Temporal analysis of radiating current densities

TL;DR

This paper mathematically analyzes the time derivatives of current densities emitting electromagnetic waves, explaining light propagation through electric and magnetic field creation, and critiques conventional retarded solutions.

Contribution

It reveals the necessity of infinite differentiability of current densities for wave emission and clarifies the physical basis of electric and magnetic field creation during light propagation.

Findings

Current densities emitting waves must be infinitely differentiable in time.

Electric and magnetic fields are generated through alternate creation during light propagation.

Conventional retarded solutions are inadequate for describing emitted fields.

Abstract

From electromagnetic wave equations, it is first found that, mathematically, any current density that emits an electromagnetic wave into the far-field region has to be differentiable in time infinitely, and that while the odd-order time derivatives of the current density are built in the emitted electric field, the even-order derivatives are built in the emitted magnetic field. With the help of Faraday's law and Ampere's law, light propagation is then explained as a process involving alternate creation of electric and magnetic fields. From this explanation, the preceding mathematical result is demonstrated to be physically sound. It is also explained why the conventional retarded solutions to the wave equations fail to describe the emitted fields.