Classical Electrodynamics in Terms of Direct Interparticle Action

Advanced action in classical electrodynamics

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 argument that clarifies the origin and physical meaning of these advanced effects, and we compare ordinary electrodynamics with a toy model of el...

Classical Electrodynamics

Inconsistency in Classical Electrodynamics

I show that the standard approach to modeling phenomena involving microscopic classical electrodynamics is mathematically inconsistent. I argue that there is no conceptually unproblematic and consistent theory covering the same phenomena to which this inconsistent theory can be thought of as an approximation; and I propose a set of conditions for the acceptability of inconsistent theories. 1. I...

Quantum-classical crossover in electrodynamics

A classical field theory is proposed for the electric current and the electromagnetic field interpolating between microscopic and macroscopic domains. It represents a generalization of the density functional for the dynamics of the current and the electromagnetic field in the quantum side of the crossover and reproduces standard classical electrodynamics on the other side. The effective action ...

Instantaneous fields in classical electrodynamics

– In this paper we express the retarded fields of Maxwell’s theory in terms of the instantaneous fields of a Galilei-invariant electromagnetic and we find the vector function χL whose spatial and temporal derivatives transform the Euclidean fields into the retarded ones. We conclude that the instantaneous fields can formally be introduced as unphysical objects into classical electrodynamics whi...