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29
Relativistic electrodynamics: various postulates and ratiocinations”, PIER—Progress
 In Electromagnetic Research
, 2005
"... Abstract—Presently various models consistent with Einstein’s Special Relativity theory are explored. Some of these models have been introduced previously, but additional models are possible, as shown here. The topsyturvy model changes the order of postulates and conclusions of Einstein’s original t ..."
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Abstract—Presently various models consistent with Einstein’s Special Relativity theory are explored. Some of these models have been introduced previously, but additional models are possible, as shown here. The topsyturvy model changes the order of postulates and conclusions of Einstein’s original theory. Another model is given in the spectral domain, with the relativistic Doppler Effect formulas replacing the Lorentz transformation. In this model a new principle tantamount to the constancy of the speed of light in vacuum is stated and analyzed, dubbed as the constancy of light slowness in vacuum. Because the slowness is derived in the spectral domain from the Doppler Effect formulas, this result is not trivially semantic. It is shown that potentials and equations of continuity can replace the Maxwell Equations used by Einstein for his “Principle of Relativity” in electrodynamics. It is also shown that defining convection currents and assuming the currentcharge densities transformations can replace
Nonrelativistic electromagnetic scattering: "Reverse engineering" using the Lorentz force formulas", PIERProgress
 In Electromagnetic Research
, 2002
"... ABSTRACT—For almost a century, velocity dependent scattering problems are solved in the context of Einstein’s Special Relativity theory. Most interesting problems involve nonuniform motion, which is heuristically justified by assuming the validity of the “instantaneous velocity ” approximation. The ..."
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ABSTRACT—For almost a century, velocity dependent scattering problems are solved in the context of Einstein’s Special Relativity theory. Most interesting problems involve nonuniform motion, which is heuristically justified by assuming the validity of the “instantaneous velocity ” approximation. The present study attempts to provide a consistent postulational foundation by introducing boundary conditions based on the Lorentz force formulas. The methodology used here is dubbed “reverse engineering”: Being aware of the relativistic results, we show that they are replicated, (at least) to the first order in cv /=β by the present method. Specific problems are discussed to demonstrate the power of the method, and pave the way to future research in this problem area. Specifically, by realizing that at the boundary we deal with signals, which are derived from waves, only the latter being subject to the wave equations, it is feasible to apply boundary conditions and construct appropriately the scattered waves in space. It is shown that the present approach is also consistent with the Minkowski constitutive relations which are exploited for solving problems where the medium moves parallel with respect to the boundaries.
QUASI DOPPLER EFFECTS ASSOCIATED WITH SPATIOTEMPORAL TRANSLATORY, MOVING, AND ACTIVE BOUNDARIES by
"... Moving sources and spatiotemporally dependent boundaries have been introduced in the past, in order to facilitate analyses of the so called “Doppler effect ” phenomena. Here a model is introduced for generalized situations involving translatory and moving surfaces on which certain boundary or source ..."
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Moving sources and spatiotemporally dependent boundaries have been introduced in the past, in order to facilitate analyses of the so called “Doppler effect ” phenomena. Here a model is introduced for generalized situations involving translatory and moving surfaces on which certain boundary or source conditions are prescribed. The ambiguity arising from analyses of Dopplerlike effects in electromagnetics as well as acoustics, in which the (mathematical) translatory surface is not explicitly distinguished from the (physical) moving object is carefully discussed here, and the role of physics, e.g., in the form of Einstein’s Special Relativity theory, is considered. The present approach facilitates the general reformulation of the Doppler effect class of problems and suggests meaningful first order v c / (relative velocity) approximations which can then be employed for more complicated problems. Quasi Doppler effects are introduced in order to replace the inherent “inverse problem ” nature of the scattering Doppler effect with a “forward problem ” formulation which allows for a broader scope of problems and approximations. This facilitates the representation of relativistically exact but complicated solutions in terms of simpler expressions involving first order velocity effects. In turn, this facilitates new approximate solutions for problems not considered previously. By further distinguishing amplitude and phase effects, even simpler expressions, inconsistent in v c / , can be used. This is also helpful in assessing the validity of some heuristic approximations suggested in the past. 2 We start with a general analysis of the Doppler effects initiated by complicated surfaces, providing some general guidelines and insight for our ability to analyze increasingly complicated problems.
NONRELATIVISTIC BOUNDARY CONDITIONS AND SCATTERING IN THE PRESENCE OF ARBITRARILY MOVING MEDIA AND OBJECTS: CYLINDRICAL PROBLEMS
"... Abstract—Recently nonrelativistic boundary conditions, based on the Lorentz force formulas, have been investigated. It was shown that to the first order in the relative velocity v/c the results for scattering problems are in agreement with the exact relativistic formalism. Examples for scattering b ..."
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Abstract—Recently nonrelativistic boundary conditions, based on the Lorentz force formulas, have been investigated. It was shown that to the first order in the relative velocity v/c the results for scattering problems are in agreement with the exact relativistic formalism. Examples for scattering by material objects moving in free space have been discussed. Presently the feasibility of nonrelativistically solving scattering problems involving arbitrary material media is investigated. For concreteness, two representative canonical problems were chosen: scattering by a uniformly moving circular cylinder, and the related problem of a cylinder at rest, comprised of a uniformly moving medium in the cylindrical crosssectional plane. The investigation demonstrates that solving such problems is feasible, and indicates the complexity involved in such an analysis. The main highlights are that we need to evaluate the phases and
Broadband spatiotemporal differentialoperator representations for velocitydependent scattering
 Progress In Electromagnetic Research, PIER
"... Abstract—A novel approach based on spatiotemporal differentialoperators is developed here for broadband, velocitydependent scattering. Unlike the spectraldomain representations, the new method facilitates a compact formulation for scattering by arbitrary excitation signals, in the presence of mov ..."
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Abstract—A novel approach based on spatiotemporal differentialoperators is developed here for broadband, velocitydependent scattering. Unlike the spectraldomain representations, the new method facilitates a compact formulation for scattering by arbitrary excitation signals, in the presence of moving objects. In free space (vacuum), relativistically exact formulas are developed. After developing the general theory, analysis of relativistically exact freespace scattering by cylinders, and a halfplane, are examined. For cylinders the analysis shows that in the far field pulses are located on circles in the comoving referenceframe where the object is atrest. In other reference frames this feature is valid only as an approximation. These results apply also to the diffractive part of the halfplane scattered field. The geometricaloptics contribution is associated with planewaves and obeys the appropriate transformations. The various zones for these fields in an arbitrary referenceframe are analyzed. 1.
A quest for systematic constitutive formulations for general field and wave systems based on the Volterra differential operators
 PIER — Progress In Electromagnetics Research, Editor
, 2000
"... Abstract−A systematic formulation of constitutive relations for general field systems is explored, which takes into account the main material features. These are dispersion, inhomogeneity, which can be present in linear and nonlinear systems. There are two main difficulties associated with existing ..."
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Abstract−A systematic formulation of constitutive relations for general field systems is explored, which takes into account the main material features. These are dispersion, inhomogeneity, which can be present in linear and nonlinear systems. There are two main difficulties associated with existing representations: Dispersion is usually referred to in the spectral domain, while inhomogeneity is obviously a spatiotemporal phenomenon; moreover, the existing representations involve spatiotemporally dependent integrals, and those suggest nonlocal interaction which raises relativistic causality issues. The present approach introduces new representations in terms of Volterra differential operators, which obviate these difficulties within the domain of their validity, allowing for spatiotemporal representation of both dispersion and inhomogeneity, in linear and nonlinear systems. Minkowskis methodology for representation of material properties in the presence of moving media is reexamined in view of the new constitutive relations, especially as regards Maxwells equations of Electrodynamics.
DIFFERENTIALOPERATORS FOR CIRCULAR AND ELLIPTICAL WAVEFUNCTIONS IN FREESPACE RELATIVISTIC SCATTERING
"... ABSTRACT—A novel method is presented for scattering by cylinders uniformly moving in freespace. The method is based on the application of differentialoperators to the reststate scattered waves. This method is applicable to any solution of the Helmholtz wave equation expressed in terms of a separa ..."
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ABSTRACT—A novel method is presented for scattering by cylinders uniformly moving in freespace. The method is based on the application of differentialoperators to the reststate scattered waves. This method is applicable to any solution of the Helmholtz wave equation expressed in terms of a separable coordinatesystem, in particular it is demonstrated here for circular and elliptical wavefunctions. The analysis applies to arbitrary cylindrical geometries and is based on
FREESPACE RELATIVISTIC LOWFREQUENCY SCATTERING BY MOVING OBJECTS
"... Abstract—The present study brings together two aspects of electromagnetic theory: the recently discussed lowfrequency series expansions based on the concept of Consistent Maxwell Systems, and Einstein’s Relativistic Electrodynamics. Combined, this facilitates the analysis of pertinent lowfrequency ..."
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Abstract—The present study brings together two aspects of electromagnetic theory: the recently discussed lowfrequency series expansions based on the concept of Consistent Maxwell Systems, and Einstein’s Relativistic Electrodynamics. Combined, this facilitates the analysis of pertinent lowfrequency scattering problems involving objects moving with arbitrary constant velocities in free space. The lowfrequency series expansions start with leading terms that are prescribed by solutions of the vector Laplace equation, thus significantly simplifying the conventional analysis in terms of the Helmholtz wave equation. The method is demonstrated by deriving relativistically exact explicit results leading terms for perfectly conducting circularcylindrical and spherical scatterers. The results apply to arbitrary reference frames where the objects are observed in motion. For simplicity of notation expressions are given in terms of spatiotemporal coordinates native to the object’s restframe. Subsequent substitution of the Lorentz transformation for the coordinates is then a straightforward matter. Previous exact relativistic results for scattering by moving objects have demonstrated the existence of velocity induced mode coupling. It is shown that the lowfrequency expansions used here display the same effects for various orders of the partial fields appearing in the series. 1.
SIMULTANEITY, CAUSALITY, AND SPECTRAL REPRESENTATIONS
"... of the spatiotemporal worldview, and proposed a representative alternative based on the Fourier transform as a mathematical model. It was argued that this so called spectral representation, by virtue of the invertibility of the Fourier transform, is fully equivalent to our conventional spatiotemp ..."
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of the spatiotemporal worldview, and proposed a representative alternative based on the Fourier transform as a mathematical model. It was argued that this so called spectral representation, by virtue of the invertibility of the Fourier transform, is fully equivalent to our conventional spatiotemporal worldview, although in the two systems the information is ordered in a radically different manner. Criticism of the new conception can be traced back to the fundamental principles of simultaneity and causality, whose role in the spectral domain has not been sufficiently demonstrated. These questions are carefully investigated in the present study. Simple but concise examples are used to verbally and graphically clarify the mathematics involved in integral transforms, like the Fourier transform under consideration. The transition from the spatiotemporal domain to the spectral domain entails not only a different patterning of data points. What is
>1< The Method of Images in VelocityDependent Systems
"... Abstract—This study investigates the application of image methodology to velocitydependent wave systems. Special Relativity is used for the analysis of waves scattered by arbitrary moving objects in the presence of a perfectlyconducting planeinterface. The various scenarios considered involve geo ..."
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Abstract—This study investigates the application of image methodology to velocitydependent wave systems. Special Relativity is used for the analysis of waves scattered by arbitrary moving objects in the presence of a perfectlyconducting planeinterface. The various scenarios considered involve geometrical, material, and kinematic symmetries. Cases discussed include freespace, material media atrest, and material media in motion, with respect to the planeinterface boundary. The last configuration is elaborated for two different scenarios: the first assumes the same medium velocity throughout space when the plane boundary is removed; the second introduces two symmetrical velocityfields in the halfspaces involved, with a jump in flow direction at the interface. Where the method applies it simplifies the analysis, and the results enrich