von Laue's Theorem and Its Applications

TL;DR

This paper rigorously proves von Laue's theorem and its generalized form, analyzing electromagnetic momentum and energy in electrostatic fields, and introduces a criterion for Lorentz invariance.

Contribution

It provides a detailed proof of von Laue's theorem, extends it to a generalized form, and applies it to analyze electromagnetic fields and invariance criteria.

Findings

Total electromagnetic momentum and energy do not form a Lorentz four-vector.

The generalized von Laue's theorem offers a criterion for Lorentz invariance.

Application to electrostatic fields in different spatial regions.

Abstract

von Laue's theorem, as well as its generalized form, is strictly proved in detail for its sufficient and necessary condition (SNC). This SNC version of Laue's theorem is used to analyze the infinitely extended electrostatic field produced by a charged metal sphere in free space, and the static field confined in a finite region of space. It is shown in general that the total (Abraham = Minkowski) EM momentum and energy for the electrostatic field cannot constitute a Lorentz four-vector. A derivative von Laue's theorem, which provides a criterion for a Lorentz invariant, is also presented.