Classical Theory Of Electrodynamics Research Articles

Theory of Classical Electrodynamics with Topologically Quantized Singularities as Electric Charges

AbstractA theory of classical electrodynamics, where the only admissible electric charges are topological singularities in the electromagnetic field, is formulated. Charge quantization is accounted by the Chern theorem, such that Dirac magnetic monopoles are not needed. The theory allows positive and negative charges of equal magnitude, where the sign of the charge corresponds to the chirality of the topological singularity. Given the trajectory of the singularity, one can calculate electric and magnetic fields identical to those produced by Maxwell's equations for a moving point charge, apart from a multiplicative constant factor related to electron charge and vacuum permittivity. The theory is based on the relativistic Weyl equation in frequency‐wavevector space, with eigenstates comprising the position, velocity, and acceleration of the singularity, and eigenvalues defining the retarded position of the charge. From the eigenstates, one calculates the Berry connection and the Berry curvatures, and identifies the curvatures as electric and magnetic fields.

Development of an on-board system for diagnosing the technical condition of the tread surface of the wheels of wagons

Introduction. The aim of the study is to develop a basic configuration of the on-board system for diagnosing the technical condition of the wheels tread surface of a wagon while the train is running and to model its operation.Materials and methods. The theoretical studies are based on the methods of Lagrange's analytical mechanics, the theory of oscillations and classical electrodynamics. The simulation was carried out for a flat design scheme using numerical methods. The results were processed using the developed algorithm implemented in the programming language of the Mathcad system.Results. This article studies the problem of the negative impact of local wear of the wheel tread surface on the state of the carriage chassis of the car and the rail track, as well as on the safety of train traffic. The authors propose a basic configuration of an on-board system for diagnosing wheel pairs of a wagon with an autonomous power supply with a power of up to 10 W, which simultaneously acts as a sensor. A mathematical model of diagnostic signals for local wheel wear has been constructed, and an algorithm for their detection has been developed based on the results. A criterion for estimating the geometric parameters of wear is formulated and its threshold values for slots of various depths are calculated. Alarms have been identified that suggest a reduction in the speed of the train.Discussion and conclusion. The solution of the stated problem is important both in the operation of existing cars and in the development of new, innovative cars with an axle load of 27–30 tf and speeds of up to 140 km/h. Timely detection of local wear of the tread surface of wagon wheels will increase the level of traffic safety and reduce the cost of repairing cars and rail tracks.

When Fields Are Not Degrees of Freedom

We show that in the Maxwell-Lorentz theory of classical electrodynamics most initial values for fields and particles lead to an ill-defined dynamics, as they exhibit singularities or discontinuities along light-cones. This phenomenon suggests that the Maxwell equations and the Lorentz force law ought rather to be read as a system of delay differential equations, that is, differential equations that relate a function and its derivatives at different times. This mathematical reformulation, however, leads to physical and philosophical consequences for the ontological status of the electromagnetic field. In particular, fields cannot be taken as independent degrees of freedom, which suggests that one should not add them to the ontology.

The Coulomb Energy of Finite Size Nucleus from the Study of Classical Electrodynamics Theory

The Coulomb Energy of Finite Size Nucleus from the Study of Classical Electrodynamics Theory

Probing Vacuum Polarization Effects with High-Intensity Lasers

These notes provide a pedagogical introduction to the theoretical study of vacuum polarization effects in strong electromagnetic fields as provided by state-of-the-art high-intensity lasers. Quantum vacuum fluctuations give rise to effective couplings between electromagnetic fields, thereby supplementing Maxwell’s linear theory of classical electrodynamics with nonlinearities. Resorting to a simplified laser pulse model, allowing for explicit analytical insights, we demonstrate how to efficiently analyze all-optical signatures of these effective interactions in high-intensity laser experiments. Moreover, we highlight several key features relevant for the accurate planning and quantitative theoretical analysis of quantum vacuum nonlinearities in the collision of high-intensity laser pulses.

Fundamentals and model of resonance helicity and energy transfer between two magnetoelectric chiral particles

We establish a classical electrodynamic theory for the non-radiative transfer of field helicity (RHELT) and energy (RET) between a donor and an acceptor, both being dipolar, magnetoelectric and bi-isotropic, chiral in particular, with rotating excited dipoles. We introduce orientational factors that control this process. Also, a RHELT and RET interaction radius is put forward. The detection of RHELT adds a wealth of information contained in the helicity of the transferred fields, never used or established to date. The nature of these dipolar magnetoelectric bi-isotropic particles and/or molecules with induced dipoles possessing angular momentum, enriches the number of variables and associated effects. Hence the landscape involved in this transfer phenomenon, never explored before, is significantly broader than in conventional FRET. In this way, chiral interacting objects convey terms in the equations of transfer rate of helicity and energy that are discriminatory, so that one can extract information on their structural chirality handedness and polarization rotation. As such, not only the rate of electromagnetic helicity transfer, but also that of energy transfer may be negative, which for the latter means an enhanced emission from the donor in pressence of acceptor, a phenomenon which does not exist in conventional FRET. Importantly, both the RHELT and RET rates, as well as the RHELT interaction radius, are very sensitive to changes in the helicity, or state of polarization, of the illumination, as well as to the polarization of the excited electric and magnetic dipole moments of donor and acceptor. Finally, we introduce the observable quanties in terms of which one can obtain the transfer rates and interaction radii.

Stochastic Electrodynamics: The Closest Classical Approximation to Quantum Theory

Stochastic electrodynamics is the classical electrodynamic theory of interacting point charges which includes random classical radiation with a Lorentz-invariant spectrum whose scale is set by Planck’s constant. Here, we give a cursory overview of the basic ideas of stochastic electrodynamics, of the successes of the theory, and of its connections to quantum theory.

Light-by-light Scattering in Lead--Lead Collisions in the ATLAS Experiment

Light-by-light (LbyL) scattering, ! , is a quantum-mechanical process, forbidden by the classical theory of electrodynamics, but possible in Quantum Electrodynamics via a loop diagram. Despite the small cross section, it is theoretically possible to observe this process in ultra-peripheral high-energy heavy-ion collisions. Based on 0.48 nb􀀀1 of 2015 Pb+Pb data, a first direct evidence of LbyL scattering was established by the ATLAS Collaboration in 2017. In total, 13 events were found in the signal region with a background expectation of 2:60:7 events. The excess corresponds to 4.4 significance over the background-only hypothesis. In November 2018, the new dataset of Pb+Pb collisions was collected by the ATLAS experiment with an integrated online luminosity of 1.7 nb􀀀1. This recent dataset has been employed to perform a preliminary study using the control sample from ! e+e􀀀 process.

Subharmonic resonance and critical eccentricity for the classical hydrogen atomic system

Subharmonic resonance behaviors are investigated for the classical hydrogen atom, with classical radiation damping and circularly polarized light acting on the classical electron. This study is intended for both potential experimental applications as well as for deeper theoretical purposes. Long resonant states are predicted for realistic Rydberg atoms and highly excited hydrogen states. Several previously undiscovered physical effects are predicted. First, the semimajor axis remains relatively constant when in subharmonic resonance; second, the eccentricity steadily increases until a maximum, critical value is reached, at which point orbital decay sets in. If the initial orbit is circular, this critical eccentricity value is shown to always be the same for each subharmonic condition, regardless of the initial orbital radius. An analytic derivation for this result is presented. The illustrated dynamics are of interest for the classical theory of stochastic electrodynamics (SED) regarding whether SED can fundamentally describe more of quantum phenomena, particularly atomic excited state behavior and related emission and absorption spectra. Also of interest are how classical resonances can be imposed on a near continuum of quantum states. Finally, there may be future technological applications, such as “reading” and “writing” information into Rydberg atoms in the form of subharmonic resonances.

Modeling the Interaction of Electrodynamic Fields to Circuit Elements

ABSTRACTCurriculum typically addresses classical electrodynamic field theory and circuit analysis (with resistors, capacitors, and inductors) separately. As such, there exists a gap relating the two. This work provides a strong tie between these two disciplines that is useful for bridging this gap. Prior work establishes a relationship between electrodynamic fields and circuit elements, but application to circuit analysis remains ambiguous because of the path-dependent node voltages formulated. This paper develops a model resulting in path-independent node voltages that are necessary for circuit analysis techniques. The model is based on the electric field and the magnetic vector potential. Both fields have components associated with the circuit elements as well as external or excitation sources. The model is applicable for determining the coupling of excitation electrodynamic fields to transmission lines. This paper provides a rigor and collective work not found elsewhere in electrodynamic or circuit theory literature.

Magnetic Monopoles and the Quantum Theory of Magnetism in Matter

Electricity and magnetism are common features of our world. The subject of electromagnetic fields in empty space populated only by point charges or smooth charge distributions in space is well understood. In that case, one deals with the classical theory of electrodynamics developed by J.C. Maxwell in 1864. Electromagnetism in the presence of matter is, however, a completely different problem. Microscopic electric behavior of homogeneous substances can in general be characterized fairly simply and completely. The theory that enables us to do this is fairly well understood. Sadly the situation is quite different for magnetism in matter. The study there is phenomenological. That is, the substance is characterized by a number of parameters and the experimentally determined relations among them. We are not aware of any successful microscopic theory of magnetism in matter. The microscopic theory of magnetic substances, a topic of fundamental and technological importance, is the subject of this paper.

Force, torque, linear momentum, and angular momentum in classical electrodynamics

The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz force law. Whereas Maxwell's equations relate the fields to their material sources, Poynting's theorem governs the flow of EM energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and the fields. An alternative force law, first proposed by Einstein and Laub, exists that is consistent with Maxwell's equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetized medium, the Einstein-Laub (E-L) formulation of EM force and torque does not invoke hidden entities under such circumstances. Moreover, total force/torque exerted by EM fields on any given object turns out to be independent of whether the density of force/torque is evaluated using the law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.

Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC

Light-by-light scattering (γγ → γγ) is a quantum-mechanical process that is forbidden in the classical theory of electrodynamics. This reaction is accessible at the Large Hadron Collider thanks to the large electromagnetic field strengths generated by ultra-relativistic colliding lead ions. Using 480 μb−1 of lead–lead collision data recorded at a centre-of-mass energy per nucleon pair of 5.02 TeV by the ATLAS detector, here we report evidence for light-by-light scattering. A total of 13 candidate events were observed with an expected background of 2.6 ± 0.7 events. After background subtraction and analysis corrections, the fiducial cross-section of the process Pb + Pb (γγ) → Pb(∗) + Pb(∗)γγ, for photon transverse energy ET > 3 GeV, photon absolute pseudorapidity |η| < 2.4, diphoton invariant mass greater than 6 GeV, diphoton transverse momentum lower than 2 GeV and diphoton acoplanarity below 0.01, is measured to be 70 ± 24 (stat.) ± 17 (syst.) nb, which is in agreement with the standard model predictions.

Light-by-light scattering in ultra-peripheral Pb+Pb collisions at [formula omitted] with the ATLAS detector

Light-by-light scattering (γγ→γγ) is a quantum-mechanical process that is forbidden in the classical theory of electrodynamics. This reaction is accessible for the first time at the Large Hadron Collider thanks to the large electromagnetic field strengths generated by ultra-relativistic colliding lead (Pb) ions. Using 480μb−1 of Pb+Pb collision data recorded at a centre-of-mass energy per nucleon pair of 5.02 TeV by the ATLAS detector, we report evidence for the γγ→γγ process. A total of 13 candidate events are observed with a background expectation of 2.6±0.7 events. After background subtraction and analysis corrections, the fiducial cross-section of the process Pb+Pb(γγ)→Pb(⁎)+Pb(⁎)γγ has been measured to be 70±24 (stat.)±17 (syst.) nb, which is in agreement with the Standard Model predictions.

Transfer of energy between a pair of molecules near a plasmonic core-shell nanoparticle: Tunability and sensing

Our model is applied to the calculation of interaction energy between a pair of dipolar molecules (point dipoles) in the vicinity of a nanoshell monomer with core-shell structure, based on the dipole quasi-electrostatic theory of classical electrodynamics and using the Drude and Maxwell-Garnett model. In other words, this work discusses the intermolecular energy transfer from a donor molecule to an acceptor molecule near a spherical nanoparticle that is important for practical applications like sensing. It is shown that the proximity of plasmonic nanoparticles can have a strong effect on the energy transfer between molecules. In addition to the influence of the size, composition, embedding medium, and the filling fraction of doped particles on the interaction energy, the contribution of the dipolar, quadrupolar, octupolar, hexadecapolar, triakontadipolar, and higher order multipole interactions is presented and analyzed. Briefly, we will show that it is possible to achieve enhanced energy transfer by manipulation of different parameters as mentioned above.

Hilbert space theory of classical electrodynamics

Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commuting observables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of the much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al, Phys. Rev. A 88, 052108 (2013), it is pointed out that quantum processes that preserve the positivity or nonpositivity of the Wigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.

Radiated power and radiation reaction forces of coherently oscillating charged particles in classical electrodynamics

For the foreseeable future, the analysis and design of the complex systems needed to generate intense beams of radiation via the process of coherent emission into free-space will depend on the principles and methods of classical electrodynamics (CED). But the fields and forces predicted by the currently accepted CED theory are manifestly incompatible with Maxwell's equations' energy integral as applied to the process of coherent emission into free-space. It is the purpose of this paper to review the evidence for these limitations of conventional CED, to identify an alternative formulation of CED that does not suffer from these defects, and to describe how the predictions of this more physically realistic formulation of electrodynamics, including the role of the advanced interactions allowed by Maxwell's equations and thermodynamics, might be tested by experiment and applied to enhance the capabilities of devices and systems employing the mechanism of ``radiation into free-space.''

Transition radiation of electrons with a nonzero orbital angular momentum

Several experimental groups have recently obtained the socalled vortex electrons (electrons with orbital angular momentum (OAM) of ≤ 100) with energies of ~ 300 keV. The angular momentum of such elec� trons becomes proportional to the OAM value, which leads to the corresponding increase in the electron magnetic moment. In this work, we investigate the transition radiation from the "charge + magnetic moment" system by means of the classical electrodynamics theory. The circular polarization of optical tran� sition radiation reaches its maximum level to ~ 70%, which allows using this effect for the independent mea� surement of the electron orbital momentum value.

The Effect of Metal Type on the Separate Dielectric Layer-Dependent Plasmon Coupling in Al–Au Bimetallic Metal-Dielectric-Metal Nanoshells

Metal type-dependent plasmonic absorption properties of Al–Au bimetallic metal-dielectric-metal nanoshells have been investigated theoretically by using the quasi-static theory of classical electrodynamics. It has been found that the three-layered nanoshells present different surface plasmon resonance (SPR) properties when the metal type of the inner core and outer shell is exchanged. For Al-dielectric-Au nanoshell, the |ω−−〉 band takes the major role of the absorption spectrum. Whereas for Au-dielectric-Al nanoshell, the |ω−+〉 mode has the highest intensity. The corresponding physical origin has been attributed to the different optical parameters of Au and Al, which results in different local field enhancement and plasmon energy at each plasmon hybridization mode. The plasmonic absorption properties also depend on the thickness of the separate layer and are further affected by the metal type of the inner core and outer shell. For Al-dielectric-Au nanoshell, the increasing separate layer thickness results in distinct red shift of |ω−+〉 peak but slight blue shift of the |ω+−〉 peak. For Au-dielectric-Al nanoshell, the |ω+−〉 and |ω−+〉 modes fade down and blue shifts, whereas the major peak corresponding to the |ω−−〉 mode blue shifts and gets intense firstly and then red shifts and decreases as the thickness is increased. These results indicate that different plasmon hybridization modes of the multilayered nanoshell could be enhanced selectively by choosing different type of metal as the outer shell.

The slaying of the iMongers

Bohr's Theory of the Atom, the Theory of Classical ElectroDynamics, Newtonian Cosmology, the Theory of Infinitesimals (Early Calculus), Aristotle's Theory of Motion, Olbers' Paradox, the Classical Theory of the Electron, Kirchoff's Theory of Diffraction: by far the most prominent (if not the only) cases of allegedly inconsistent scientific theories mustered so far from the staggering total amount of all scientific texts of past and present—recently babtised the substratum of science, by S. Psillos and R. Hendry. One case from mathematics invented for application in physics (to describe motion), and seven cases from physics. P. Vickers' expanded PhD Thesis Understanding Inconsistent Science is not the first book devoted to purported cases of ‘inconsistent science’, but it is the first monograph on the subject-matter by a single author. Perhaps it is also the last one, because Vickers concludes (p. 217, spoiler alert!, my italics):