Spacetime Diagrams (these things) are really great tools to show how FTL travel or communication necessarily implies a break in causality (like so). That's obviously a problem for FTL.

However, if you have two parallel worldlines, instantaneous travel doesn't actually have the potential to break causality as near as I can tell, at least according to those same worldlines. There's only a problem if there is a line which isn't parallel.

So my question is, is there anything I've missed here? Causally speaking, is there anything stopping FTL travel from being possible only between objects that are relatively stationary? As in, instead of ruling out the FTL travel itself, you instead rule out FTL travel to objects which are not relatively stationary. Is there something else that breaks causality here?

And actually it's probably more complicated than that, as I'm only looking at instantaneous travel. Perhaps you could go at a "slower" pace, but still FTL between points that are moving relative to one another and still not break causality? You just have to be going at a low enough speed to avoid breaking causality--which is not necessarily the speed of light.

Not suggesting how this would be possible in practice, just the causal implications. Thinking of ways FTL travel could avoid time travel/breaking causality for some observers/actors.