Inertial Objects: Acceleration & Direction

[PeterDonis]

on stepping back a moment, it doesn't matter whether we use proper velocity, or coordinate velocity, or whatever

Yes, it does. You continue to ignore the key fact that has already been explained to you several times: any actual observable must depend only on invariant quantities. Your scenario does not disprove this at all; your repeated attempts to show that it does only show that you still don't understand the key fact I just stated. You need to stop trying to convince anyone else of your claims, and take a step back and consider that key fact carefully, and continue doing that until you understand what it means.

At this point I am closing the thread since you are continuing to repeat your errors without responding to the corrections you have been given.