The radiation reaction problem for an electric charge moving in flat space-time of three dimensions is discussed. The divergences stemming from the pointness of the particle are studied. A consistent regularization procedure is proposed, which exploits the Poincaré invariance of the theory. Effective equation of motion of radiating charge in an external electromagnetic field is obtained via the consideration of energy-momentum and angular momentum conservation. This equation includes the effect of the particle's own field. The radiation reaction is determined by the Lorentz force of point-like charge acting upon itself plus a non-local term which provides finiteness of the self-action.
In quantum electrodynamics, the quantitatively most successful theory in the history of science, intercharge forces obeying the inverse square law are due to the exchange of space-like virtual photons. The fundamental quantum process underlying applications as diverse as the gyromagnetic ratio of the electron and electrical machinery is then Møller scattering $ee \to ee$. Analysis of the quantum amplitude for this process shows that the corresponding intercharge force acts instantaneously. This prediction has been verified in a recent experiment.
The symmetric tensor energy-impulse of interaction of collective of electric charges with an electromagnetic field is received. A system of covariant energy and momentum conservation equations or a system of equations for the collective motion of charged particles is derived from this tensor. From this system Expressions are derived for collective electrodynamics forces. From the energy-momentum tensor derived the tensor of collective electrodynamics forces is.
A new model for calculating the Casimir-Lifshitz force per unit length for two dielectric rods is proposed, based on the Green function method of classical electrodynamics and the Lorentz model for permittivity.
In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive equations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive…
I show that the main statement of [Phys. Rev. Lett. 105, 094802 (2010), arXiv:1005.2617] is wrong. Other inconsistences of this Letter are also discussed.
Equation of motion of Sommerfeld sphere in the field of Coulomb center is numerically investigated. It is shown that contrary to Lorentz-Dirac equation in the attractive case there are physical solutions. In the repulsive case sphere gains less energy then that should be according to relativistic equation of motion of point charge without radiation force.
The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for the electric field of a moving charge predicts that, for the particular spatial configuration considered, the inductive force vanishes in the frame in which the magnet is in motion and the test charge at rest. In contrast, consistent results, in different frames, are given by the recently derived formulae of relativistic classical electrodynamics.
We consider a self-action problem for an electric charge arbitrarily moving in flat spacetime of three dimensions. Its electromagnetic field satisfies the Maxwell equations in Minkowski space of three dimensions. In this space electromagnetic waves propagate not just at a speed of light, but also at all speeds smaller than or equal to the speed of light. The massive particle may "fill" its own field, which acts on it just like an external one. The radiation reaction is determined by Lorentz force of point-like charge acting upon itself plus non-local term which provides finiteness of the self-…
In this work, the theory of second gradient electrodynamics, which is an important example of generalized electrodynamics, is proposed and investigated. Second gradient electrodynamics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian density. Second gradient electrodynamics possesses a weak nonlocality in space and time. In the framework of second gradient electrodynamics, the retarded Green functions, first-order derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, gen…
We discuss, in the context of classical electrodynamics with a Lorentz invariant cut-off at short distances, the self-force acting on a point charged particle. It follows that the electromagnetic mass of the point charge occurs in the equation of motion in a form consistent with special relativity. We find that the exact equation of motion does not exhibit runaway solutions or non-causal behavior, when the cut-off is larger than half of the classical radius of the electron.
The Maxwell electromagnetic and the Lorentz type force equations are derived in the framework of the R. Feynman proper time paradigm and the related vacuum field theory approach. The electron inertia problem is analyzed within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle. The modified Abraham- Lorentz damping radiation force is derived, the electromagnetic electron mass origin is argued.
Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with an instantaneous inter-charge force. Problems discussed include small angle Rutherford scattering, Jackson's recent `torque paradox' and circular Keplerian orbits. Results consistent with special relativity are obtained only with an instantaneous interaction. The impossiblity of stable circular motion with retarded fields in either classical electromagnetism…
The time evolution of a charged point particle is governed by a second-order integro-differential equation that exhibits advanced effects, in which the particle responds to an external force before the force is applied. In this paper we give a simple physical argument that clarifies the origin and physical meaning of these advanced effects, and we compare ordinary electrodynamics with a toy model of electrodynamics in which advanced effects do not occur.
The problem of self forces and radiation reaction is solved by conservation of energy methods. The longstanding problem of constant acceleration is solved, and it is shown that the self force does indeed affect the particle's motion, as expected on physical grounds. The relativistic generalization is also presented.
We introduce an effective field theory approach that describes the motion of finite size objects under the influence of electromagnetic fields. We prove that leading order effects due to the finite radius $R$ of a spherically symmetric charge is order $R^2$ rather than order $R$ in any physical model, as widely claimed in the literature. This scaling arises as a consequence of Poincaré and gauge symmetries, which can be shown to exclude linear corrections. We use the formalism to calculate the leading order finite size correction to the Abraham-Lorentz-Dirac force.
Born-Infeld (BI) electrodynamics is motivated by the infinite self-energy of the point charge in Maxwell electrodynamics. In BI electrodynamics, an upper bound $b$ is imposed on the electric field, thus limiting the self-energy of the point charge. This is a review paper in which we motivate the BI Lagrangian and from it derive the field equations. We find the stress-energy tensor in BI. We calculate the potential due to the point charge in BI. We find order $b^{-2}$ wave solutions to BI in $1+1$ dimensions. We examine BI plane waves normally incident on a mirror.
Up until now, a consistent causal theory of point charged particles (for example electrons) interacting with electromagnetic field is not known. The well-known problem is that the standard Lorentz force alone (in the case of point particles) does not lead to a theory in which momentum and energy are conserved. The need of radiation reaction force (or self-force) thus arises. The well known candidate for such force, the Lorentz-Abraham-Dirac reaction force, gives non-causal particle behavior, i.e., the particle starts to move before the arrival of external electromagnetic fields. Alternative, c…
The aim of this paper is to investigate the fundamental problems of retardation and radiation caused by non-uniformly moving point sources using the theories of electrodynamics and elastodynamics. This paper investigates and compares the retarded electromagnetic fields and the retarded elastodynamic fields. For the non-uniform motion of a general point source, the Liénard-Wiechert type potentials and the radiation and nonradiation fields are derived for a point charge and for a point force.
In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the energy-momentum tensor and the Lorentz force density are presented. For an electric point charge, the generalized Lienard-Wiechert potentials and the corresponding electromagnetic field strength tensor are given as retarded integral expressions. Explicit formulas for the electromagnetic potential vector and electromagnetic field strength tensor of a uniformly moving po…
Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory …
It is shown how point charges and point dipoles with finite self-energies can be accomodated into classical electrodynamics. The key idea is the introduction of constitutive relations for the electromagnetic vacuum, which actually mirrors the physical reality of vacuum polarization. Our results reduce to conventional electrodynamics for scales large compared to the classical electron radius $r_0\approx 2.8\times10^{-13}$ cm. A classical simulation for a structureless electron is proposed, with the appropriate values of mass, spin and magnetic moment.
In this paper we propose an approach to the problem of two body motion in classical electrodynamics that takes into account the electromagnetic radiation and the radiation reaction forces. The resulting differential equations are solved numerically.
Mainly on nano-scale, but maybe not exclusively, it can be imagined a spontaneous charge disjunction inside certain media due to the fluctuations, collisions, wall effects, radiation or/and other presently unknown interactions. The repulsive Casimir-Lifshitz force may be also a good candidate as a source of this kind of phenomenon. To cover this assumption mathematically an additional term should appear in the Maxwell equations. As a consequence of this term, similar Klein-Gordon equations with a negative mass term will be obtained for the electric and magnetic fields. These equations may have…
The self force of electrodynamics is derived from a scalar field. The resulting equation of motion is free of all of the problems that plague the Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant field is solved and the solution has intuitive appeal.
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic 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…
A macroscopic theory for the dynamics of elastic, isotropic matter in presence of electromagnetic fields is proposed here. We avail of Gordon's general relativistic derivation of Abraham's electromagnetic energy tensor as starting point. The necessary description of the elastic and of the inertial behaviour of matter is provided through a four dimensional generalisation of Hooke's law, made possible by the introduction of a four dimensional ``displacement'' vector. As intimated by Nordstroem, the physical origin of electrostriction and of magnetostriction is attributed to the change in the con…
Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine dynamics, and electromagnetic forces depend directly on fields. However, physical conservation principles come from symmetries such as those following from Noether's theorem, and these require potentials for their statement. Examples are given of potentials that describe fields correctly but that violate conservation principles, demonstrating that the correct sta…
We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However it turns out that radiation reaction receives no change due to Lorentz violation whereas electromagnetic mass manifests anisotropy.
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 cons…
We present a first-principles' prediction that two charged particles of masses M_1 and M_2 separated R apart in a dielectric vacuum act on each other always an attractive force in addition to other known forces in between. This component attractive force on one charge results as the Lorentz force in the radiation depolarization- and magnetic- fields of the other charge, being an attractive radiation force, and is in addition to the ordinary repulsive radiation force. The exact solution for the attractive radiation force is F_g=G' M_1M_2/R^2, an identical formula to Newton's law of gravitation.…
In this paper we obtain the expression for the self-force in the model with the Lagrangian containing additional terms, quadratic in Maxwell tensor derivatives (so-called Bopp-Podolsky electrodynamics). Features of this force are analyzed for various limiting cases. When a charged particle moves along straight line with a uniform acceleration, an explicit formula is found. In the framework of the considered model, an observable renormalized particle mass is shown to depend on its acceleration. This dependence allows, in principle, to extract experimentally a value of the particle bare mass.
The region very close to an electron ($r << r_0 = e^2/mc^2 \approx 2.8\times 10^{-13}$ cm) is, according to quantum electrodynamics, a seething maelstrom of virtual electron-positron pairs flashing in and out of existence. To take account of this well-established physical reality, a phenomenological representation for vacuum polarization is introduced into the framework of classical electrodynamics. Such a model enables a consistent picture of classical point charges with finite electromagnetic self-energy. It is further conjectured that the reaction of a point charge to its own electromagneti…
Using the canonical formalism, Compagno and Persico [J. Phys. A: Math. Gen. 35 (2002) 3629--45] have calculated the 'radiation-reaction' force on a uniform spherical charge moving rigidly, slowly and slightly from its position at the time when the transverse electric field is assumed to vanish. This force is shown to result in the same time-averaged self-force as that which has been obtained by different means for the test charge of a Bohr--Rosenfeld field-measurement procedure and which Compagno and Persico claimed to be incorrect.
The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M - these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r,t) and M(r,t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. T…
Exploding wires are widely used in many experimental setups and pulsed power systems. However, many aspects of the process of wire fragmentation still remain unclear. If the current density is not too high, the wire may break up in the solid state. In a series of papers, see references therein, Graneau argued that neither mechanical vibrations induced by the electromagnetic pinch force nor thermal expansion could have been responsible for the wire disintegration because they were too weak. To explain the phenomenon he appealed to the obsolete Ampere force law as opposed to the conventional Bio…
A manifestly gauge-invariant hamiltonian formulation of classical electrodynamics has been shown to be relativistic invariant by the construction of the adequate generators of the Poincare Lie algebra [Physica, 76, No. 3, 421-444 (1974)]. The original formulation in terms of reduced distribution functions for the particles and the fields is applied here to the case of two charges interacting through a classical electrodynamical field. On the other hand, we have been able in previous work to introduce irreversibility at the fundamental level of description [Ann. Phys., 311, 314-349 (2004)] by r…
It is demonstrated how all the mechanical equations of classical electrodynamics (CEM) may be derived from only Coulomb's inverse square force law, special relativity and Hamilton's Principle. The instantaneous nature of the Coulomb force in the centre-of-mass frame of two interacting charged objects, mediated by the exchange of space-like virtual photons, is predicted by QED. The interaction Lagrangian of QED is shown to be identical, in the appropriate limit, to the potential energy term in the Lorentz-invariant Lagrangian of CEM. A comparison is made with the Feynman-Wheeler action-at-a-dis…
In this paper we consider some new classical effects obtained for a planar electrodynamics with the presence of a higher order derivatives term. The model can be interpreted as a kind of extension for the $3d$ Maxwell-Chern-Simons electrodynamics with higher order derivatives. We consider setups with stationary field sources describing point-like charges and Dirac points. We also investigate this model with the presence of a conducting line (in $3d$ dimensions, it is the equivalent of a conducting plate in $4d$ dimensions). In this case we calculate the propagator for the gauge field and the i…
The axiomatic structure of the electromagnetic theory is outlined. We will base classical electrodynamics on (1) electric charge conservation, (2) the Lorentz force, (3) magnetic flux conservation, and (4) on the Maxwell-Lorentz spacetime relations. This yields the Maxwell equations. The consequences will be drawn, inter alia, for the interpretation and the dimension of the electric and magnetic fields.
In classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the terms of self-rotation. The analysis of this eq. shows that on one hand, there is no "runaway" solutions, peculiar to the Lorentz-Dirac eq. of radiating point particle, on the other hand, there appear new problems, among them is the nonexistence of solution for some external moments of force.
Radiation force in Abraham-Lorentz-Dirac equation is revisited for possible signature of irreversible action in the dynamics. The analysis shows that the classical electron can dissipate out a certain fraction of field energy that distinguishes itself from the well known Larmor radiation loss. The thermal power loss is shown to follow bi-quadratic acceleration functionality, which is akin to the characteristics of Hawking-Unruh radiation emission from warm surrounding field of a non-inertial observer. Reversibility in nonstationary evolution is possible at the expense of power from concerned e…
On simple example is shown that a model of mechanically extended source of radiation in classical electrodynamics indeed has some problems with radiation reaction force. So one cannot, in general case, state, that the present situation with classical dynamics of mechanically extended sources of radiation is "very satisfactory".
Starting with the most general form of Maxwell's macroscopic equations in which the free charge and free current densities, rho_free and J_free, as well as the densities of polarization and magnetization, P and M, are arbitrary functions of space and time, we compare and contrast two versions of the Poynting vector, namely, S=ExB/mu_0 and S=ExH. Here E is the electric field, H the magnetic field, B the magnetic induction, and mu_0 the permeability of free space. We argue that the identification of one or the other of these Poynting vectors with the rate of flow of electromagnetic energy is int…
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just as it postulates the existence and properties of electric charges and currents. Maxwell's macroscopic equations are mathematically exact and self-consistent differential equations that relate the electromagnetic (EM) field to its sources, namely, electric charge-density $ρ_{free}$, electric current-density $J_{free}$, polarization P, and magnetization M. At…
