aberration and radiation pressure in the Klein and Poincare' models

lavenda, bernard (2009) 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, one-way
Doppler shift, and Poincare', two-way Doppler shift, disc models of hyperbolic geometry, respectively.
Aberration, like the Thomas precession, is related to the angular defect, and is a kinematical eect
rather than relativistic. At the angle of parallelism, determined by a stationary observer looking
at a moving object in the direction normal to its motion, the rotation of the object is related to
its Lorentz contraction that an observer sees traveling at the same speed as the object. The origin
of the Lorentz contraction is the angular defect, while the angle of parallelism is an asymptotic
limit, providing the unique link between circular and hyperbolic functions. The relative velocity
provides an upper limit on the angle of incidence with the radiation pressure vanishing at the angle
of parallelism. Two-way, second-order Doppler shifts can be used to establish experimentally the
existence of an angle of parallelism.