Indeed. Then Alice would never return from a realm in which logical contradiction, fantasy, limitless imagination without foundation, and the absence of common sense reigned supreme. That seems to be the realm which much of modern theoretical, so-called, "physics" is stuck in, eh, AG?
It could be argued that their feet 'are not firmly anchored on the ground' Moronium.
BTW I received no response from another anti SR thread when I responded with a SR based methodology to replicate Ovyind Gron's Figure 9 Part C 'optical appearance' solution to a relativistically rolling ring problem.
Maybe you would like to explain how you would solve the problem of determining the emission times of 16 equally distanced points around the circumference of a relativistically rolling ring so that the photons emitted from each point all reached a camera/observer at a fixed point on the road the ring is traveling along, at the same time?
The following solution (red points labelled 1 to 16 above) was developed on another forum (link at the bottom) and it only uses x, y and t dimensions as the z axis = 0 to prevent distortion due to Born rigidity issues that is not a concern to this problem. I wasn't entirely 100% convinced that the solution was correct so I asked the 2 guys who developed it (after many many attempts and dead ends) to order the results in emission order so that any variations in the relativistic velocity could be identified. The following image shows that the axle velocity does not vary and is also consistent with the angular velocity of each emission point as the ring rolls along.
Just so you don't try to reinvent the wheel again (no pun intended) I will describe the basic SR method used below.
Several frames are used, a wheel frame, an axle frame and a road frame where the camera/observer sits. The emission points along the circumference of the wheel and the camera observer are all in the plane of rotation of the ring and the respective emission points are plotted in this plane (this plane does not actually exist as a 'frame' as such due to z = 0. This plane could actually be regarded as an SR time space as opposed to a variable GR space time). On this plane a straight line drawn from any of the emission points to the camera/observer represents the actual distance/time and path traveled by any photon emitted from an emission point, that all arrive at the camera/observer at the same time.
The solution is relatively simple once you realize that the x and y readings at each emission point on the time space plane form a right angled triangle with the stationary camera/observer and the photon travel time/distance from the emission point is the hypotenuse of that triangle (of height y and length x, x and y being the location of the emission point). The emission point is back calculated from the length contracted location of the tip of a spoke (the emission point is on the rings circumference at the end of the spoke) with respect to the axle location at the time of emission. This relationship between the emission point and the axle location allows you to further cross check the rings constant velocity i.e. the differences between the x positions of the axle at the photon emission times give you the velocity of the axle between emission points.
Please note that if you also apply time dilation to the process identified above you just put yourself back in 'wonderland' with respect to c being a constant in the time space plane used. If you search for Ovyind Gron's latest papers you will find that he has applied his work extensively to atomic models because things like QM have difficulties with accurate times and locations of things on atomic scales.
I also realize that, as well as atomic scales, the SR based solution methodology above can be applied on galactic scales as well when an observer/camera is in the same plane of rotation of a series of objects rotating around a common center of mass. i.e. a side on galaxy. It is a trivial exercise to extend this 'side on' galactic model (that represents maximum shift) to a basic 'front on' galactic model (that represents minimal shift) where all photons emitted at the same time from points all around the circumference of a rotating ring will arrive at the relatively stationary camera/observer at the same time if their photon paths are not blocked or distorted along the way.
So, in these 2 basic models and everywhere in between, the angle of the camera/observer to the plane of rotation of the rotating sources is the main determinant of the amount of shift of the emitted photons received by a camera/observer at rest relative to the center of mass of rotating sources. The only other trivial part required to create a general SR based galactic 'optical appearance' model is to factor in the relative motion of the center of mass of the galaxy with respect to the stationary camera/observer.
Edited by LaurieAG, 29 March 2019 - 10:52 PM.