I don't deal with 4-vectors on a regular basis, and haven't taught the Modern section in quite a while. SO...be gentle. I'm trying to understand this.
JD said:" What we care about is the coordinate system. Moe himself is moving toward the future at the rate of 60 minutes per hour, in accordance with answer (B), but his coordinate system is not. In particular the contours of constant time in his coordinate system are not moving, and those are what we normally use to measure spacetime positions, velocities, et cetera."
Does this mean that there are continually "new" coordinate systems that are instantaneous with Moe, but that we have chosen a coordinate system at a fixed space-time point with which to measure all other space-time action? I haven't thought of coordinate systems in this way, at least not recently (maybe I did while as a grad student in survey class of GR). I've always thought of Moe actually BEING the coordinate system so that the answer to (B) would be (0,0,0,0). But if "the contours of constant time ... not moving," is it really "his coordinate system?" Isn't it a coordinate system that we chose at a single time which has no special velocity relative to him? And what is a real problem in which this makes a difference in what we would measure? Not playing devil's advocate here; really looking to understand the nuances of this 4-vector coordinate system definition.