Lorentz-transformation and Galileo-transformation windows

Abstract

We define Lorentz-transformation windows as windows that change the direction of transmitted light rays like a Lorentz transformation. Similarly, Galileo-transformation windows change the direction of transmitted light rays like a Galileo transformation. This light-ray-direction change distorts the scene seen through such a window in the same way in which the scene would be distorted in a photo taken with a camera moving through the scene. Lorentz-transformation windows can also undo the distortion of the scene when moving at relativistic velocity relative to it. For small angles between the direction of the light rays and the direction of the velocity, Galileo-transformation windows can be realised with relatively simple telescope windows, which consist of arrays of identical micro-telescopes.