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.     

Quirino Majorana’s Experiments on the Speed of Light and Gravitational Absorption

Quirino Majorana (1871–1957) was an outstanding Italian experimental physicist who investigated a wide range of phenomena during his long career in Rome,Turin, and Bologna. We focus on his experiments in Turin during 1916–1921 and in Bologna during 1921–1934 to test the validity of Albert Einstein’s postulate on the constancy of the speed of light and to detect gravitational absorption. These experiments required extraordinary skill, patience, and dedication, and all of them confirmed Einstein’s postulate and Isaac Newton’s law of universal gravitation to high precision. Had they not done so, Majorana’s fame among historians and physicists no doubt would be much greater than it is today. Giorgio Dragoni is Professor of History of Physics at the University of Bologna. Giulio Maltese is a Roman member of the Italian Society for the History of Physics and Astronomy. Luisa Atti is a Bolognese member of the Association for the Teaching of Physics.     

Regular Twists: Replicating Coulomb’s Wire-Torsion Experiments

I discuss our replication of the wire-torsion experiments that Charles Augustin Coulomb (1736–1806) reported in a session of the Paris Académie des Sciences in 1784. I first explain the nature and purpose of the replication method and then apply it to an analysis of Coulomb’s experiments. I conclude by placing Coulomb’s presentation of his memoir into its specific historical contest.     

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.     

Einstein’s “Zur Elektrodynamik...” (1905) Revisited, With Some Consequences

Einstein, in his “Zur Elektrodynamik bewegter K?rper”, gave a physical (operational) meaning to “time” of a remote event in describing “motion” by introducing the concept of “synchronous stationary clocks located at different places”. But with regard to “place” in describing motion, he assumed without analysis the concept of a system of co-ordinates.In the present paper, we propose a way of giving physical (operational) meaning to the concepts of “place” and “co-ordinate system”, and show how the observer can define both the place and time of a remote event. Following Einstein, we consider another system “in uniform motion of translation relatively to the former”. Without assuming “the properties of homogeneity which we attribute to space and time”, we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, “one-way” and “two-way” velocities of light, symmetry, the “group property” of inertial reference frames, length contraction and time dilatation, and the “twin paradox”. Finally, we point out a flaw in Einstein’s argument in the “Electrodynamical Part” of his paper and show that the Lorentz force formula and Einstein’s formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck’s formula for mass suffices. (Except for the reference to Planck’s formula, we restrict ourselves to Physics of 1905.)     

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.     

Enrico Fermi’s Discovery of Neutron-Induced Artificial Radioactivity:The Influence of His Theory of Beta Decay

We analyze the influence of Enrico Fermi’s theory of beta decay, which he formulated in December 1933, on his experimental discovery of neutron-induced artificial radioactivity four months later, in March 1934.We discuss Gian Carlo Wick’s application of Fermi’s theory in interpreting Frédéric Joliot and Irène Curie’s discovery of alpha-particle-induced artificial radioactivity, and how Fermi was then influenced by his theory in planning his neutron-bombardment experiments, in his decision to use a radon-beryllium (Rn-Be) neutron source, and in his choice of the elements he bombarded with Rn-Be neutrons. Our analysis is based crucially on Fermi’s first laboratory notebook, the Hirpine Notebook, which is preserved in the Oscar D’Agostino Archives in the Technical Institute “Oscar D’Agostino” in Avellino, Italy, and on the materials that are preserved in the Fermi Archives in the Domus Galilaeana in Pisa. These documents enable us to reconstruct Fermi’s discovery of neutron-induced artificial radioactivity and to assign an exact date to it of March 20, 1934.     

Relativistic compact objects in isotropic coordinates

We present a matrix method for obtaining new classes of exact solutions for Einstein’s equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein’s equations to two independent Riccati-type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic-type fluid with an equation of statep =γρ is discussed in detail.     

Schrödinger’s Cat Meets Einstein’s Twins: A Superposition of Different Clock Times

The phenomenon of quantum superposition, which allows a physical system to exist in different states ‘simultaneously’, is one of the most bizarre notions in physics. Here we illustrate an even more bizarre example of it: a superposed state of a physical system consisting of both an ‘older’ version and a ‘younger’ version of that system. This can be accomplished by exploiting the special relativistic effect of time dilation featuring in Einstein’s famous twin paradox.     

Geometry of the thermodynamics of the black holes in Ho<Emphasis Type="Italic">ř</Emphasis>ava-Lifshitz gravity

Recently, a non-relativistic renormalizable theory of gravity has been proposed by Hořava. This theory is essentially a field theoretic model for a UV complete theory of gravity and it reduces to Einstein’s general relativity at large distances. Subsequently, Cai and his collaborators have obtained black hole solution in this gravity theory and studied the thermodynamic properties of the black hole solutions. In present work, we investigate the geometric thermodynamics of the above black hole solutions and examine the possibilities of any phase transition.     

The English Galileo: Thomas Harriot and the Force of Shared Knowledge in Early Modern Mechanics

I discuss the work of the English mathematician and philosopher Thomas Harriot (1560–1621), analyzing especially his work on projectile motion, and comparing it to that of his contemporary Galileo Galilei (1564–1642). I argue that although their work on projectile motion was carried out independently and displays both similarities and differences, it shows that they focused on common challenging objects of study that embodied what I term “points of contact” between preclassical and classical mechanics. I also argue that their shared knowledge defined the space of possible solutions to the problem of projectile motion, although the inferential pathways they followed through their shared knowledge proceeded in exactly opposite directions. I conclude that their work suggests that the lines of development in early modern mechanics converged in such a way that the long-term development of science was largely unaffected by the peculiarities in an individual scientist’s work.     

Louis Essen and the Velocity of Light: From Wartime Radar to Unit of Length

Louis Essen (1908–1997), working at the National Physical Laboratory in Teddington, England, was the first scientist to realize that the value for the velocity of light used widely during World War II was incorrect. In 1947 he published his first determination of it, which was 16 kilometers per second higher than the accepted value, causing a great deal of controversy in the scientific community. His new value was not accepted for several years, until it was shown that it improved the precision of range-finding by radar. Essen’s result has remained as the internationally accepted value despite a number of attempts to improve on it. I discuss Essen’s work and also examine other optical and nonoptical determinations that were made in the United States, and their limits of accuracy. I also identify the reasons why it took so long for Essen’s new value to be accepted, and how it led to changes in the definition of the units of length and time.     

Accelerating black holes in anti-de Sitter universe

A physical interpretation of theC-metric with a negative cosmological constantΛ is suggested. Using a convenient coordinate system it is demonstrated that this class of exact solutions of Einstein’s equations describes uniformly accelerating (possibly charged) black holes in anti-de Sitter universe. Main differences from the analogous de Sitter case are emphasised. Dedicated to my academic teacher Prof. J. Bičák on the occasion of his 60th birthday. This work was supported by the grant GACR-202/99/0261 of the Czech Republic and GAUK 141/2000 of Charles University in Prague.     

A K Raychaudhuri and his equation

Amal Kumar Raychaudhuri died on June 18, 2005. This essay follows the lecture which I gave in honour of this great Indian scientist and teacher on December 26, 2005 in Puri, India. Invited plenary talk delivered at the International Conference on Einstein’s Legacy in the New Millennium, December 15–22, 2005, Puri, India.     

Possible Minkowskian language in two-level systems

One hundred years ago, in 1908, Hermann Minkowski completed his proof that Maxwell’s equations are covariant under Lorentz transformations. During this process, he introduced a four-dimensional space called the Minkowskian space. In 1949, P.A.M. Dirac showed the Minkowskian space can be handled with the light-cone coordinate system with squeeze transformations. While the squeeze is one of the fundamental mathematical operations in optical sciences, it could serve useful purposes in two-level systems. Some possibilities are considered in this report. It is shown possible to cross the light-cone boundary in optical and two-level systems while it is not possible in Einstein’s theory of relativity.     

The Politics of Forgetting: Otto Hahn and the German Nuclear-Fission Project in World War II

As the co-discoverer of nuclear fission and director of the Kaiser Wilhelm Institute for Chemistry, Otto Hahn (1879–1968) took part in Germany‘s nuclear-fission project throughout the Second World War. I outline Hahn’s efforts to mobilize his institute for military-related research; his inclusion in high-level scientific structures of the military and the state; and his institute’s research programs in neutron physics, isotope separation, transuranium elements, and fission products, all of potential military importance for a bomb or a reactor and almost all of it secret. These activities are contrasted with Hahn’s deliberate misrepresentations after the war, when he claimed that his wartime work had been nothing but “purely scientific” fundamental research that was openly published and of no military relevance.     

The Newtonian limit of spacetimes for accelerated particles and black holes

Solutions of vacuum Einstein’s field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite objects. Their Newtonian limit is analyzed using the Ehlers frame theory. Generic spacetimes with axial and boost symmetries are first studied from the Newtonian perspective. The results are then illustrated by specific examples such as C-metric, Bonnor–Swaminarayan solutions, self-accelerating “dipole particles”, and generalized boost-rotation symmetric solutions describing freely falling particles in an external field. In contrast to some previous discussions, our results are physically plausible in the sense that the Newtonian limit corresponds to the fields of classical point masses accelerated uniformly in classical mechanics. This corroborates the physical significance of the boost-rotation symmetric spacetimes. Dedicated to the memory of Jürgen Ehlers (29 December 1929 to 20 May 2008).     

The geometrical unification of gravity with its source

I give a personal retrospect covering the years during which Mashhoon, myself and others developed a unification of the gravitational field and its source (matter). In this geometrical approach, Einstein’s 4D field equations of general relativity with a source are derived from the 5D Ricci equations for apparent vacuum. The main equations are given, along with comments on how they were arrived at. They describe gravity, electromagnetism and a scalar field. This induced-matter or space–time–matter theory is in agreement with observation and invites further development. Mass, Matter and Mashhoon: a Tribute to Bahram Mashhoon on his 60th Birthday.     

Equations of motion for Einstein’s field in non-integer dimensional space

Equations of motion for Einstein’s field in fractional dimension of 4 spatial coordinates are obtained. It is shown that time dependent part of Einstein’s wave function is single valued for only 4-integer dimensional space.