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It is shown that the correct expressions for momentum and kinetic energy of a particle moving at high speed were already implicit in physics going back to Maxwell. The demonstration begins with a thought experiment of Einstein by which he derived the inertial equivalence of energy, independently of the relativity postulates. A simple modification of the same experiment does the rest.
We discuss three ways of obtaining the Born approximations for Coulomb scattering: The standard way, making use of a convergence factor ("screening"), Oppenheimer's way using cylindrical (instead of spherical) coordinates, and finally Landau and Lifshitz' way. The last one although it does require some background from the theory of generalized functions is nevertheless a very instructive and important technique deserving more exposure to physicists.
I describe the early, from the nineteen sixties, history of attempts at quantizing General Relativity.
An introduction describing Walter Greiner's scientific life for the topical volume to be published by EPJA
The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that operational prescriptions, which are integral to experimental physics, have been largely ignored. This has undoubtedly exacerbated attempts to find a solution to the "measurement problem". In this paper, we fully embrace the ensemble interpretation of quantum mechanics that obviates the need to entertain reduction of the state vector, one of the primary dilemmas of the measurement problem. The other major aspect of the measurement problem, the necessity of describing measurements in terms of classical concepts, remains. However, we argue that the ultimate interface with experiments is described by operational prescriptions and not in terms of the concepts of classical theory. The pedestrian approach presented here suggests that the measurement problem is, in some sense, ill-posed and might never be resolved. This state of affairs is, in part, the result of searching for a theoretical answer to what is fundamentally an experimental question. This point of view is tenable so long as one is willing to view physical theories as providing models of nature rather than complete descriptions of reality. Among other things, these considerations lead us to suggest that the Copenhagen interpretation's insistence on the classicality of the measurement apparatus should be replaced by the requirement that a measurement, which is specified operationally, should simply be of sufficient precision.
In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While their interrelations are examined closely, these four facets of symmetry are scrutinised one after the other in great detail. This decomposition allows us to examine closely the multiple different roles symmetry plays in many places in physics. Furthermore, some connections with others disciplines like neurobiology, epistemology, cognitive sciences and, not least, philosophy are proposed in an attempt to show that symmetry can be an organising principle also in these fields.
In 1847 Christian Ludwig Gerling, Marburg (Germany), suggested the solar parallax to be determined by measuring the position of Venus close to its inferior conjunction, especially at the stationary points, from observatories on nearly the same meridian but widely differing in latitude. James M. Gilliss,astronomer at the newly founded U.S. Naval Observatory, enthusiastically adopted this idea and procured a grant for the young astronomical community of the United States for an expedition to Chile. There they were to observe several conjunctions of Venus and oppositions of Mars, while the accompanying measurements were to be taken at the US Naval Observatory in Washington D.C. and the Harvard College Observatory at Cambridge, USA. This expedition was supported by A. v. Humboldt, C.F. Gauß, J.F. Encke, S.C. Walker, A.D. Bache, B. Peirce and others. From 1849 to 1852 not only were astronomical, but also meteorological and magnetic observations and measurements recorded, mainly in Santa Lucia close to Santiago, Chile. By comparing these measurements with those taken simultaneously at other observatories around the world the solar parallax could be calculated, although incomplete data from the corresponding northern observatories threatened the project's success. In retrospect this expedition can be recognized as the foundation of the Chilean astronomy. The first director of the new National Astronomical Observatory of Chile was Dr. C.W. Moesta, a Hessian student of Christian Ludwig Gerling's. The exchange of data between German, American and other astronomers during this expedition was well mediated by J.G. Flügel, consul of the United States of America and representative of the Smithsonian Institution in Europe, who altogether played a major role in nurturing the relationship between the growing scientific community in the U.S. and the well established one in Europe at that time.
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were only occasionally cited in the 19th century --- besides Hankel, foremost by George Stokes and Maurice Lévy --- and even less so in the 20th until they were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists.
The traveling-wave tube is a critical subsystem for satellite data transmission. Its role in the history of wireless communications and in the space conquest is significant, but largely ignored, even though the device remains widely used nowadays. This paper present, albeit non-exhaustively, circumstances and contexts that led to its invention, and its part in the worldwide (in particular in Europe) expansion of TV broadcasting via microwave radio-relays and satellites. We also discuss its actual contribution to space applications and its conception. The originality of this paper comes from the wide period covered (from first slow-wave structures in 1889 to present space projects) and from connection points made between this device and commercial exploitations. The appendix deals with an intuitive pedagogical description of the wave-particle interaction.
The Einstein Archives contain a considerable collection of calculations in the form of working sheets and scratch paper, documenting Einstein's scientific preoccupations during the last three decades of his life until his death in 1955. This paper provides a brief description of these documents and some indications of what can be expected from a more thorough investigation of these notes.
The history of renormalization is reviewed with a critical eye, starting with Lorentz's theory of radiation damping, through perturbative QED with Dyson, Gell-Mann & Low, and others, to Wilson's formulation and Polchinski's functional equation, and applications to "triviality", and dark energy in cosmology.
From 28 to 30 January 1933 was held at the Institut Henri Poincaré (Paris) the first International Conference of Nonlinear Oscillations organized at the initiative of the Dutch physicist Balthazar Van der Pol and of the Russian mathematician Nikolaï Dmitrievich Papaleksi. The discovery of this forgotten event, whose virtually no trace remains, was made possible thanks to the report written by Papaleksi at his return in USSR. This document has revealed, one the one hand, the list of participants who included French mathematicians: Alfred Liénard, Élie and Henri Cartan, Henri Abraham, Eugène Bloch, Léon Brillouin, Yves Rocard, ... and, on the other hand the content of presentations and discussions. The analysis of the minutes of this conference presented here for the first time highlights the role and involvement of the French scientific community in the development of the theory of nonlinear oscillations.
In a previous paper (part I), the mathematical properties of the cosmic microwave background radiation power spectrum which presents oscillations were discussed. Here, we discuss the physical interpretation: a power spectrum with oscillations is a rather normal characteristic expected from any fluid with clouds of overdensities that emits/absorb radiation or interact gravitationally with the photons, and with a finite range of sizes and distances for those clouds. The standard cosmological interpretation of "acoustic" peaks is just a particular case; peaks in the power spectrum might be generated in scenarios within some alternative cosmological model that have nothing to do with oscillations due to gravitational compression in a fluid. We also calculate the angular correlation function of the anisotropies from the WMAP-7yr and ACT data, in an attempt to derive the minimum number of parameters a polynomial function should have to fit it: a set of polynomial functions with a total of six free parameters, apart from the amplitude, is enough to reproduce the first two peaks. However, the standard model with six tunable free parameters also reproduces higher order peaks, giving the standard model a higher confidence. At present, while no simple function with six free parameters is found to give a fit as good as the one given by the standard cosmological model, we may consider the predictive power of the standard model beyond an instrumentalist approach (such as the Ptolemaic astronomy model of the orbits of the planets).
Revised translation of Kaluza's historic 1921 paper, "Zum Unitätsproblem der Physik," on 5-dimensional spacetime, used to unify gravity and electromagnetism. This version is based, in part, on a 1984 translation provided by T. Muta, but revised and formatted using LaTeX to closely match the original paper in appearance and pagination. Kaluza's original notation is restored.
Here we discuss how some medieval scholars in the Western Europe viewed the form of the world and the problem of the Antipodes, starting from the Natural History written by Pliny and ending in the Hell of Dante Alighieri. From the center of the Earth, Dante and Virgil came to the Antipodes: eventually, their existence was accepted. Among the others, we will discuss the works of the Venerable Bede and Sylvester the Second.
It has been 20 years since planning began for the 1995 United Nations International Conference on Near-Earth Objects. The conference proceedings established the scientific basis for an international organizational framework to support research and collective actions to mitigate a potential near-Earth object (NEO) threat to the planet. Since that time, researchers have conducted telescope surveys that should, within the coming decade, answer many questions about the size, number, and Earth impact probability of these objects. Space explorations to asteroids and comets have been successfully carried out, including sample recovery. Laboratory experiments and computer simulations at Sandia National Laboratories have analyzed the effects of soft X-ray radiation on meteorites - which might help researchers develop a way to redirect an incoming asteroid by vaporizing a thin layer of its surface. An Action Team on NEOs, established in 2001 in response to recommendations of the Third United Nations Conference on the Exploration and Peaceful Uses of Outer Space, identified the primary components of NEO mitigation and emphasized the value of finding potentially hazardous NEOs as soon as possible. Recommendations from the Action Team are meant to ensure that all nations are aware of the NEO danger; and to coordinate mitigation activities among nations that could be affected by an impact, as well as those that might play an active role in any eventual deflection or disruption campaign.
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth" of the mathematical formalism of quantum mechanics and then proceed to investigate the theory's implications for the physical world. One of the outcomes has been endless discussions of the quantum measurement problem, wave/particle duality, the non-locality of entangled quantum states, Schroedinger's cat, and other philosophical conundrums. In this essay, I take the point of view that quantum mechanics is a mathematical model, a human invention, and rather than pondering what the theory implies about our world, I consider the transposed question: what is it about our world that leads us to a quantum mechanical model of it? One consequence is the realization that discrete quanta, the quantum of action in particular, leads to the wave nature and statistical behavior of matter rather than the other way around.