Storming a Citadel: Mathematical Theory and Experimental Practice

Based upon a comparison of the viscosity experiments of James Clerk Maxwell (1831–1879) and Oskar Emil Meyer (1834–1909) in the 1860s, I argue that mathematical theory plays a significant role in both aspects of experimental practice, the design and construction of an experimental apparatus and the transformation of the observed experimental data into the value of a physical quantity. I argue further that Maxwell’s and Meyer’s evaluation of each other’s theoretical and experimental work depended significantly on the mathematical tools they employed in their theories.     

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.     

Science, Technology, and the Niels Bohr Institute in Occupied Denmark

I argue that research in the basic sciences during the German occupation of Denmark, which began on April 9, 1940, suffered considerably, while research and development in technology enjoyed improved conditions as Danish industry moved toward the requirements of the German wartime economy. Several organizations were created to further Danish–German scientific and cultural collaboration or to manifest Danish cultural identity. The staff of the Danish Technical College and the number of their publications remained largely constant although no papers appeared in British or American journals after 1941. Danish universities massively resisted collaboration and maintained an illusion of “business as usual.” At the Niels Bohr Institute, laboratory equipment continued to be constructed and developed and scientists continued to publish in Danish and other Scandinavian journals, although they were increasingly isolated owing to their inability to obtain foreign scientific journals and to correspond with foreign scientists. The Niels Bohr Institute was occupied from December 6, 1943, to February 3, 1944, a surprisingly short period, owing, I argue, to strategic compromises in following incompatible orders from the German army, security police, and civilian administration. Finally, I offer an interpretation of Niels Bohr’s vehemently negative reaction to Werner Heisenberg in their meeting in Copenhagen in September 1941.     

Richard Gans: The First Quantum Physicist in Latin America

Richard Gans (1880–1954) was appointed Professor of Physics and Director of the Institute of Physics of the National University of La Plata,Argentina, in 1912 and published a series of papers on quantum physics between 1915 and 1918 that marked him as the first quantum physicist in Latin America. I set Gans’s work within the context of his education and career in Germany prior to 1912 and his life and work in Argentina until 1925, as well as the foundation of the Institute of Physics of the National University of La Plata in 1906–1909 and its subsequent development by Emil Bose (1874–1911). I conclude by commenting on Gans’s life after he returned to Germany in 1925 and then immigrated once again to Argentina in 1947.     

Poincaré’s Relativistic Physics: Its Origins and Nature

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability to detect absolute motion, or motion relative to the ether, to the principle of relativity, and its mathematics ensured that it would be compatible with that principle. Although Poincaré’s aim and theory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory but as an independent endeavor. Poincaré was led to advance the principle of relativity as a consequence of his reflections on late nineteenth-century electrodynamics; of his conviction that physics should be formulated as a physics of principles; of his conventionalistic arguments on the nature of time and its measurement; and of his knowledge of the experimental failure to detect absolute motion. The nonrelativistic theory of electrodynamics of Hendrik A.Lorentz (1853–1928) of 1904 provided the means for Poincaré to elaborate a relativistic physics that embraced all known physical forces, including that of gravitation. Poincaré did not assume any dynamical explanation of the Lorentz transformation, which followed from the principle of relativity, and he did not seek to dismiss classical concepts, such as that of the ether, in his new relativistic physics. Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar Ilan University.     

Lagrangian fractional mechanics — a noncommutative approach

The extension of coordinate-velocity space with noncommutative algebra structure is proposed. For action of fractional mechanics considered on such a space the respective Euler-Lagrange equations are derived via minimum action principle. It appears that equations of motion in the noncommutative framework do not mix left and right derivatives thus being simple to solve at least in the linear case. As an example, two models of oscillator with fractional derivatives are studied. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Otto Hahn: Responsibility and Repression

The role that Otto Hahn (1879–1968) played in the discovery of nuclear fission and whether Lise Meitner (1878–1968) should have shared the Nobel Prize for that discovery have been subjects of earlier studies, but there is more to the story. I examine what Hahn and the scientists in his Kaiser Wilhelm Institute for Chemistry in Berlin-Dahlem did during the Third Reich, in particular, the significant contributions they made to the German uranium project during the Second World War. I then use this as a basis for judging Hahn’s postwar apologia as the last president of the Kaiser Wilhelm Society and first president of its successor, the Max Planck Society.     

Weimar Physics: Sommerfeld’s Seminar and the Causality Principle

The development of quantum mechanics in the period 1920–1927 posed challenges to the understanding of causality and its incorporation into the new dynamics. Though aware of these challenges to the classical concepts of causality and to the conservation laws of energy and momentum, Arnold Sommerfeld and the members of his seminar never wavered in their commitment to the conservation laws because of their belief in the “preestablished harmony” between mathematics and physics that Felix Klein, David Hilbert, and Hermann Minkowski had championed. I survey these developments and trace how the concept of causality was reformulated in scattering theory by Gregor Wentzel, Enrico Fermi, and Giulio Racah.     

Dick Crane��s California Days

Horace Richard Crane (1907–2007) was born and educated in California. His childhood was full of activities that helped him become an outstanding experimental physicist. As a graduate student at the California Institute of Technology (1930–1934), he had the good fortune to work with Charles C. Lauritsen (1892–1968) just as he introduced accelerator-based nuclear physics to Caltech. They shared the euphoric excitement of opening up a new field with simple, ingenious apparatus and experiments. This work prepared Crane for his career at the University of Michigan (1935–1973) where in the 1950s, after making the first measurement of the electron’s magnetic moment, he devised the g−2 technique and made the first measurement of the anomaly in the electron’s magnetic moment. A man of direct, almost laconic style, he made lasting contributions to the exposition of physics to the general public and to its teaching in high schools, community colleges, four-year colleges, and universities. I tell how he became a physicist and describe some of his early achievements.     

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.     

In Memoriam Ludwig Boltzmann: A Life of Passion

Ludwig Boltzmann (1844–1906) died just over a century ago. In commemoration of his death, I sketch his pioneering contributions to thermodynamics and statistical mechanics within the context of his often troubled life.     

Why Should We Interpret Quantum Mechanics?

The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this epistemic view of states appears to solve foundational problems of quantum mechanics only at the price of being essentially incomplete.     

Chandrasekhar’s book <Emphasis Type="Italic">An Introduction to the Study of Stellar Structure</Emphasis>

For me, and for many astrophysicists of my generation, Chandrasekhar’s book An Introduction to the Study of Stellar Structure was very important. I could not have done my PhD (1962–1965) without it. Much more recently (1998) I realized that I could not have written my lecture course on thermodynamics and statistical mechanics without much of it, particularly the first chapter. I shall present anecdotal evidence that the influence of his discussion on the second law of thermodynamics has been important not just for astrophysics but for a much wider range of physics.     

In Memoriam

In 1905 Lord Kelvin (1824–1907) was awarded the second John Fritz Medal for a lifetime of outstanding achievements in science and technology. I sketch Kelvin’s life, education, and work in thermodynamics, electrical technology, and instrumentation, and his role in the laying of the Atlantic cable. I then turn to Kelvin’s four visits to America, in 1876 on the centenary of the Declaration of Independence of the United States of America; in 1884 when he gave his famous Baltimore Lectures at The Johns Hopkins University; in 1897 when he visited Niagara Falls for the third time and advised George Westinghouse (1846–1914) on how to develop its enormous water power for the generation of electricity; and in 1902 when he advised George Eastman (1854–1932) on the development of the photographic industry. Written in connection with the Kelvin Centenary Year 2007; see “Celebrating the Life of Lord Kelvin,” University of Glasgow News Review No. 11 (2007), 4. Matthew Trainer: Matthew Trainer received his M.Phil. degree in physical sciences at the University of Edinburgh in 1980 and currently is a laboratory instructor at the University of Glasgow where his research focuses in part on the life and work of Lord Kelvin.     

Philipp Frank,Richard von Mises,and the Frank-Mises

The theoretical physicist Philipp Frank (1884–1966) and the applied mathematician Richard von Mises (1883–1953) both received their university education in Vienna shortly after 1900 and became friends at the latest during the Great War.They were attached to the Vienna Circle of Logical Positivists and wrote an influential two-part work on the differential and integral equations of mechanics and physics, the Frank-Mises, of 1925 and 1927, with its second edition following in 1930 and 1935.This work originated in the lectures that the mathematician Bernhard Riemann (1826–1866) delivered on partial differential equations and their applications to physical questions at the University of G?ttingen between 1854 and 1862, which were edited and published posthumously in1869 by the physicist Karl Hattendorff (1834–1882).The immediate precursor of the Frank-Mises, however, was the extensive revision of Hattendorff’s edition of Riemann’s lectures that the mathematician Heinrich Weber (1842–1913) published in two volumes, the Riemann-Weber, of 1900 and 1901, with its second edition following in 1910 and 1912. I trace this historical lineage, explore the nature and contents of the Frank-Mises, and discuss its complementary relationship to the first volume of the text that the mathematicians Richard Courant (1888–1972) and David Hilbert (1862–1943) published on the methods of mathematical physics in 1924, the Courant-Hilbert,which, when it and its second volume of 1937 were translated into English and extensively revised in 1953 and 1961, eclipsed the classic Frank-Mises.     

Fritz Reiche and the Emergency Committee in Aid of Displaced Foreign Scholars

I discuss the family background and early life of the German theoretical physicist Fritz Reiche (1883–1969) in Berlin; his higher education at the University of Berlin under Max Planck (1858–1947); his subsequent work at the University of Breslau with Otto Lummer (1860–1925); his return to Berlin in 1911, where he completed his Habilitation thesis in 1913, married Bertha Ochs the following year, became a friend of Albert Einstein (1879–1955), and worked during and immediately after the Great War. In 1921 he was appointed as ordentlicher Professor of Theoretical Physics at the University of Breslau and worked there until he was dismissed in 1933. He spent the academic year 1934–1935 as a visiting professor at the German University in Prague and then returned to Berlin, where he remained until, with the crucial help of his friend Rudolf Ladenburg (1882–1952) and vital assistance of the Emergency Committee in Aid of Displaced Foreign Scholars, he, his wife Bertha, and their daughter Eve were able to emigrate to the United States in 1941 (their son Hans had already emigrated to England in 1939).From 1941–1946 he held appointments at the New School for Social Research in New York, the City College of New York, and Union College in Schenectady, New York, and then was appointed as an Adjunct Professor of Physics at New York University, where his contract was renewed year-by-year until his retirement in 1958.     

George Hartley Bryan, Ludwig Boltzmann, and the Stability of Flight

A century ago, George Hartley Bryan (1864–1928) published his classic book, Stability in Aviation. I draw together some strands from events that awakened his interest in the nascent science of aviation, in particular the stability of flight. Prominent among those who influenced him was Ludwig Boltzmann (1844–1906), who held Bryan in high esteem for his contributions to thermodynamics and kinetic theory. I argue that the seeds of Bryan’s interest in aviation were sown at the British Association meeting at Oxford in the summer of 1894, at which Boltzmann was guest of honor. A joint discussion between Section A (Mathematical and Physical Science) and Section G (Mechanical Science) was devoted to the problems of flight, during the course of which Boltzmann revealed a hitherto unsuspected enthusiasm for flying.     

<Emphasis Type="Italic">N</Emphasis> = 4 supersymmetric Eguchi-Hanson sigma model in <Emphasis Type="Italic">d</Emphasis> = 1

We show that it is possible to construct a supersymmetric mechanics with four supercharges possessing not conformally flat target space. A general idea of constructing such models is presented. A particular case with Eguchi-Hanson target space is investigated in detail: we present the standard and quotient approaches to get the Eguchi-Hanson model, demonstrate their equivalence, give a full set of nonlinear constraints, study their properties and give an explicit expression for the target space metric. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Relational EPR

We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of “non-locality”, when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.     

Aspects of the Mach–Einstein Doctrine and Geophysical Application (A Historical Review)

The present authors have given a mathematical model of Mach's principle and of the Mach–Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach–Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by C. Neumann, Mach, Friedl?nder and Einstein—result from the Riemannian dynamics with the Mach–Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t². In this paper, secular consequences of the Mach–Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation of the parameter α is the order of magnitude , where H₀ is the instantaneous value of the Hubble constant: . The relation of the secular consequences of the Mach–Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed.