On the Faster-Than-Light Motions in Electrodynamics

消除经典电动力学中的无限自能

Eliminating Infinite Self-Energies From Classical Electrodynamics

本文通过假设电磁场张量具有对称部分，消除经典电动力学中点粒子的无限自能问题，同时推导出洛伦兹-亚伯拉罕-狄拉克方程，并探讨广义相对论的关联。

On the stability of uniform motion

We show that the uniform motion of a homogeneous distribution of electric charge can be stable or unstable depending on its geometry. When the electrodynamic body is perturbed from a state of rest, it starts to perform fast oscillations, irrespective of the frequency of the perturbation. This nonlinear oscillation is the result of the feedback interaction between Coulombian and radiative fields. The resulting spontaneous symmetry breaking of the Lorentz group implies that the principle of inertia only holds on average and suggests that the default state of matter is not necessarily uniform mot…

One-Dimensional Central-Force Problem for Sommerfeld Sphere in Classical Electrodynamics: Some Numerical Results

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.

On Radiation Reaction in Classical Electrodynamics

The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that they bare several problems. In particular, almost all solutions are dynamically unstable, and therefore, highly questionable. The question remains whether better equations of motion than LAD can be found to describe the dynamics of charges in the electromagnetic fields. In this paper we present an approach to derive such equations of motions, taking as input the Maxwell equations and a particular …

Stability of Uniform Rectilinear Motion of Charged Shell in Sommerfeld Model with Self-Action

It is proved that in classical electrodynamics the uniform rectilinear motion of charged "rigid" sphere with self-action (Sommerfeld model) is stable.

Electrodynamics of a Worldsheet of Lightlike Current

An equation of motion is derived for a topologically cylindrical worldsheet of lightlike electromagnetic current, embedded in 3+1 dimensions in a smooth external electromagnetic field. Then it is shown that the static circle of uniformly distributed lightlike current solves this equation with the external field replaced by the self-field. From a characterisation of the singular behavior of the field strength near a general worldsheet, it is argued that the worldsheet of lightlike current has a well-defined dynamics. The energy-momentum tensor of the system and the possible coupling of the syst…

Classical Tunneling of Sommerfeld Sphere in Classical Electrodynamics

One-dimensional motion of Sommerfeld sphere in the case of potential barrier is numerically investigated. The effect of classical tunneling is found out - Sommerfeld sphere overcomes the barrier and finds itself in the forbidden, from classical point of view, area.

The basic open question of classical electrodynamics

For the first time a method is devised for non-iterative modeling of motion of a radiating, electrified pointlike mass that has an internal structure. New, supplementary kinetic constants of accelerated charged particles are defined, that can be assessed by analysis of their trajectories in an accelerator.

The Self-Force of a Charged Particle in Classical Electrodynamics with a Cut-off

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.

Classical electrodynamics from the motion of a relativistic fluid

We show that there exists a choice of gauge in which the electromagnetic 4-potential may be written as the difference of two 4-velocity vector fields describing the motion of a two-component space-filling relativistic fluid. Maxwell's equations are satisfied immediately, while the Lorentz force equation follows from the interactions of sources and sinks. The usual electromagnetic quantities then admit new interpretations as functions of the local 4-velocities. Electromagnetic waves are found to be described by oscillations of the underlying medium which can therefore be identified with the `lu…

点电荷在恒定电场作用下沿直线运动的辐射反应问题

Radiation-Reaction on the Straight-Line Motion of a Point Charge accelerated by a constant applied Electric Field in an Electromagnetic Bopp-Landé-Thomas-Podolsky vacuum

本文研究BLTP电动力学中点电荷在恒定电场作用下沿直线运动的辐射反应问题，揭示其在短时间内的物理合理性及长时间行为的非物理性。

On the nonradiating motion of point charges

We investigate the possible existence of nonradiating motions of systems of point charges, according to classical electrodynamics with retarded potentials. We prove that two point particles of arbitrary electric charges cannot move for an infinitely long time within a finite region of space without radiating electromagnetic energy. We show however with an example that nonradiating accelerated motions of systems of point charges do in general exist.

Self force in 2+1 electrodynamics

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…

Classical electrodynamics of point charges

A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once removed without affecting the locality and the relativistic covariance of the theory, and with no need for mass renormalization. The procedure is first used to obtain a finite expression for the electromagnetic energy-momentum of the system. We show that the relativistic Lorentz-Dirac equation can be deduced from the conservation of this electromagnetic ene…