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.)     

Role models for complex networks

We present a framework for automatically decomposing (“block-modeling”) the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph (“block model”) depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both two-mode and one-mode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy.     

On the collective excitations and the existence of the gap in the degenerate Bose gas spectrum

Themodel of degenerate weakly nonideal Bose gas is considered without the assumption on the C-number nature of creation and annihilation operators of particles in the zero-momentum state. It was shown that the “density-density” Green’s function pole defines the Bogolyubov spectrum of phonon-roton-type collective excitations. The single-particle excitation spectrum is characterized by the gap whose value is defined by the particle density in the “condensate”.     

On “Gauge Renormalization” in Classical Electrodynamics

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined.     

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.     

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.     

Concepts of Time in Physics: A Synopsis

I summarize the historical development of concepts of time in physics from antiquity to the end of the twentieth century. Editors’ Note: Max Jammer received the American Physical Society/American Institute of Physics Abraham Pais Prize for the History of Physics for 2007, “For his groundbreaking historical studies of fundamental concepts in physics, including his comprehensive account of the development of quantum mechanics.” We publish here his Pais Prize Lecture, which was presented at the APS meeting in Jacksonville, Florida, on April 16, 2007.     

On Visibility in the Afshar Two-Slit Experiment

A modified version of Young’s experiment by Shahriar Afshar indirectly reveals the presence of a fully articulated interference pattern prior to the post-selection of a particle in a “which-slit” basis. While this experiment does not constitute a violation of Bohr’s Complementarity Principle as claimed by Afshar, both he and many of his critics incorrectly assume that a commonly used relationship between visibility parameter V and “which-way” parameter K has crucial relevance to his experiment. It is argued here that this relationship does not apply to this experimental situation and that it is wrong to make any use of it in support of claims for or against the bearing of this experiment on Complementarity.     

Ettore Majorana’s Course on Theoretical Physics: A Recent Discovery

We analyze in some detail the course that Ettore Majorana gave on theoretical physics at the University of Naples between January and March 1938, just prior to his mysterious disappearance. We discuss, in particular, the recently discovered Moreno Lecture Notes, in which all of Majorana’s lectures are recorded, six of which are not present in those that are preserved in the Domus Galilaeana in Pisa, Italy. Antonino Drago is a retired professor of history of physics at the University of Naples “Federico II.” Salvatore Esposito is a researcher on theoretical physics and history of physics at the University of Naples “Federico II.”     

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.     

Deconstructing Wigner’s density matrix concerning the mind-body question

In honor of the centennial of Eugene Wigner’s birth, a possible interpretation is given of the density matrix appearing in his classic paper, “Remarks on the mind-body question.” It is argued that nearinstantaneous vanishing of the quantum coherences of the reduced density matrix of the measured object would occur either in the case of Wigner’s friend, or in the case of any complex measuring automaton (conscious or not) making the measurement.     

Nonlocality Without Nonlocality

Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all. This paper is dedicated to the memory of John A. Wheeler.     

Relational Interpretation of the Wave Function and a Possible Way Around Bell’s Theorem

The famous “spooky action at a distance” in the EPR-scenario is shown to be a local interaction, once entanglement is interpreted as a kind of “nearest neighbor” relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the “nearest neighbor” relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, “position” becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the “weird” aspects, like the particle-wave duality, the non-locality of entanglement, or the “mystery” of the double-slit experiment, disappear. Furthermore, this picture circumvents the restrictions set by Bell’s inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics. PACS: 03.65.Ud, 04.60.Nc     

Atomic Energy is ��Moonshine��: What did Rutherford Really Mean?

In the 1930s Ernest Rutherford (1871–1937) repeatedly suggested, sometimes angrily, that the possibility of harnessing atomic energy was “moonshine.” Yet, as war approached he secretly advised the British government to “keep an eye on the matter.” I suggest that Rutherford did not really believe his “moonshine” claim but did have profound reasons for making it. If I am correct, then this casts additional light on his personality, stature, and career.     

Bell’s Theorem,Many Worlds and Backwards-Time Physics: Not Just a Matter of Interpretation

The classic “Bell’s Theorem” of Clauser, Holt, Shimony and Horne tells us that we must give up at least one of: (1) objective reality (aka “hidden variables”); (2) locality; or (3) time-forwards macroscopic statistics (aka “causality”). The orthodox Copenhagen version of physics gives up the first. The many-worlds theory of Everett and Wheeler gives up the second. The backwards-time theory of physics (BTP) gives up the third. Contrary to conventional wisdom, empirical evidence strongly favors Everett-Wheeler over orthodox Copenhagen. BTP allows two major variations—a many-worlds version and a neoclassical version based on Partial Differential Equations (PDE), in the spirit of Einstein. Section 2 of this paper discusses the origins of quantum measurement according to BTP, focusing on the issue of how we represent condensed matter objects like polarizers in a model “Bell’s Theorem” experiment. The backwards time telegraph (BTT) is not ruled out in BTP, but is highly speculative for now, as will be discussed. The views herein are not anyone’s official views, but this does constitute work produced on government time.     

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.     

A Conversation with Robert F. Christy – Part II

Robert F. Christy, Institute Professor of Theoretical Physics Emeritus at Caltech, recalls his wartime work at Los Alamos on the critical assembly for the plutonium bomb (“the Christy bomb”); the Alamogordo test, July 16, 1945; the postwar concerns of ALAS (Association of Los Alamos Scientists); his brief return to the University of Chicago and move to Caltech; friendship with and later alienation from Edward Teller; work with Charles and Tommy Lauritsen and William A. Fowler in Caltech’s Kellogg Radiation Laboratory; Freeman Dyson’s Orion Project; work on the meson and RR Lyrae stars; fellowship at Cambridge University; 1950s Vista Project at Caltech; his opposition to the Strategic Defense Initiative; and his post-retirement work for the National Research Council’s Committee on Dosimetry and on inertial-confinement fusion.     

Network robustness to targeted attacks. The interplay of expansibility and degree distribution

We study the property of certain complex networks of being both sparse and highly connected, which is known as “good expansion” (GE). A network has GE properties if every subset S of nodes (up to 50% of the nodes) has a neighborhood that is larger than some “expansion factor” φ multiplied by the number of nodes in S. Using a graph spectral method we introduce here a new parameter measuring the good expansion character of a network. By means of this parameter we are able to classify 51 real-world complex networks — technological, biological, informational, biological and social — as GENs or non-GENs. Combining GE properties and node degree distribution (DD) we classify these complex networks in four different groups, which have different resilience to intentional attacks against their nodes. The simultaneous existence of GE properties and uniform degree distribution contribute significantly to the robustness in complex networks. These features appear solely in 14% of the 51 real-world networks studied here. At the other extreme we find that ∼40% of all networks are very vulnerable to targeted attacks. They lack GE properties, display skewed DD — exponential or power-law — and their topologies are changed more dramatically by targeted attacks directed at bottlenecks than by the removal of network hubs.     

A Simple Example of “Quantum Darwinism”: Redundant Information Storage in Many-Spin Environments

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the “objects of interest.” Exactly how this information is inscribed in the environment is essential for the emergence of “the classical” from the quantum substrate. In this paper, we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system’s state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of “the fittest information” (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment’s role in the quantum-classical transition beyond the traditional paradigm of decoherence.