Aberration and radiation pressure in the Klein and Poincare models

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.