The appearance of the objects rolling at relativistic speeds

Abstract

In the late 1950s Terrell and Penrose produced a series of papers dealing with the appearance of the rapidly moving bodies while in rectilinear motion as photographed by a simple, pinhole camera. A few more articles on the same subject followed, for example, Penrose showed that a sphere is always seen having an exactly circular outline, at any velocity, at any distance and for any line of sight. In the present paper, we will deal with a more complex type of motion, the combination of translation and rotation that can be seen when observing the wheels of a vehicle passing by. Since Terrell and Penrose wrote their papers, great advances in the camera simulation via computer representation have been made. The field that deals with the simulation of realistic cameras via computers is called ray tracing. In the current paper, we will combine two different disciplines, relativistic physics and three-dimensional graphics to derive new results. Our paper is divided in two main parts, in the first half, we will derive the relativistic equations for rolling motion without slip and we will make some connections with the physical requirements of a relativistic ray-tracing algorithm. In the second half, we will review the foundations of classical ray-tracing algorithms and we will introduce the additional features for operation at relativistic speeds. We will demonstrate an interesting self-canceling effect of the relativistic Doppler shift on the colors wavelengths of the moving object.PACS No.: 03.30.+p