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.
Darn it, I can't remember the proof. And I've been thinking about it all weekend. I used to be able to reproduce it at the drop of a hat. It was quite simple, not unlike the proof of the time dilation equation in special relativity that's taught to every high-school physics student: i.e., you start with a boxcar traveling near c, and observers inside and outside of the boxcar. But I can't remember the trick for changing it from a proof involving t1 and t2 for the two observers to a proof involving the observed order of events. Of course, there is always the possibility I completely misunderstood the implications of the proof. But I doubt it since it was just high-school algebra. Anyway, if I ever remember it I'll post it and let you rip it apart. :-)
(There were some restrictions. I do remember that. Thanks again for even talking to me about this.)
Therefore, the man inside the boxcar will observe the light beams strike opposite ends of the car at different times; namely, he'll see the the westbound beam arrive at the end of the boxcar about a nanosecond after the eastbound beam. The eastbound beam wins.
But for a man outside the boxcar the "order" of these two events is reversed, depending, of course, on how fast the boxcar is going. In other words, the westbound beam can win.
The time order of these events is relative to who is doing the observing.
Physicist, I know your time is valuable, and I do not want you to waste a second of it on this if you don't want to. I just wanted to tell you of the so-called "proof." I know you've mentioned a "time like ordering" and a "space like ordering" and I think I've got to think about that some more. Plus I've found a long article that I think will help me figure out where my own train has jumped the tracks. :-)