity in 1917 in order to predict a static universe, his “biggest blunder.” However, serious doubts about this reported statement have been raised in recent years. We interrogate the legend of Einstein’s “biggest blunder” statement in the context of our recent studies of Einstein’s cosmology in his later years. We find that the remark is highly compatible with Einstein’s cosmic models of the 1930s, with his later writings on cosmology, and with independent reports by at least three physicists. We conclude that there is little doubt that Einstein came to view the introduction of the cosmological constant term as a serious error and that he very likely labelled the term his “biggest blunder” on at least one occasion. This finding may be of some relevance for those theoreticians today who seek to describe the recently discovered acceleration in cosmic expansion without the use of a cosmological constant term.     

Stationary solutions,energy, and the Bel-Robinson tensor

The absence of stationary source-free solutions and the positive energy problem in general relativity are discussed, at the linearized level, in terms of the Bel-Robinson tensor. The possibility is raised that there may exist stationary solutions to the full Einstein equations in five dimensions.Dedicated to Achille Papapetrou on the occasion of his retirement.Supported in part by NSF grant No. PHY-76-07299.     

Can massive gravitons be an alternative to dark energy?

In this work, we explore some cosmological implications of the model proposed by M. Visser in 1998. In his approach, Visser intends to take into account mass for the graviton by means of an additional bimetric tensor in the Einstein?s field equations. Our study has shown that a consistent cosmological model arises from the Visser?s approach. The most interesting feature is that an accelerated expansion phase naturally emerges from the cosmological model, and we do not need to postulate any kind of dark energy to explain the current observational data for distant type Ia supernovae (SNIa).     

Black holes and groups of type E 7

We report some results on the relation between extremal black holes in locally supersymmetric theories of gravity and groups of type E ₇, appearing as generalized electric-magnetic duality symmetries in such theories. Some basics on the covariant approach to the stratification of the relevant symplectic representation are reviewed, along with a connection between special K?hler geometry and a ??generalization?? of groups of type E ₇.     

Conformations and enthalpies of formation of methylenecyclohexane, 1,4‐dimethylenecyclohexane,cyclohexanone, 4‐methylenecyclohexanone, 1,4‐cyclohexanedione,and their mono‐ and dioxa derivatives by G3(MP2)//B3LYP calculations

A computational study of the stable conformations and gas‐phase enthalpies of formation at 25 °C of the title compounds has been carried out by G3(MP2)//B3LYP calculations. The work stems from our early observations on the thermodynamic and NMR spectroscopic properties of 2‐methylenetetrahydropyran and related compounds suggesting a dominating chair conformation, with poor p–π overlap in the ? O? C?C moiety, for these compounds. Besides computational verification of the chair conformation of 2‐methylenetetrahydropyran, the work was extended to find out the stable conformations of a number of other related compounds and to evaluate the relative stabilities of the various conformers. Another important goal of the work was the estimation of the gas‐phase enthalpies of formation of the present compounds, for which such literature data are scarce. A significant error in the literature value of the enthalpy of formation of methylenecyclohexane was found. Finally, the relative enthalpy levels of the isomeric compounds of this work are discussed. The high thermodynamic stability of the compounds containing an ester functional group, ? O? C?O, relative to the stability of isomeric compounds with an ? O? C?C moiety in place of the ester function, is demonstrated. Copyright © 2009 John Wiley & Sons, Ltd.