Part 1

Abstract

I maintain that light always travels in a straight line from its emission point to its observation point at c (in a vacuum) and the details contained within this thread comply at all times with this basic rule of SR.

There are some misconceptions about with regards to the discrete paths that in transit photons take, after they are emitted from a rotating/orbiting source, until they are captured by an observer. I will initially describe a solution to the relativistic rolling wheel/ring "optical appearance" problem outlined in Øyvind Grøn's PHD paper "Space geometry in rotating reference frames: A historical appraisal" to show how SR has been used to construct a plane of "retarded points in time" to solve the problem. I will then outline how this method/plane can be extended to plot the paths of in transit photons and verify that the method/plane presented is just a direct extension of mainstream SR though. Please also note that there is no mention whatsoever of the word 'orbit' in Øyvind Grøn's paper and SR is not GR.

Modeling relativistic rolling/orbiting wheels/rings in SR

Unfortunately copies of Øyvind Grøn's paper are no longer available without payment (it is a very interesting read). Not only does it provide a compendium of all the various approaches through history, he puts forward a solution (albeit without any methodology/math) to a intriguing problem, Figure 9 part C below. The images below are from the following post on another forum that produced the same solution. http://www.thephysicsforum.com/speci...html#post12704

From Grøn's paper

One thing the paper did not mention is that the length of straight lines drawn from each of the emission points to the camera in the image are equal to the actual distances and path traveled by the photon due to the construction of the plane of retarded points of time. This is because all of the units of the models x and y dimensions (z=0 to remove issues of Born rigidity) can be regarded as time.The positions of points on a rolling ring at retarded points of time were calculated with reference to 0 K by Ø. Grøn [111]. The result is shown in Fig. 9. Part C of the figure shows the “optical appearance” of a rolling ring, i.e. the positions of emission events where the emitted light from all the points arrives at a fixed point of time at the point of contact of the ring with the ground. In other words it is the position of the points when they emitted light that arrives at a camera on the ground just as the ring passes the camera.

Adapting this plane/model to other rotation/orbit applications is made easier when you realise that theobserver/camera is stationary and in the same plane as the rotating/orbiting wheel/ring. I contributed to the solution shown by suggesting that the results should be in emission order to determine if the axle velocity between emission events is consistent.

Part 1 of 3