Adventures of a Theoretical Physicist, Part I: Europe

I was born in Budapest, Hungary, on July 7, 1907, and this first part of my interview with Andor Frenkel focuses on my life and work in Europe. After my elementary and secondary education I studied mathematics at the University of Budapest for two years. I went to the University of G?ttingen in 1928 where I attended Max Born’s lectures on quantum mechanics, which influenced me to change from mathematics to physics, and as a consequence I focused on filling the gaps in my physics background. When ready to turn to research work I followed the advice of my friend Edward Teller and spent three months in Werner Heisenberg’s group at the University of Leipzig in the summer of 1930. That fall I returned to the University of Budapest, where I received my Ph.D.degree in the summer of 1932. Two months later, because I had become entangled in the illegal Communist Party, I was arrested and sentenced to fourteen months in prison. Fifteen months after my release, I joined Lev Landau’s group at the Ukrainian Physical-Technical Institute in Kharkov, passed Landau’s so-called “theorminimum” program on my second attempt, began research on the theory of liquid helium, and lost my faith in communism following Stalin’s repressive measures. I obtained an exit visa through the Hungarian Legation and returned to Budapest in June 1937. That September, again with the help of my friend Edward Teller, I attended a conference in Paris where I met Fritz London and Edmond Bauer, who arranged for me a small scholarship and an association with the Langevin laboratory at the Collège de France. Four months later, in January 1938 Kapitza, and John F. Allen and A. Donald Misener reported their independent discovery of the superfluidity of helium, which London and I explored theoretically and I explained with my two-fluid theory later in 1938. Following the German invasion of France, my wife and I left Paris for Toulouse in June 1940, obtained exit visas to enter Spain and Portugal in February 1941, and boarded a Portuguese ship for New York the following month. The second part of this interview, covering my life and work in America, will appear in the next issue.     

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.     

What’s Wrong with this Criticism

One of the endearing traits of Asher Peres is that when somebody publishes something he knows to be wrong, he does not bother to refute it, even if the paper criticizes his own work. Life is too brief for such frivolity. As a small 70th birthday present I would like to answer one such recent attack. It’s not much of a present, since Asher will not read my paper. Why should he? He already knows this criticism is nonsense. But somebody has to set the written record straight for future historians, so I will do it as part of this celebration. Fortunately this particular issue is so easily settled that this can be a very short paper. Since Asher is a master of the very short paper, my Peresian brevity is an important part of my act of homage. The criticism I address can be found in a new formulation by Karl Hess and Walter Philipp(1) of their view that all versions of Bell’s theorem are fundamentally flawed. I focus here only on their criticism of the version in Asher’s book.(2) This essay was completed and submitted before the sad and unexpected death of Asher Peres on January 1, 2005. I have left it in its original form because I sent Asher a preprint, and he told me that his wife Aviva had enjoyed it. I like to think that perhaps he had a quick look and enjoyed it a bit himself. Life in the field of quantum foundations will not be as much fun without his opinions, his wit, and his warmth I point out that in spite of recent claims to the contrary, the proof of Bell’s theorem in Asher Peres’s book works even in the presence of time-correlated hidden variables in the detectors.     

Finitary Topos for Locally Finite,Causal and Quantal Vacuum Einstein Gravity

The pentalogy (Mallios, A. and Raptis, I. (2001). International Journal of Theoretical Physics 40, 1885; Mallios, A. and Raptis, I. (2002). International Journal of Theoretical Physics 41, 1857; Mallios, A. and Raptis, I. (2003).International Journal of Theoretical Physics 42, 1479; Mallios, A. and Raptis, I. (2004). ‘paper-book’/research monograph); I. Raptis (2005). International Journal of Theoretical Physics (to appear)is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantumcausal sets involved therein, on which a finitary (:locally finite), singularity-free, background manifold independent and geometrically prequantized version of the gravitational vacuum Einstein field equations were seen to hold, into a topos structure . We show that the category of finitary differential triads is a finitary instance of an elementary topos proper in the original sense dueto Lawvere and Tierney. We present in the light of Abstract Differential Geometry (ADG) a Grothendieck-type of generalization of Sorkin’s finitary substitutes of continuous spacetime manifoldtopologies, the latter’s topological refinement inverse systems of locally finite coverings and their associated coarse graining sieves, the upshot being that is also a finitary example of a Grothendieck topos. In the process, we discover that the subobject classifier Ω _fcq of is a Heyting algebra type of object, thus we infer that the internal logic of our finitary topos is intuitionistic, as expected. We also introduce the new notion of ‘finitary differential geometric morphism’ which, as befits ADG, gives a differential geometric slant to Sorkin’s purely topological acts of refinement (:coarse graining). Based on finitary differential geometric morphisms regarded as natural transformations of the relevant sheaf categories, we observe that the functorial ADG-theoretic version of the principle of general covariance of GeneralRelativity is preserved under topological refinement. The paper closes with a thorough discussion of four future routes we could take in order to further develop our topos-theoretic perspective on ADG-gravity along certain categorical trends in current quantum gravity research. PACS numbers: 04.60.-m, 04.20.Gz, 04.20.-q Posted at the General Relativity and Quantum Cosmology (gr-qc) electronic archive (www.arXiv.org), as: gr-qc/0507100.     

Finitary-Algebraic ‘Resolution’ of the Inner Schwarzschild Singularity

A ‘resolution’ of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Differential Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machinery of Abstract Differential Geometry (ADG) is employed. As in previous works [Mallios, A. and Raptis, I. (2001). Finitary spacetime sheaves of quantum causal sets: Curving quantum causality. International Journal of Theoretical Physics, 40, 1885 [gr-qc/0102097]; Mallios, A. and Raptis, I. (2002). Finitary Čech-de Rham cohomology. International Journal of Theoretical Physics, 41, 1857 [gr-qc/0110033]; Mallios, A. and Raptis, I. (2003). Finitary, causal and quantal vacuum Einstein gravity. International Journal of Theoretical Physics 42, 1479 [gr-qc/0209048]], which this paper continues, the starting point for the present application of ADG is Sorkin's finitary (:locally finite) poset (:partially ordered set) substitutes of continuous manifolds in their Gel'fand-dual picture in terms of discrete differential incidence algebras and the finitary spacetime sheaves thereof. It is shown that the Einstein equations hold not only at the finitary poset level of ‘discrete events,’ but also at a suitable ‘classical spacetime continuum limit’ of the said finitary sheaves and the associated differential triads that they define ADG-theoretically. The upshot of this is two-fold: On the one hand, the field equations are seen to hold when only finitely many events or ‘degrees of freedom’ of the gravitational field are involved, so that no infinity or uncontrollable divergence of the latter arises at all in our inherently finitistic-algebraic scenario. On the other hand, the law of gravity—still modelled in ADG by a differential equation proper—does not break down in any (differential geometric) sense in the vicinity of the locus of the point-mass as it is traditionally maintained in the usual manifold-based analysis of spacetime singularities in General Relativity (GR). At the end, some brief remarks are made on the potential import of ADG-theoretic ideas in developing a genuinely background-independent Quantum Gravity (QG). A brief comparison between the ‘resolution’ proposed here and a recent resolution of the inner Schwarzschild singularity by Loop QG means concludes the paper. PACS numbers: 04.60.−m, 04.20.Gz, 04.20.−q     

A Personal Adventure in Muon-Catalyzed Fusion

Luis Alvarez and colleagues discovered muon-catalyzed fusion of hydrogen isotopes by chance in late 1956. On sabbatical leave at Princeton University during that year, I read the first public announcement of the discovery at the end of December in that well-known scientific journal, The New York Times. A nuclear theorist by prior training, I was intrigued enough in the phenomenon to begin some calculations. I describe my work here, my interaction with Alvarez, and a summary of the surprising developments, both before and after Alvarez’s discovery. The rare proton–deuteron (p–d) fusion events in Alvarez’s liquid-hydrogen bubble chamber occurred only because of the natural presence of a tiny amount of deuterium (heavy hydrogen). Additionally, the fusion rate, once the proton–deuteron–muon (pdμ ⁻ ) molecular ion has been formed, is sufficiently slow that only rarely does an additional catalytic act occur. A far different situation occurs for muons stopping in pure deuterium or a deuterium–tritium (d–t) mixture where the fusion rates are many orders of magnitude larger and the molecular-formation rates are large compared to the muon’s decay rate. The intricate interplay of atomic, molecular, and nuclear science, together with highly fortuitous accidents in the molecular dynamics and the hope of practical application, breathed life into a seeming curiosity. A small but vigorous worldwide community has explored these myriad phenomena in the past 50 years.     

Ettore Majorana’s Forgotten Publication on the Thomas-Fermi Model

We analyze the forgotten communication of Ettore Majorana (1906–1938?) on the Thomas-Fermi statistical model of the atom, which he presented on December 29, 1928, during the XXII General Meeting of the Italian Physical Society in Rome, and which was published in Il Nuovo Cimento, the Society’s journal, in 1929. His communication was not mentioned subsequently in any of the numerous publications of Enrico Fermi (1901–1954) and his group in Rome, nor in any of the later accounts of Majorana’s life and work. We place Majorana’s contribution within the context of contemporary research on the subject, point out its influence on the final formulation of the Thomas-Fermi statistical model by Fermi and Edoardo Amaldi (1908–1989) in 1934, and discuss Majorana’s other scientific contributions before his mysterious disappearance in 1938. Francesco Guerra is Professor of Theoretical Physics in the Department of Physics at the University of Rome “La Sapienza.” His main fields of research are quantum-field theory, statistical mechanics of complex systems, and the history of nuclear physics. Nadia Robotti is Professor of History of Physics in the Department of Physics at the University of Genoa. Her main fields of research are the history of atomic physics, quantum mechanics, and nuclear physics.     

Bruno Rossi and the Racial Laws of Fascist Italy

Bruno Rossi (1905–1993), one of the giants of 20th-century physics, was a pioneer in cosmic-ray physics and virtually every other aspect of high-energy astrophysics. His scientific career began at the University of Florence in 1928 and continued at the University of Padua until 1938, when the Fascist anti-Semitic racial laws were passed in Italy. He was dismissed from his professorship and was forced to emigrate, as described in unpublished letters and documents that display the international character of physics and physicists. His young bride Nora Lombroso, his love of physics, and the solidarity of the physics community gave him the courage to begin a new life in Copenhagen, Manchester, and in the New World at the University of Chicago, Cornell University, Los Alamos, and after the Second World War at the Massachusetts Institute of Technology where he became the center of a worldwide research network.     

Hans Bethe, My Teacher

I sketch my experiences with Hans Bethe (1906–2005) as a teacher at Cornell University, beginning with my doctoral studies in 1961 and continuing with my work with him on a quantum-mechanics textbook. Hans Bethe, My Teacher: Based on my talk at the Bethe Memorial,Aspen Center for Physics,Aspen,CO, in August 2006. Roman Jackiw: Roman Jackiw is Jerrold Zacharias Professor of Physics at the Massachusetts Institute of Technology.     

Applications of the Dirac Form of the Maxwell Equations in Moving Dielectric Media

Maxwell equations in a resting and nonrelativisticly moving medium can be rewritten in a form of the Dirac equation. In the paper the formal analogy between an electron in the electromagnetic field and a photon in the dielectric medium has been used to consider three effects: Fresnel’s drag, mechanical Faraday effect (interpreted here as a procession of the photon spin) and Landau frequencies in a rotating medium. The third effect, up to my knowledge, is new. It predicts that only some discrete frequencies of light can propagate in a rotating medium.     

Energy deficiency of the electromagnetic-impulse pendulum with respect to the Biot-Savart-Lorentz force law

Summary This letter is intended as a clarification of several doubts cast by Moyssideset al. on the experimental technique and analysis of the electromagnetic impulse pendulum performed at MIT. These disputed points are discussed and the proposed Ampère’s force formula is shown to be able to account for the energy imbalance observed.     

The Physical Tourist

I provide a tour of Madrid, focusing especially on physical institutions that were created during the 19th and 20th centuries.These include the Astronomical Observatory close to the Prado Museum, which itself was conceived as a home for the Royal Academy of Sciences but became instead a world-famous art museum in 1819, leaving the Royal Academy of Sciences without a permanent home until 1866.The Laboratory of Physical Researches was created in 1910, and under the direction of Blas Cabrera (1878–1945), who also held a professorship at the Universidad Central, it fostered most of the Spanish research in physics at the time, in particular the famous spectroscopic researches of Miguel A. Catalán (1894–1957). Nearby were the so-called Transatlantico building and the Students’ Residence where Albert Einstein (1879–1955), for example, lectured in 1923, and which together continue to serve as a major cultural center in Madrid. Later, the physical laboratory was replaced by the National Institute of Physics and Chemistry, which was constructed with funds from the Rockefeller Foundation and inaugurated in 1932. A new University City with its Faculty of Sciences also was constructed on the northwestern outskirts of Madrid, but almost all of its buildings were totally destroyed during the devastating Spanish Civil War of 1936–1939. It was reconstructed after the war and became home, for example, to Spain’s first nuclear reactor, which achieved criticality in 1958.     

On the Link Between the Sparre Equation and Darboux–Treibich–Verdier Equation

The aim of this Letter is to explain the simple link between the widely known Darboux–Treibich–Verdier (DTV) equation and an almost unknown equation introduced and solved by comte de Sparre more than a century ago. Several equations solved earlier by Lamé, Hermite, Picard and Darboux represent particular reductions of Sparre’s equation. We show that DTV equation is not only a simple reduction of the Sparre equation but also represents its canonical form.This article was written in the framework of an ANR project GIMP: Geometry and Integrability in Mathematical Physics contract no. ANR-05-BLAN-0029-01.     

The Playful Physicist

This interview covers Arthur Schawlows professional life from his days as a graduate student at the University of Toronto, through his work with Charles Townes at Columbia University, his work at the Bell Telephone Laboratories, and into his professorship at Stanford University.This interview with Arthur L. Schawlow is adapted from an interview conducted by Joan Lisa Bromberg on January 19,1984, at Stanford University. This interview is one of some 1,000 transcribed interviews available for study by scholars at the American Institute of Physics Center for History of Physics in College Park, Maryland. Requests for reprints should be directed to John S. Rigden, Department of Physics, Washington University, St.Louis, MO 63130, USA, e-mail: jrigden@aip.org     

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.     

Infrared behavior of three-point functions in Landau gauge Yang–Mills theory

Analytic solutions for the three-gluon and ghost–gluon vertices in Landau gauge Yang–Mills theory at low momenta are presented in terms of hypergeometric series. They do not only show the expected scaling behavior but also additional kinematic divergences when only one momentum goes to zero. These singularities, which have also been proposed previously, induce a strong dependence on the kinematics in many dressing functions. The results are generalized to two and three dimensions and a range of values for the ghost propagator’s infrared exponent κ.     

Pion cloud and the sea of the nucleon

I review recent progress in understanding the structure of the nucleon sea and the role of the nucleon’s pion cloud. In particular, I discuss the consequences of the pion cloud for the ƌ−ū asymmetry in the proton, the neutron’s electric form factor, and the proton’s electric to magnetic form factor ratio.     

Coherence vs. decoherence in (some) problems of condensed matter physics

We present an ‘overview’ of coherence-to-decoherence transition in certain selected problems of condensed matter physics. Our treatment is based on a subsystem-plus-environment approach. All the examples chosen in this paper have one thing in common — the environmental degrees of freedom are taken to be bosonic and their spectral density of excitations is assumed to be ‘ohmic’. The examples are drawn from a variety of phenomena in condensed matter physics involving, for instance, quantum diffusion of hydrogen in metals, Landau diamagnetism and c-axis transport in high T _c superconductors.     

Majorana: From Atomic and Molecular, to Nuclear Physics

In the centennial of Ettore Majorana’s birth (1906–1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi’s solution of the celebrated Thomas–Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana’s seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg–Majorana forces) in his later works on theoretical nuclear physics. In all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed.