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I wouldn't say that's necessarily true, no. It's only true if their speeds are different, the direction they're travelling doesn't factor into it. In either case, their lines of constant time are the same because space is rotationally symmetric. I'm not thinking of them adjusting their calculations to some "true" sense of simultaneous, if that's what you meant in your edit, because there isn't one by definition.
~~That really depends on what you mean by time shift in your original comment. If you mean the shift in what they perceive as simultaneous, then it's not, but it seemed to me that's what you meant.~~ If you mean the difference in their age then I honestly can't remember how it factors in for the accelerating case, I haven't had to think about SR problems in a while.
Consider the Lorentz boost to convert events from Alice’s reference frame to Jane’s. The time of an event (like Bob’s current point in Alice’s frame) will differ in Jane’s by a factor of vx/c^2^ (times the Lorentz factor). Since v (their velocity relative to each other) and x (the distance to Bob) are both nonzero, the times of events in Bob’s history will differ between Alice’s frame and Jane’s. And the time shift is proportional to x, which is why the distance to Bob matters.
Cool yeah, dug through the maths and took the time to understand the situation you were describing and I understand now.
I thought you were describing a something else, and then slightly confused myself by only considering the metric and not the global picture. I was trying to abuse some old heuristic techniques and they don't quite work for this case, though it was fine for what I was picturing, where Jane and Alice are symmetric about Bob.
Thanks for taking the time to convince me.
Actually reading back over this is hilariously dumb, forgive my bad reading comprehension, that is how redshift works.