On Tamm's problem in the Vavilov-Cherenkov radiation theory

We analyse the well-known Tamm problem treating the charge motion on a finite space interval with the velocity exceeding light velocity in medium. By comparing Tamm's formulae with the exact ones we prove that former do not properly describe Cherenkov radiation terms. We also investigate Tamm's formula cos(theta)=1/(beta n) defining the position of maximum of the field strengths Fourier components for the infinite uniform motion of a charge. Numerical analysis of the Fourier components of field strengths shows that they have a pronounced maximum at cos(theta)=1/(beta n) only for the charge motion on the infinitely small interval. As the latter grows, many maxima appear. For the charge motion on an infinite interval there is infinite number of maxima of the same amplitude. The quantum analysis of Tamm's formula leads to the same results.Comment: 28 pages, 8 figures, to be published in J.Phys.D:Appl.Phy

Non-Relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we could see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in earth's gravitational field may form a gravitationally bound quantized state, which had already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are discussed in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.Comment: 12 pages, no figur

Chaotic and pseudochaotic attractors of perturbed fractional oscillator

We consider a nonlinear oscillator with fractional derivative of the order alpha. Perturbed by a periodic force, the system exhibits chaotic motion called fractional chaotic attractor (FCA). The FCA is compared to the ``regular'' chaotic attractor. The properties of the FCA are discussed and the ``pseudochaotic'' case is demonstrated.Comment: 20 pages, 7 figure

Inadequacies in the conventional treatment of the radiation field of moving sources

There is a fundamental difference between the classical expression for the retarded electromagnetic potential and the corresponding retarded solution of the wave equation that governs the electromagnetic field. While the boundary contribution to the retarded solution for the {\em potential} can always be rendered equal to zero by means of a gauge transformation that preserves the Lorenz condition, the boundary contribution to the retarded solution of the wave equation governing the {\em field} may be neglected only if it diminishes with distance faster than the contribution of the source density in the far zone. In the case of a source whose distribution pattern both rotates and travels faster than light {\em in vacuo}, as realized in recent experiments, the boundary term in the retarded solution governing the field is by a factor of the order of $R^{1/2}$ {\em larger} than the source term of this solution in the limit that the distance $R$ of the boundary from the source tends to infinity. This result is consistent with the prediction of the retarded potential that part of the radiation field generated by a rotating superluminal source decays as $R^{-1/2}$, instead of $R^{-1}$, a prediction that is confirmed experimentally. More importantly, it pinpoints the reason why an argument based on a solution of the wave equation governing the field in which the boundary term is neglected (such as appears in the published literature) misses the nonspherical decay of the field

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=(±1,0)K = (\pm 1, 0)

We show that the dragging of the axis directions of local inertial frames by a weighted average of the energy currents in the universe is exact for all linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K = (+1, -1, 0) and of Einstein's static closed universe. This includes FRW universes which are arbitrarily close to the Milne Universe, which is empty, and to the de Sitter universe. Hence the postulate formulated by E. Mach about the physical cause for the time-evolution of the axis directions of inertial frames is shown to hold in cosmological General Relativity for linear perturbations. The time-evolution of axis directions of local inertial frames (relative to given local fiducial axes) is given experimentally by the precession angular velocity of gyroscopes, which in turn is given by the operational definition of the gravitomagnetic field. The gravitomagnetic field is caused by cosmological energy currents via the momentum constraint. This equation for cosmological gravitomagnetism is analogous to Ampere's law, but it holds also for time-dependent situtations. In the solution for an open universe the 1/r^2-force of Ampere is replaced by a Yukawa force which is of identical form for FRW backgrounds with $K = (-1, 0).$ The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, and dot is the derivative with respect to cosmic time. Analogous results hold for energy currents in a closed FRW universe, K = +1, and in Einstein's closed static universe.Comment: 23 pages, no figures. Final published version. Additional material in Secs. I.A, I.J, III, V.H. Additional reference

A derivation of Maxwell’s equations using the Heaviside notation

Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E-fields and B-fields and that Faraday's Law can be derived without any relativistic assumptions about Lorentz invariance. It also widens the choice of axioms, or starting points, for understanding electromagnetism

Examples of the Zeroth Theorem of the History of Physics

The zeroth theorem of the history of science (enunciated by E. P. Fischer) and widely known in the mathematics community as Arnol'd's Principle (decreed by M. V. Berry), states that a discovery (rule, regularity, insight) named after someone (often) did not originate with that person. I present five examples from physics: the Lorentz condition defining the Lorentz gauge of the electromagnetic potentials; the Dirac delta function (x); the Schumann resonances of the earth-ionosphere cavity; the Weizsacker-Williams method of virtual quanta; the BMT equation of spin dynamics. I give illustrated thumbnail sketches of both the true and reputed discoverers and quote from their "discovery" publications.Comment: 36 pages, 8 figures. Small revisions, added material and references - Arnol'd's law, Emil Wiechert. Submitted to Am. J. Phy

Gravitomagnetism and the Clock Effect

The main theoretical aspects of gravitomagnetism are reviewed. It is shown that the gravitomagnetic precession of a gyroscope is intimately connected with the special temporal structure around a rotating mass that is revealed by the gravitomagnetic clock effect. This remarkable effect, which involves the difference in the proper periods of a standard clock in prograde and retrograde circular geodesic orbits around a rotating mass, is discussed in detail. The implications of this effect for the notion of ``inertial dragging'' in the general theory of relativity are presented. The theory of the clock effect is developed within the PPN framework and the possibility of measuring it via spaceborne clocks is examined.Comment: 27 pages, LaTeX, submitted to Proc. Bad Honnef Meeting on: GYROS, CLOCKS, AND INTERFEROMETERS: TESTING GENERAL RELATIVITY IN SPACE (22 - 27 August 1999; Bad Honnef, Germany

Attributing human mortality during extreme heat waves to anthropogenic climate change

It has been argued that climate change is the biggest global health threat of the 21st century. The extreme high temperatures of the summer of 2003 were associated with up to seventy thousand excess deaths across Europe. Previous studies have attributed the meteorological event to the human influence on climate, or examined the role of heat waves on human health. Here, for the first time, we explicitly quantify the role of human activity on climate and heat-related mortality in an event attribution framework, analysing both the Europe-wide temperature response in 2003, and localised responses over London and Paris. Using publicly-donated computing, we perform many thousands of climate simulations of a high-resolution regional climate model. This allows generation of a comprehensive statistical description of the 2003 event and the role of human influence within it, using the results as input to a health impact assessment model of human mortality. We find large-scale dynamical modes of atmospheric variability remain largely unchanged under anthropogenic climate change, and hence the direct thermodynamical response is mainly responsible for the increased mortality. In summer 2003, anthropogenic climate change increased the risk of heat-related mortality in Central Paris by ~70% and by ~20% in London, which experienced lower extreme heat. Out of the estimated ~315 and ~735 summer deaths attributed to the heatwave event in Greater London and Central Paris, respectively, 64 (±3) deaths were attributable to anthropogenic climate change in London, and 506 (±51) in Paris. Such an ability to robustly attribute specific damages to anthropogenic drivers of increased extreme heat can inform societal responses to, and responsibilities for, climate change

Beyond climate change and health: Integrating broader environmental change and natural environments for public health protection and promotion in the UK

This is the final version of the article. Available from MDPI via the DOI in this record.Increasingly, the potential short and long-term impacts of climate change on human health and wellbeing are being demonstrated. However, other environmental change factors, particularly relating to the natural environment, need to be taken into account to understand the totality of these interactions and impacts. This paper provides an overview of ongoing research in the Health Protection Research Unit (HPRU) on Environmental Change and Health, particularly around the positive and negative effects of the natural environment on human health and well-being and primarily within a UK context. In addition to exploring the potential increasing risks to human health from water-borne and vector-borne diseases and from exposure to aeroallergens such as pollen, this paper also demonstrates the potential opportunities and co-benefits to human physical and mental health from interacting with the natural environment. The involvement of a Health and Environment Public Engagement (HEPE) group as a public forum of "critical friends" has proven useful for prioritising and exploring some of this research; such public involvement is essential to minimise public health risks and maximise the benefits which are identified from this research into environmental change and human health. Research gaps are identified and recommendations made for future research into the risks, benefits and potential opportunities of climate and other environmental change on human and planetary health.The research was funded in part by the National Institute for Health Research Health Protection Research Unit (NIHR HPRU) in Environmental Change and Health at the London School of Hygiene and Tropical Medicine in partnership with Public Health England (PHE), and in collaboration with the University of Exeter, University College London, and the Met Office (HPRU-2012-10016); the UK Medical Research Council (MRC) and UK Natural Environment Research Council (NERC) for the MEDMI Project (MR/K019341/1, https: //www.data-mashup.org.uk); the Economic and Social Research Council (ESRC) Project (ES/P011489/1); and the NIHR Knowledge Mobilisation Research Fellowship for Maguire