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The effect of a hypothetical maximal proper acceleration on the mass of a charged particle is investigated in the context of particle accelerators. In particular, it is shown that maximal proper acceleration implies an increase in the kinetic energy of the particle being accelerated with respect to the relativistic energy. Such an increase in kinetic energy leads to a reduction of the luminosity of the bunches with respect to the expected luminosity in the relativistic models of the bunches. This relative loss in luminosity is of the order 10−3 to 10−5 for the Large Hadron Collider (LHC) bunches and can be of order up to 10−3 for certain laser-plasma accelerator facilities. Although the effect is small, it increases with the square of the bunch population. [ABSTRACT FROM AUTHOR]

Even if Lorentz symmetry is not a fundamental property of condensed matter physics, there are many instances where the relevant physics of some material is well described by a relativistic field theory. Actually, in some cases, this effective description is not of an exact Lorentz invariant model, but of a model including some small Lorentz-violating correction. In this case, a connection can be made between condensed matter physics and the Standard Model Extension (SME) that have been developed to look for Lorentz violation in fundamental physics. We are interested in particular in the connection between the SME and planar physics. We study the connection between part of the non-minimal SME and a planar model, and we calculate the interaction energies and torques appearing between point-like charges in the planar model. We show how the dimensional reduction leads to new sectors appearing in the planar theory and that the interplay between those sectors can lead to very distinctive phenomena. [ABSTRACT FROM AUTHOR]

Maxwell's equations can be successfully extended to electromagnetic fields having three complex-valued components rather than their usual three real-valued components. Here the implications of interpreting the imaginary-valued components as extending into time rather than space are explored. The complex-valued Maxwell equations remain consistent with the original Maxwell equations and the experimental results that they predict. Further, the extended equations predict novel phenomena such as the existence of electromagnetic waves that propagate not only through regular space but also through a separate temporal space (time) that is implied by the three imaginary components of the fields. In a vacuum, part of these imaginary valued waves propagates through time at the same rate as an observer stationary in space. While the imaginary valued field components are not directly observable, analysis indicates that they should be indirectly detectable experimentally based on secondary effects that occur under special circumstances. Experimental investigation attempting to falsify or support the existence of complex valued electromagnetic fields extending into time is merited due to the substantial theoretical and practical implications involved. [ABSTRACT FROM AUTHOR]

The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial system. We start with the three-body equations of motion, which are a subset of the equations of motion (previously derived by us) for any number of bodies. In the Minkowski space, there are 12 equations of motion. It is proved that three of them are consequences of the other nine, so their number becomes nine, as much as the unknown trajectories are. The Kepler formulation assumes that one particle (the nucleus) is placed at the coordinate origin. The motion of the other two particles is described by a neutral system with respect to the unknown velocities. The state-dependent delays arise as a consequence of the finite vacuum speed of light. We obtain the equations of motion in spherical coordinates and split them into two groups. In the first group all arguments of the unknown functions are delays. We take their solutions as initial functions. Then, the equations of motion for the remaining two particles must be solved to the right of the initial point. To prove the existence–uniqueness of a periodic solution, we choose a space consisting of periodic infinitely smooth functions satisfying some supplementary conditions. Then, we use a suitable operator which acts on these spaces and whose fixed points are periodic solutions. We apply the fixed point theorem for the operators acting on the spaces of periodic functions. In this manner, we show the stability of the He atom in the frame of classical electrodynamics. In a previous paper of ours, we proved the existence of spin functions for plane motion. Thus, we confirm the Bohr and Sommerfeld's hypothesis for the He atom. [ABSTRACT FROM AUTHOR]

The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial system. We start with the three-body equations of motion, which are a subset of the equations of motion (previously derived by us) for any number of bodies. In the Minkowski space, there are 12 equations of motion. It is proved that three of them are consequences of the other nine, so their number becomes nine, as much as the unknown trajectories are. The Kepler formulation assumes that one particle (the nucleus) is placed at the coordinate origin. The motion of the other two particles is described by a neutral system with respect to the unknown velocities. The state-dependent delays arise as a consequence of the finite vacuum speed of light. We obtain the equations of motion in spherical coordinates and split them into two groups. In the first group all arguments of the unknown functions are delays. We take their solutions as initial functions. Then, the equations of motion for the remaining two particles must be solved to the right of the initial point. To prove the existence–uniqueness of a periodic solution, we choose a space consisting of periodic infinitely smooth functions satisfying some supplementary conditions. Then, we use a suitable operator which acts on these spaces and whose fixed points are periodic solutions. We apply the fixed point theorem for the operators acting on the spaces of periodic functions. In this manner, we show the stability of the He atom in the frame of classical electrodynamics. In a previous paper of ours, we proved the existence of spin functions for plane motion. Thus, we confirm the Bohr and Sommerfeld’s hypothesis for the He atom.

There has been ongoing debate about the efficacy and mechanism of action of neuromodulation devices in pain relief applications. It has recently been suggested that both issues may be resolved if electromagnetic theory is incorporated into the understanding and application of this technology, and we therefore undertook an in silico analysis to further explore this idea. We created a CAD replication of a standard neuromodulation electrode array with a generic linear 3/6 mm 8‐contact lead, developed a parameterized algorithmic model for the pulse delivered by the device and assigned material properties to biologic media to accurately reflect their electromagnetic properties. We then created a physical simulation of the device's output both in air and in the biophysical environment. The simulations confirmed the presence of an electromagnetic field (EM field). Variations in programming of the device affected the strength of the EM field by orders of magnitude. The biologic media all absorbed the EM field, an effect which was particularly pronounced in cerebrospinal fluid and muscle. We discuss the implications of all these findings in relation to the literature. We suggest that knowledge of electromagnetic theory and its application within the biophysical space is required for the optimal use of neuromodulation devices in pain relief applications. [ABSTRACT FROM AUTHOR]

In classical electrodynamics, the well-known Lorentz force law falls short of providing a satisfactory result for the trajectory of point-like charged particles when considering that particle's own self-force. While there have been many historical attempts, Gralla, Harte and Wald developed a new model for classical charged particles that is free from pathologies while being consistent with Maxwell's equations and conserves stress-energy. Expanding upon this approach, we derive a relativistically correct, modified Lorentz force law in vector form, which includes radiation reaction, and spin- and magnetic moment-dependent correction terms, suitable to be included in classical electrodynamics lectures and beam dynamics simulation tools. As by-products we obtain evolution equations for mass, spin angular momentum and the radiated power. We compare the new equations to the classical ones and use the new equations to conduct numerical simulations, showing that the results are free of any nonphysical artifacts, and which might be possible to test in future experiments at particle accelerators. The new equations foster improved insight into beam dynamics. [ABSTRACT FROM AUTHOR]

Maxwell’s equations can be successfully extended to electromagnetic fields having three complex-valued components rather than their usual three real-valued components. Here the implications of interpreting the imaginary-valued components as extending into time rather than space are explored. The complex-valued Maxwell equations remain consistent with the original Maxwell equations and the experimental results that they predict. Further, the extended equations predict novel phenomena such as the existence of electromagnetic waves that propagate not only through regular space but also through a separate temporal space (time) that is implied by the three imaginary components of the fields. In a vacuum, part of these imaginary valued waves propagates through time at the same rate as an observer stationary in space. While the imaginary valued field components are not directly observable, analysis indicates that they should be indirectly detectable experimentally based on secondary effects that occur under special circumstances. Experimental investigation attempting to falsify or support the existence of complex valued electromagnetic fields extending into time is merited due to the substantial theoretical and practical implications involved.

Recently, a number of experimental observations on the superluminal group velocities of pulses propagating in dispersive media have led to reconsidering electromagnetism theory in an unconventional framework. To consider faster-than-light phenomena, it is not necessary to replace the current relativistic theory, but it is sufficient to extend it to superluminal motions in a way that preserves the principle of causality. In the present paper, a new approach to study superluminal motions is proposed, which avoids introducing unphysical complex quantities and allows for the formulation of equations that are covariant according to a hyperbolic metric. In the framework of this formalism, Maxwell equations and the single-photon wave equation are obtained through superluminal transformations of ordinary equations. It is shown that the covariant and contravariant components of the superluminal electromagnetic field determine its magnitude and direction, respectively. Furthermore, the solutions of the transformed Maxwell equations are X-shaped ways propagating in the superluminal spacetime region that is delimited by the infinite light cone and the two-sheeted hyperboloid perpendicular to it. Instead, in quantum mechanics, the covariant and contravariant components of the electromagnetic field are proportional to the right- and left-handed helicities of the single photon, respectively. [ABSTRACT FROM AUTHOR]

The Aharonov–Bohm phase shift in a particle interference pattern when electrons pass a long solenoid is identical in form with the optical interference pattern shift when a piece of retarding glass is introduced into one path of a two-beam optical interference pattern. The particle interference-pattern deflection is a relativistic effect of order 1 / c 2 , though this relativity aspect is rarely mentioned in the literature. Here we give a thorough analysis of the classical electromagnetic aspects of the interaction between a solenoid or toroid and a charged particle. We point out the magnetic Lorentz force which the solenoid or toroid experiences due to a passing charge. Although analysis in the rest frame of the solenoid or toroid will involve back Faraday fields on the charge, the analysis in the inertial frame in which the charge is initially at rest involves forces due to only electric fields where forces are equal in magnitude and opposite in direction. The classical analysis is made using the Darwin Lagrangian. We point out that the classical analysis suggests an angular deflection independent of Planck’s constant ħ , where the deflection magnitude is identical with that given by the traditional quantum analysis, but where the deflection direction is unambiguous. [ABSTRACT FROM AUTHOR]

The problem of the electromagnetic radiation produced by charge distributions in the framework of a semiclassical approach proposed in the work by Bagrov, Gitman, Shishmarev, and Farias Jr. [J. Synchrotron Rad. 27, 902–911 (2020)] is addressed here. In this approach, currents, generating the radiation are considered classically, while the quantum nature of the radiation is kept exactly. Quantum states of the electromagnetic field are solutions of Schrödinger's equation, and relevant quantities to the problem are evaluated with the aid of transition probabilities. This construction allows us to introduce the quantum transition time in physical quantities and assess its role in radiation problems by classical currents. Radiated electromagnetic energies are studied in detail and a definition for the rate at which radiation is emitted from sources is presented. In calculating the total energy and rate radiated by a pointlike charged particle accelerated by a constant and uniform electric field, it is discovered that these results are compatible with results obtained by other authors in the framework of the classical radiation theory under an appropriate limit. Numerical and asymptotic analyses of the results are also performed. [ABSTRACT FROM AUTHOR]

We find an exact closed-form expression for the magnetostatic interaction energy between a point magnet and a ring magnet in terms of complete elliptic integrals. The exact expression for the energy exhibits an equilibrium point close to the axis of symmetry of the ring magnet. Our methodology will be useful in investigations concerning magnetic levitation, and in the study of Casimir levitation.

An important issue in phenomenological macroscopic electrodynamics of moving media is the definition of the energy and momentum of the electromagnetic field in matter. Rather surprisingly, this topic has demonstrated a remarkable longevity, and the problem of the electromagnetic energy and momentum in matter remained open, despite numerous theoretical and experimental investigations. We overview the definition of the momentum of light in matter and demonstrate that, for the correct understanding of the problem, one needs to carefully distinguish situations when the material medium is modeled either as a background for light or as a dynamical part of the total system. The status of Minkowski and Abraham energy-momentum tensors of the electromagnetic field is clarified for the two particular types of complex matter, the spinning fluid and the liquid crystal medium, and summarized for the case of general anisotropic moving material media with a linear constitutive law. [ABSTRACT FROM AUTHOR]

In the present paper spin equations for three-body problem of classical electrodynamics are introduced. They should be considered jointly with 3-body equations of motion derived in a previous paper of the author. The system of spin equations is an overdetermined one. It is shown that the independent spin equations are nine in number as many as the components of the unknown spin functions. The system obtained will be solved by the fixed-point method in a next paper.

In this contribution, we develop a model that describes light extinction in the presence of arbitrary aerosols. In doing so, we take advantage of the fact that during measurements with the ELPI+-system, aerosol particles of any shape are internally mapped to spherical surrogates. The developed model is particularly simple and depends on only a few parameters, namely on densities and refractive indices of the measured aerosol particles. As proof of principle, the model is in first applications used to determine extinction coefficients and mass-specific extinction for an infrared light source with a peak wave length of 880 nm. Detailed studies concentrate on two aerosols exemplary for characteristic values of the input parameters: a paraffin aerosol in a bench-scale setup and soot from a flaming n-heptane fire in a room-scale setup (test fire TF5 according to EN54). As main results, we find values for mass-specific extinction that are different in the considered cases. Moreover, obtained results differ in part more than a factor of three from literature values typically used in practical applications. We explicitly assess reasons for deviations found and finally propose a simple way how future light-extinction studies can be performed comparatively easily using the ELPI+-system. [ABSTRACT FROM AUTHOR]

We show that the comment by Franklin (Int. J. Mod. Phys. A 36, 2175001 (2021)) on our paper "Lorentz transformation of a charge-current density and "relativistic polarization" of a moving current loop" (Int. J. Mod. Phys. A 36, 2175001 (2021)), like the previous publication of this author entitled "Complete Lorentz transformation of a charge-current density" (Int. J. Mod. Phys. A 35, 2050061 (2020)), contains fundamental errors in the physical interpretation of Lorentz transformations, which are once again disclosed with some particular examples. [ABSTRACT FROM AUTHOR]

The primary goal of the present paper is to prove an existence-uniqueness of periodic solution of the equations of motion for the 3-body problem of classical electrodynamics. The equations of motion were derived in a recent paper of the author. Particular case of this problem is the He-atom – the simplest multi-electronic atom. We have applied our previous results to 3-body problem introducing radiation terms and in this manner we have obtained a system of 12 equations of motion. We have proved that three equations are a consequence of the first 9 ones, so that we consider 9 equations for 9 unknown functions. We introduce a suitable operator in a specific function space and formulate conditions for the existence-uniqueness of fixed point of this operator that is a periodic solution of the 3-body equations of motion. Finally, we verify the conditions obtained for the He-atom.

The primary purpose of the present paper is to continue the previous investigations of the author and apply the technique from the two-body problem of classical electrodynamics to the three-body problem. We derive equations of motion with radiation terms which are neutral type nonlinear differential equations with statedependent delays. The derivation approach is analogous to that of the two body-problem, which allows a unified consideration of the problem for any number of bodies. In the next paper, we prove the existence of periodic solution of the three-body problem and in such a way the Bohr-Sommerfeld postulate for stationary states is confirmed.

The conventional definition of electric polarization as the “dipole moment per unit volume” is valid only for the special case of well-separated dipoles. An alternative general approach is to view polarization as a characteristic not of a single charge distribution but rather of an adiabatic transition between two nearby states. Polarization can then be rigorously defined as the integral of the current density over that transition. In contrast with the “Modern Theory of Polarization,” which is fully quantum-mechanical, in this paper polarization is considered from the classical perspective. Such treatment is less fundamental but simpler, has pedagogical advantages and, importantly, is subject to fewer constraints. Polarization can be rigorously and unambiguously defined for periodic or nonperiodic charge distributions, finite or infinite, microscale or macroscale, electrically neutral or non-neutral, continuous or discrete, at any temperature; polarization can be spontaneous or induced. A previous classical (non-quantum) analysis by Russakoff (Am J Phys 1970) was (i) limited to the Clausius–Mossotti/Lorenz–Lorentz model of molecular dipoles, and (ii) involves multipole expansions, which the analysis of this paper shows to be redundant.The traditional dipole model of polarization is a straightforward special case of the proposed definition. A number of illustrative examples are presented.

Starting from Coulomb gauge scheme, we can eliminate the instant Coulomb force and replace it by propagating retarded Coulomb force field, in the realm of classical electrodynamics. Our proof is based on Thidé’s treatment and the conundrum surrounding the at-a-distance interaction is clearly solved, as shown in this article.

Light emitted from atoms during transitions of electrons from higher to lower discrete states has the form of photons carrying energy and angular momentum. This paper considers the process of emission of a single photon from the hydrogen atom by using quantum theory and Maxwell's equations [W. Gough, Eur. J. Phys. 17, 208, 1996; L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1965); J. D. Jackson, Classical Electrodynamics (John Wiley & Son, New York, 1975, 1982); P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, Inc., New York, 1953)]. The electric and magnetic fields of a photon arise from the time-dependent quantum probability densities of the orbit and the spin current. This paper is an extension of the semiclassical description of photon emission published by the author earlier in 1999 [M. Kowalski, Phys. Essays 12, 312 (1999)]. In the semiclassical approach, the Coulomb force and a radiation resistance force have been taken into account to get time-dependent emission of the photon. In both the quantum and semiclassical cases, the transition takes place within a time interval equal to one period of the photon's wave. The creation of a one-wavelength-long photon is supported by the results of experiments using ultrafast (ultrashort) laser pulses to generate excited atoms, which emit light pulses shorter than two photon wavelengths [F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009); H. Kapteyn and M. Murnane, Phys. World 12, 31 (1999)]. [ABSTRACT FROM AUTHOR]

In a recent publication, a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with N order of derivatives and M rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for N = M = 1 and linearized Gauss–Bonnet gravity for N = M = 2. In this paper, the nature of the connection between these two well-explored physical models is further investigated by means of an additional common property; a complete dual formulation. First, we give a review of Gauss–Bonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized Gauss–Bonnet gravity is then developed. It is shown that the dual formulation of linearized Gauss–Bonnet gravity is analogous to the homogenous half of Maxwell's theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the nonhomogenous half of Maxwell's theory, the first invariant derived from the procedure in N = M = 2 can be introduced. The complete gauge invariance of a model with respect to Noether's first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spin- n curvature tensors for all N = M = n are the field strength tensors for each n. These completely gauge invariant models correspond to the Maxwell-like higher spin gauge theories whose equations of motion have been well explored in the literature. [ABSTRACT FROM AUTHOR]

The present work is motivated by recent experiments aimed to measure the propagation velocity of bound electromagnetic (EM) field (Missevitch, et al. in EPL 93:64004, 2011; de Sangro et al. in Eur Phys J C 75:137, 2015) that reveal no retardation in the absence of EM radiation. We show how these findings can be incorporated into the mathematical structure of special relativity theory that allows us to reconsider some selected problems of classical and quantum electrodynamics. In particular, we come to the conclusion that the total four-momentum for a classical system "particles plus fields" ought to be a present state function of moving charges if EM radiation is negligible. In quantum domain, we analyze novel definition of the momentum operator recently suggested in the study of quantum phase effects (Kholmetskii et al. in Sci. Rep. 8:11937, 2018). It implies that bound EM field energy and momentum are to be present state functions, too. Being in agreement with reported experiments, these conclusions suggest the necessity to carry out more precise experimental verifications for additional and independent determination of propagation properties of bound EM fields. A scheme of a possible experiment on this subject is also proposed. [ABSTRACT FROM AUTHOR]

We show that the claim by Franklin (Int. J. Mod. Phys. A 35, 2050061 (2020)) with respect to the vanishing charge distribution over the perimeter of an electrically neu-tral moving current loop is erroneous and is based on a misinterpretation of physi- cal meaning of Lorentz transformations. Moreover, we show that the development of nonvanishing electric dipole moment by a moving current loop (which we named as "relativistic polarization") represents a direct implication of covariant formulation of classical electrodynamics of material media. In this respect, we analyze some subtle effects related to the motion of magnetic dipoles in an electromagnetic field and disclose their physical meaning. [ABSTRACT FROM AUTHOR]

A general expression is obtained for retarded potentials for a system of equations of macroscopic electrodynamics with fractional Caputo derivatives with respect to time. An analog of the Lienard–Wiechert potentials is obtained. All expressions contain a nonlocal (time-distributed) delay, which takes the temporal dispersion in the system into account. [ABSTRACT FROM AUTHOR]

When accelerated by a constant force in the lab frame, a classical charge experiences no self force. In this case, the particle radiates without dissipating its kinetic and potential energy. But what happens when the particle enters another region with equal and opposite acceleration? Does the oscillating charge lose its mechanical energy similar to a radiating dipole, even though it seems to lose no mechanical energy within each region of constant acceleration? In this paper, I will show how mechanical energy is transferred to radiation energy via the Schott energy when the particle crosses the boundary between the two regions. In particular, I will show how preacceleration, which is usually regarded as an unphysical effect of the Lorentz–Abraham–Dirac self force, is essential for the energy transfer. Moreover, I will show that the commonly adopted Landau–Lifshitz approximation, which removes preacceleration, introduces second-order secular energy error. On a more fundamental level, the validity of classical electrodynamics is in fact questionable because quantum effects are likely important. The classical prediction can be tested experimentally by observing frequency chirping of radiation, whereby micro physics leaves signatures on macroscopic scales. The required experimental accuracy is estimated. Trap experiments of this type is complementary to collider experiments that endeavor to observe radiation reaction for elementary particles. [ABSTRACT FROM AUTHOR]

In the two-dimensional case, we construct nondegenerate Hamiltonians that describe electron motion in an electromagnetic field and have additional integrals of motion quadratic in momentum. We completely classify the quasi-Stäckel Hamiltonians related to these systems in the cases where the leading approximation in momenta of the additional integral depends quadratically on the coordinates. We consider reductions of such systems that are symmetric under rotation about the z axis. [ABSTRACT FROM AUTHOR]

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics is found by developing a procedure which can be used to derive completely gauge-invariant models. The procedure involves building the most general Lagrangian for a particular order of derivatives (N) and a rank of tensor potential (M), then solving such that the model is completely gauge-invariant (the Lagrangian density, equation of motion and energy–momentum tensor are all gauge-invariant). In the case of N = 1 order of derivatives and M = 1 rank of tensor potential, electrodynamics is uniquely derived from the procedure. In the case of N = 2 order of derivatives and M = 2 rank of symmetric tensor potential, linearized Gauss–Bonnet gravity is uniquely derived from the procedure. The natural outcome of the models for classical electrodynamics and linearized Gauss–Bonnet gravity from a common set of rules provides an interesting connection between two well-explored physical models. [ABSTRACT FROM AUTHOR]

Electromagnetic fields carry momentum: Pem =∞0(E × B) dt. But if the centre of energy of a (localized) system is at rest, its total momentum must be zero. The compensating term has come to be called 'hidden' momentum: Ph =-Pem. It is (typically) ordinary mechanical momentum, relativistic in nature, and is 'hidden' only in the sense that it is not associated with motion of the system as a whole--only with that of its constituent parts. This article develops a catalogue of field momenta and hidden momenta for ideal electric and magnetic dipoles--both the 'standard' variety made from electric charges and currents and the 'anomalous' variety made from hypothetical magnetic monopoles and their currents--in the presence of electric and magnetic fields (which themselves may be produced by 'standard' or 'anomalous' sources). [ABSTRACT FROM AUTHOR]

The Landau–Lifshitz (LL) equation has been proposed as the classical equation to describe the dynamics of a charged particle in a strong electromagnetic field when influenced by radiation reaction. Until recently, there has been no clear experimental verification. However, aligned crystals have remedied the situation: here, as in Nielsen et al CERN NA63 Collaboration (2020 Phys. Rev. D 102 052004), we report on a quantitative experimental test of the LL equation by measuring the emission spectra of electrons and positrons penetrating aligned single crystals. The recorded spectra are in remarkable agreement with simulations based on the LL equation of motion with moderate quantum corrections for recoil and, in the case of electrons in axially aligned crystals, spin and reduced radiation intensity.

We report on the quantitative experimental illustration of elementary optomechanics within the classical regime. All measurements are performed in a commercial dilution refrigerator on a mesoscopic drumhead aluminium resonator strongly coupled to a microwave cavity, using only strict single-tone schemes. Sideband asymmetry is reported using in-cavity microwave pumping, along with noise squashing and back-action effects. Results presented in this paper are analysed within the simple classical electric circuit theory, emphasizing the analogous nature of classical features with respect to their usual quantum description. The agreement with theory is obtained with no fitting parameters. Besides, based on those results a simple method is proposed for the accurate measurement of the ratio between microwave internal losses and external coupling.

We report three non-electromagnetic fields, which satisfy Maxwell equations. The very existence of these fields challenges the view that Maxwell equations hold only for electromagnetic fields. The reported fields are velocity fields that belong to a massive, charged particle. They are gauge-related to electromagnetic vector potentials. The significance of the vector potential has been repeatedly addressed until recent times in the pursue of reaching a self-consistent formulation of classical electrodynamics (CED). This is an important goal, because CED has a wide domain of validity and because it serves as a model for several quantum field theories. Our results exhibit the existence of some rather unexpected ties between Maxwell and Lorentz equations. • There are non-electromagnetic fields which satisfy Maxwell equations. • Variational calculus uncovers an intrinsic relationship between Lorentz and Maxwell equations. • Particle-like and wave-like features linked to a single particle may show up at the classical level. [ABSTRACT FROM AUTHOR]

The classical electrodynamics for X-boson model is studied to understand it propagation in the space–time. The Maxwell equations of model and the correspondents wave equations are obtained. It indicate the dispersion relations of a massive and massless particle, that we interpret as photon and the X-boson. Thereby, a full diagonalization of the model is introduced to get a Maxwell sector summed up to Proca sector. Posteriorly, the X-fields and X-potentials of a relativistically moving charge is obtained in terms of a time-proper integral, and as an example, we calculate the fields and potentials for a charge in uniform moving. Finally, the gauge symmetry and gauge transformations were discussed. [ABSTRACT FROM AUTHOR]

The chaining process of a system of interacting carbon nanotubes (CNTs) under an alternating current electric field is investigated at two regions of different electric field characteristics. For the region of uniform electric field (far from the electrodes), a two-dimensional multiparticle approach based on the dielectrophoretic (DEP) theory and classical mechanics is proposed to investigate the CNT rotational and translation motion. For this scenario, CNT rotation and alignment along the electric field direction occurs first, followed by the translation and chaining processes which were found to be highly dependent on the CNT-to-CNT initial configuration. On the other hand, the presence of high electric field gradients governs the CNT chaining at regions near the electrodes. DEP forces caused by such gradients were computed by finite element analysis and compared to the magnitude of the CNT-to-CNT interacting forces at zones of uniform electric fields. A critical distance of CNT-to-CNT separation was estimated, which determines if a CNT is attracted towards the electrode or if it is attracted by other CNTs away from the electrodes. Experimental evidence of CNTs dynamic motion under electric fields is presented to support the predicted trends. [ABSTRACT FROM AUTHOR]

We use the path integral form of quantum electrodynamics (QED) to show that a causal classical limit to QED can be derived by functionally integrating over the photon coordinates, starting from an initial photon vacuum and ending in a final coherent radiation state driven by the anticipated classical charged particle trajectories. The resulting charged particle transition amplitude depends only on particle coordinates. When the ħ→0 limit is taken, only those particle paths that are not constrained by the final radiation state are varied. These results demonstrate that the collapse from an infinity of charged particle paths, a path integral description, to causally interacting classical trajectories, a stationary-action description, is critically dependent on including final coherent state radiation and maintaining the distinction between particle paths that are free to vary and those trajectories that can be monitored by the final state radiation. [ABSTRACT FROM AUTHOR]

Using the example of classical electrodynamics, I argue that the concept of fields as mediators of particle interactions is fundamentally flawed and reflects a misguided attempt to retrieve Newtonian concepts in relativistic theories. This leads to various physical and metaphysical problems that are discussed in detail. In particular, I emphasize that physics has not found a satisfying solution to the self-interaction problem in the context of the classical field theory. To demonstrate the superiority of a pure particle ontology, I defend the direct interaction theory of Wheeler and Feynman against recent criticism and argue that it provides the most cogent formulation of classical electrodynamics. [ABSTRACT FROM AUTHOR]

We carry out the classical analysis of spin–orbit coupling in hydrogen-like atoms, using the modern expressions for the force and energy of an electric/magnetic dipole in an electromagnetic field. We disclose a novel physical meaning of this effect and show that for a laboratory observer the energy of spin–orbit interaction is represented solely by the mechanical energy of the spinning electron (considered as a gyroscope) due to the Thomas precession of its spin. Concurrently we disclose some errors in the old and new publications on this subject. [ABSTRACT FROM AUTHOR]

By the covariant statement of the distance in space-time separating transmitter and receivers, the emission and absorption of the retarded and advanced waves are all simultaneous. In other words, for signals carried on electromagnetic waves (advanced or retarded) the invariant interval ( cdt ) 2 − dr 2 between the emission of a wave and it's absorption at the non-reflecting boundary is always identically zero. Utilizing this principle, we have previously explained the advantages of including the coherent radiation reaction force as a part of the solution to the boundary value problem for FELs that radiate into “free space” (Self Amplified Spontaneous Emission (SASE) FELs) and discussed how the advanced field of the absorber can interact with the radiating particles at the time of emission. Here we present an analytical test which verifies that a multilayer mirror can act as a band pass filter and can contribute to microbunching in the electron beam. Here we will discuss motivation, conditions and requirements, and method for testing this effect. [ABSTRACT FROM AUTHOR]

It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics if instead of considering the electron to be a particle, we consider an electrically charged classical wave field-an 'electron wave'-which is held by the electrostatic field of the proton. It is shown that quantum mechanics must be considered not as a theory of particles but as a classical field theory in the spirit of classical electrodynamics. In this case, we are not faced with difficulties in interpreting the results of the theory. In the framework of classical electrodynamics, all of the well-known regularities of the spontaneous emission of the hydrogen atom are obtained, which is usually derived in the framework of quantum electrodynamics. It is shown that there are no discrete states and discrete energy levels of the atom: the energy of the atom and its states change continuously. An explanation of the conventional corpuscular-statistical interpretation of atomic phenomena is given. It is shown that this explanation is only a misinterpretation of continuous deterministic processes. In the framework of classical electrodynamics, the nonlinear Schrödinger equation is obtained, which accounts for the inverse action of self-electromagnetic radiation of the electron wave and completely describes the spontaneous emissions of an atom. [ABSTRACT FROM AUTHOR]

A model for the dynamics of a classical point charged particle interacting with higher order jet fields is introduced. In this model, the dynamics of the charged particle is described by an implicit ordinary second-order differential equation. Such equation is free of run-away and pre-accelerated solutions of Dirac's type. The theory is Lorentz invariant, compatible with the first law of Newton and Larmor's power radiation formula. Few implications of the new equation in the phenomenology of non-neutral plasmas is considered. [ABSTRACT FROM AUTHOR]

A brief scientific essay on the history of classical electrodynamics development in the 18th through 20th centuries is given.