Couple of questions as to how to interpret the Minkowski diagram when it comes to intergalactic space. 1) To begin, I'll make some pre-assumptions to the question, which you may correct if I'm wrong: 1a) Within any given galaxy, the distances between it's constituent stars is roughly equal over time due to the gravitational well holding the galaxy together. Thus, for the most part, we can have some sense of an absolute or stable sense of space and distance between objects within a given galaxy (or galaxy cluster). 1b) Between any two given galaxies, the distance between the galaxies and, hence, the distances between the constituent stars in the galaxies, increases over time, and increases at a rate proportional to the distance between the galaxies. 2) My supposition based on these pre-assumptions is that the Minkowski diagram/metric only holds true for the first condition (1a). Why? Say I'm Bob sitting in galaxy A, and I send Alice off through the galaxy by applying some force to her. Well, I'm confident that, in this instance I'm bound by the Minkowski metric and I can't send her off at a velocity that is going to exceed the speed of light. In fact, when I look at the Minkowski diagram, I see that the hyperbolic lines of constant time asymptote at the null, or light cone, lines and there's NO WAY I can send her off faster than the speed of light. I'm trying pretty hard to send her off as fast as I can, and I've sent her away from me at 99.999c, but I just can't seem to get her going any faster. That is, until I reach the end of the galaxy. Once she shoots into intergalactic space, she's now got the "tailwind" of the scale factor to push her over c. So that means that once my beloved Alice is some way into intergalacitc space, I will see her as moving away from me at faster than the speed of light? Where am I wrong here? 3) Relativistic velocity addition--I'm still sitting here in galaxy A, and my girl Alice is now hanging out in galaxy Y pretty close to the cosmic horizon. In fact, the galaxy she's sitting in is traveling away from me at .7c. Just for fun, I tell her to throw a baseball across her galaxy in the same direction she is travelling away from me, at .5c. So what happens now? Can we really believe that relativistic velocity addition here is going to "add up" when we have this scale factor thing to contend with? What is my observation of the speed of the baseball going to be? 4) Considering the above argument, my real question is it seems to me that the Minkowski diagram only applies to "intra" galactic processes. Do we have an equivalent diagram for "inter" galactic processes? For example, the current theory is that there are, in fact, galaxies receding from us at faster than c beyond the cosmic horizon. Considering such, the traditional Minkowski diagram breaks down because, obviously, a (massive) galaxy receding from us at 1.25c is not going to fit into a traditional Minkowski diagram framework. 5) What is the equivalent diagram we deal with here for intergalactic processes? My first guess is that it would a FRW-related thing, but the FRW is not a metric-related equation that is designed to warp the shape of the light cone in the same way that the Schwarzschild solution to GR field equations provide a modification of the flat space metric. Is it? That is, the Schwarzschild solution modifies the flat space metric by changing the unity constant placed before the variables "t" and "x" in the equation (tau)^2 = (1) t^2 - (1) x^2 with (tau)^2 = (function) t^2 - (function) x^2. I like the Minkowski diagram. I think it tells us a lot about space and time locally, and we like to get all fancy about it because it adds to the SR component of the GPS system and the atomic clock thing on the airplane experiment. But does it work "universally" for interactions between objects in intergalactic space? Or does it break down there in some inexplicable way? Or does it break down in an explicable way where we can use some sort of "modified" Minkowski diagram in order to model these interactions?