Aberration and radiation pressure in the Klein and Poincare models

TL;DR

This paper explores how aberration and radiation pressure in hyperbolic geometry models relate to moving mirrors, Doppler shifts, and the angle of parallelism, providing insights into experimental verification of geometric properties.

Contribution

It clarifies the distinction between aberration and radiation pressure in Klein and Poincaré models and proposes using Doppler shifts to experimentally confirm the angle of parallelism.

Findings

Aberration relates to pressure on absorbing surfaces.

Radiation pressure vanishes at the angle of parallelism.

Doppler shifts can experimentally verify hyperbolic geometry properties.

Abstract

Aberration and radiation pressure reflected by a moving mirror are examples of the Klein and Poincar\'e models of hyperbolic geometry, respectively. Reflection at a moving mirror produces a two-way Dopper shift. Its one-way counterpart, aberration, has nothing to do with the radiation pressure on a moving mirror, but, rather with the pressure on a completely absorbing surface. Both pressures vanish when the angle of parallelism is reached. Two-way, second-order Doppler shifts can be used to establish experimentally the existence of an angle of parallelism.