Problem Of Classical Electrodynamics Research Articles

Interpretations and Naturalness in the Radiation-Reaction Problem

After more than a century of history, the radiation-reaction problem in classical electrodynamics still surprises and puzzles new generations of researchers. Here, we revise and explain some of the paradoxical issues that one faces when approaching the problem, mostly associated with regimes of uniform proper acceleration. The answers we provide can be found in the literature and are a synthesis of a large body of research. We only present them in a personal way that may help in their understanding. Besides, after the presentation of the standard answers, we motivate and present a twist to those ideas. The physics of emission of radiation by extended charges (charges with internal structure) might proceed in a surprising oscillating fashion. This hypothetical process could open up new research paths and a new take on the equivalence principle.

Dark Matter as Variations in the Electromagnetic Zero-Point Field Induced by Baryonic Matter

Cold dark-matter, as a solution to the so-called dark-matter problem, suffers from a major internal conflict: In order to dodge direct detection for so long, it must have an unobservably small (non gravitational) interaction with mundane matter, and yet it manages to ‘conspire’ with it such that, in single galaxies, its distribution can be inferred from that of mundane matter via the MOND phenomenology. This conflict is avoided if the missing, transparent component of the energy-momentum tensor is due to variations in some electromagnetic ‘zero point field’ (ZPF) which is sourced by mundane matter and contains both its advanced and retarded fields. The existence of a ZPF thus modulated by mundane matter, follows from a proper solution to the self-force problem of classical electrodynamics (CED), recently proposed by the author, which renders CED compatible with the statistical predictions of QM. The possibility that ‘dark matter’ is yet another, hitherto ignored facet of good-old classical electrodynamics, therefore seems no less plausible than it being a highly exotic and conspirative new form of matter. Tests for deciding between the two are proposed.

Electromagnetic surface wave propagation in a metallic wire and the Lambert W function

We revisit the solution due to Sommerfeld of a problem in classical electrodynamics, that of the propagation of an electromagnetic axially symmetric surface wave (a low-attenuation single TM01 mode) in a cylindrical metallic wire, and his iterative method to solve the transcendental equation that appears in the determination of the propagation wave number from the boundary conditions. We present an elementary analysis of the convergence of Sommerfeld's iterative solution of the approximate problem and compare it with both the numerical solution of the exact transcendental equation and the solution of the approximate problem by means of the Lambert W function.

Evanescent-wave Johnson noise in small devices

In many quantum computer architectures, the qubits are in close proximity to metallic device elements. The fluctuating currents in the metal give rise to noisy electromagnetic fields that leak out into the surrounding region. These fields are known as evanescent-wave Johnson noise. The noise can decohere the qubits. We review and update the general theory of this effect for charge qubits subject to electric noise and for spin and magnetic qubits subject to magnetic noise. A mapping of the quantum-mechanical problem onto a problem in classical electrodynamics simplifies the calculations. The focus is on relatively simple geometries in which analytical calculations can be done. Results are presented for the local noise spectral density in the vicinity of cylindrical conductors such as small antennae, noise from objects that can be treated as dipoles, and noise correlation functions for several geometries. We summarize the current state of the comparison of theory with experimental results on decoherence times of qubits. Emphasis is placed on qualitative understanding of the basic concepts and phenomena.

An elementary argument for the magnetic field outside a solenoid

The evaluation of the magnetic field inside and outside a uniform current density infinite solenoid of uniform cross-section is an elementary problem in classical electrodynamics that all undergraduate Physics students study. Symmetry properties of the cylinder and the judicious use of Ampere’s circuital law leads to correct results; however it does not explain why the field is non zero for a finite length solenoid, and why it vanishes as the solenoid becomes infinitely long. An argument is provided in Farley and Price (2001 Am. J. Phys. 69 751), explaining how the magnetic field behaves outside the solenoid and not too far from it, as a function of the length of the solenoid. A calculation is also outlined for obtaining the field just outside the circular cross section solenoid, in the classic text Classical Electrodynamics by Jackson, 3rd edn (John Wiley and Sons, Inc.), problems 5.3–5.5. The purpose of this paper is to provide an elementary argument for why the field becomes negligible as the length of the solenoid is increased. A quantitative analysis is provided for the field outside the solenoid, at radial distances large compared to the linear dimension of the solenoid cross section.

Conceptual problems in classical electrodynamics: No more toils and trouble?

In previous work I have argued that classical electrodynamics is beset by deep conceptual problems, which result from the problem of self-interactions. Symptomatic of these problems, I argued, is that the main approach to modeling the interactions between charges and fields is inconsistent with the principle of energy–momentum conservation. Zuchowski (2013) reports a formal result that shows that the so-called ‘Abraham model' of a charged particle satisfies energy–momentum conservation and argues that this result amounts to a refutation of my inconsistency claim. In this paper I defend my claims against her criticism and argue that she has succeeded neither in refuting my inconsistency argument nor in showing that the conceptual problems of classical electrodynamics have been solved.

A basic theory for the interference of wave packets reflected from stationary and moving boundaries

In this paper, the interference of wave packets reflected from a stationary boundary and a moving boundary respectively are discussed. The present theory is based on the boundary value problem of classical electrodynamics, especially with the moving boundary which gives rise Doppler effect. Various distinguished interference properties are investigated and a rigorous expression for the velocity measurement of the moving mirror is provided. At the end, the paper points out that many similar and important problems are waiting for us to explore.

Some problems of classical electrodynamics

In this lecture, I discuss issues that usually escape attention of students in electrodynamics. These are the questions of (1) what the photon observed in nature “looks like,” (2) how an interference pattern arises from a source containing a lot of incoherently emitting atoms, and (3) how light “slows down” in a medium. Answers to these questions, if discussed at all, are scattered over various textbooks. Here, I follow our textbook [1].

On dual representation in classical electrodynamics

A discussion is given of the use of the dual representation in solving multipole radiation and electromagnetic wave diffraction problems in classical electrodynamics. In the method discussed, actual electric field sources are replaced by 'magnetic' ones. It is shown that despite the absence of Dirac magnetic monopoles, such formalism allows for a physical interpretation of some frequently used methods.

A geometric analysis of the Maxwell field in a vicinity of a multipole particle and a new family of special functions

A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a novel trajectory-adapted coordinate system, which simplifies considerably the equations. The solution is given in terms of a series, where a new family of special functions arises in a natural way. Singular behaviour of the field near to the particle may be analyzed this way up to an arbitrary order. Application to the self-interaction problems in classical electrodynamics is discussed.

A classical spinor approach to the quantum/classical interface

A promising approach to the quantum/classical interface is described. It is based on a formulation of relativistic classical mechanics in the Clifford algebra of physical space. Spinors and projectors arise naturally and provide powerful tools for solving problems in classical electrodynamics. They also reproduce many quantum results, allowing insight into quantum processes.PACS Nos.: 03.65.Ca, 03.65.Ta, 04.20.Gz, 02.10.Xm

Conceptual Problems in Classical Electrodynamics*

In Frisch 2004 and 2005 I showed that the standard ways of modeling particle-field interactions in classical electrodynamics, which exclude the interactions of a particle with its own field, results in a formal inconsistency, and I argued that attempts to include the self-field lead to numerous conceptual problems. In this paper I respond to criticism of my account in Belot 2007 and Muller 2007. I concede that this inconsistency in itself is less telling than I suggested earlier but argue that existing solutions to the theory's foundational problems do not support the kind of traditional philosophical conception of scientific theorizing defended by Muller and Belot.

Radiation Reaction, Renormalization and Poincaré Symmetry

We consider the self-action problem in classical electrodynamics of a massive point-like charge, as well as of a massless one. A consistent regularization procedure is pro- posed, which exploits the symmetry properties of the theory. The radiation reaction forces in both 4D and 6D are derived. It is demonstrated that the Poincare-invariant six-dimensional electrodynamics of the massive charge is renormalizable theory. Unlike the massive case, the rates of radiated energy-momentum tend to infinity whenever the source is accelerated. The external electromagnetic fields, which do not change the velocity of the particle, ad- mit only its presence within the interaction area. The eective equation of motion is the equation for eigenvalues and eigenvectors of the electromagnetic tensor. The interference part of energy-momentum radiated by two massive point charges arbitrarily moving in flat spacetime is evaluated. It is shown that the sum of work done by Lorentz forces of charges acting on one another exhausts the eect of combination of outgoing electromagnetic waves generated by the charges.

Radiation reaction and renormalization via conservation laws of the Poincaré group

We consider the self-action problem in classical electrodynamics of a point-like charge arbitrarily moving in at space-time of four or six dimensions. A consistent regularization procedure is proposed which exploits the symmetry properties of the theory. The energy-momentum and angular momentum balance equations allow us to derive the radiation reaction forces in both 4D and 6D. It is shown that a point-like source in 6D possesses an internal angular momentum with the magnitude which is proportional to the square of acceleration. 6D action functional contains, apart from the usual bare mass, an additional renormalization constant which corresponds to the curvature of the world line (i. e. to the magnitude of internal angular momentum of bare particle). It is demonstrated that the Poincar e-invariant six-dimensional electrodynamics is renormalizable theory.

On the regularization procedure in classical electrodynamics

We consider the self-action problem in classical electrodynamics. A strict geometrical sense of commonly used renormalization of mass is made. A regularization procedure is proposed which relies on energy–momentum and angular momentum balance equations. We correct the expression for angular momentum tensor obtained by us in a previous paper (2002 J. Phys. A: Math. Gen. 35 831).

Dynamics and causality constraints

The physical meaning and the geometrical interpretation of causality implementation in classical field theories are discussed. Causality in field theory are kinematical constraints dynamically implemented via solutions of the field equations, but in a limit of zero-distance from the field sources part of these constraints carries a dynamical content that explains old problems of classical electro-dynamics with deep implications to the nature of physical interactions.

Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles.

An exact calculation of the radiation intensity, angular momentum loss, and the recoil force for the most general type of source, characterized by electric, magnetic, and toroid multipole moments and radii of any multipolarity and an arbitrary time dependence, is presented. The results are expressed in terms of time derivatives of the multipole moments and mean radii of the corresponding distributions. Although quite cumbersome, the formulas found by us represent exact results in the correct multipole analysis of configurations of charges and currents that contain toroidal sources. So the longstanding problem in classical electrodynamics of relating the radiation properties of a system to quantities completely describing its internal electromagnetic structure is thereby exactly solved. By particularizations to the first multipole contributions, corrections to the familiar formulas from books are found, mostly on account of the toroid moments and their interference with the usual electric and magnetic ones.

The Radiation Reaction Problem in a Simple Coupled Model

The complete description of the interaction between an external electromagnetic field and a charged particle causing it to radiate is one of the most fundamental problems in classical electrodynamics. Here we provide a simple coupled model that describes via the Lagrangian of the physical system the full radiation reaction process resulting from the particle–field interactions which simulate the electromagnetic ones. The particle and field evolution equations obtained from the Lagrangian are studied as an initial value problem giving rise to the particle's radiation reaction equation, which includes the complete interaction with the field. Using stability theory we analyze this equation and prove that every solution is global uniform asymptotically stable, evidencing that the particle coupled to the field radiates. The model proves to be interesting, for it clearly illustrates the particle–field interaction process and shows the radiation's origin.

4/3 problem in classical electrodynamics.

We evaluate the self-force acting on an extended nonrelativistic charged particle, in the framework of classical electrodynamics with a cutoff at short distances. We show that in the regularized Maxwell theory, the point particle limit is finite and well defined. As a result, the electromagnetic mass of a point particle enters the equation of motion in a form consistent with the special theory of relativity. \textcopyright{} 1996 The American Physical Society.

Friction force with non-instantaneous interaction between moving harmonic oscillators

The friction force acting between two weakly interacting, harmonic oscillators which move slowly with respect to each other, is considered. In a previous paper the case of instantaneous interaction was treated (J.S. H∅ye and I. Brevik, Physica A 181 (1992) 413) and the expression for the force was obtained by use of a variety of methods in statistical mechanics. The present paper deals with the case of non-instantaneous interaction. It turns out that in order to obtain a complete description one has to take into account the medium (e.g., a thermal vacuum field or crystal lattice) through which the interaction propagates. We consider successively the cases where one, respectively two, oscillators are present in interaction with the medium. Our discussion has a bearing on the self-interaction problem in classical electrodynamics. As a check of the general formalism, the self-interaction on a dielectric spherical particle moving in a thermal radiation field is evaluated by considering the momentum transfer from absorbed radiation.