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Eckard,
I have read arguments both for and against SR.
I agree that it is somewhat problematic to assign the same clock time to all points of single reference frame, because everything seen within the reference frame is in space-time and therefore there is temporal distribution within that observed space-time. The data from furthest objects taking the longest to arrive, the nearest the shortest. So the furthest objects are seen further back in time. However it is modeling the observer perspective. To the observer everything he sees, the reconstructed images of external reality, are apparently existing -at the same time-. This relativity relates to the appearances of the image of reality, reconstructed from received data. Not what actually exists without any transmission delay.IMHO.
I also agree with your point about not having stationary points. In my essay I draw attention to the universal trajectory of the earth and how that trajectory would seem to alter as the scale of observation increases. So the observer who is stationary is only stationary from his perspective. If it is -his perspective- under consideration then he can be rightly regarded as stationary.
The overlap of past and future when each assigns his clock to all he sees in his present is not a such a big problem.This is because past and future are not actual realms but are related to the interception of data from which an image of reality is formed. Data not yet received can be considered to be in the future, data that has already been received and is no longer present experience can be considered the past. Of course how each would regard the data depends on his relative perspective. It is not objectively past, present or future, as its name depends on the observers viewpoint.
I know that this is considered to be happening in a space-time manifold and it is generally thought that concrete objects are distributed in both time and space within it. However it is an explanatory mathematical model which does not say for itself exactly what it represents. I am not convinced Einstein knew exactly what it represents. He seemed to think it was a model concrete reality itself. He and Godel were very troubled by time and spent a lot of time trying to comprehend it.I think it works but only as a representation of image reality formed from received data and not as a model of foundational reality in which change and causality occurs.Curved or flat it is still just space-time.
If you have already got the matter clarified in your own mind then there is little point in me saying any more. I have merely said what I think on the matters raised. As community voting will be closing soon you look likely to be a finalist. I am very glad to see that. Georgina.