Lorentz Invariance of Absorption and Extinction Cross Sections of a Uniformly Moving Object

TL;DR

This paper demonstrates that absorption and extinction cross sections of a uniformly moving object are Lorentz invariant, while scattering cross sections are not, with detailed analysis and calculations for a sphere at relativistic speeds.

Contribution

It provides a detailed analysis of how Lorentz invariance applies to absorption, extinction, and scattering cross sections of moving objects, highlighting differences for non-co-moving observers.

Findings

Absorption and extinction cross sections are Lorentz invariant.

Scattering cross section is not Lorentz invariant.

All cross sections approach zero as the object recedes at speeds near c.

Abstract

The energy absorption and energy extinction cross sections of an object in uniform translational motion in free space are Lorentz invariant, but the total energy scattering cross section is not. Indeed, the forward-scattering theorem holds true for co-moving observers but not for other inertial observers. If a pulsed plane wave with finite energy density is incident upon an object, the energies scattered, absorbed, and removed from the incident signal by the object are finite. The difference between the energy extinction cross section and the sum of the total energy scattering and energy absorption cross sections for a non-co-moving inertial observer can be either negative or positive, depending on the object's velocity, shape, size, and composition. Calculations for a uniformly translating, solid, homogeneous sphere show that all three cross sections go to zero as the sphere recedes directly from the source of the incident signal at speeds approaching c, whether the material is a plasmonic metal (e.g., silver) or simply a dissipative dielectric material (e.g., silicon carbide).