The first thing I'll have to convince myself of (Aaargh! Shades of Halliday and Resnick!) is that there is a point midway between here and there for which Here and There's velocities are equal and opposite. When I think about two guys running in opposite directions, I don't automatically see that that is true. But I'm sure for galaxies, it is true since you said it, and it's up to me to work out the details.
Also it's very interesting to me that you've mentioned, in effect, the relativity of the time-order of events, which when I first saw the proof, almost destroyed my belief that the universe was a rational place. I mean, can everyone imagine, you can indentify a frame of reference for which John Kennedy died before Lee Harvey Oswald pulled the trigger? And that that frame of reference, and the view of the world you get from it, is as legitimate as our own? In other words, you can mathematically prove that Oswald is innocent!
Physics is truly, truly, a marvel. And I say that without an nanogram of sarcasm, only wonder.
Ah, but in that case, there's a "ether": the sidewalk.
Also it's very interesting to me that you've mentioned, in effect, the relativity of the time-order of events, which when I first saw the proof, almost destroyed my belief that the universe was a rational place. I mean, can everyone imagine, you can indentify a frame of reference for which John Kennedy died before Lee Harvey Oswald pulled the trigger?
No, you can't, because those have a timelike event ordering. (In the case of two "simultaneous" events, the ordering is spacelike. That means that the interval--time difference squared minus space difference squared--is negative; for timelike separation, it's positive.) If there's one thing that the observers all must agree upon, it's causality.