Another relativity question

Factual Questions
1

One of the main features of Special Relativity is that no signal can travel faster than light. To demonstrate this, most works on the subject use “world line” diagrams (did I get that right?) that show that if a signal goes between two points faster than light, then it’s possible to have a frame of reference where that signal goes backwards in time, which is a big no-no.

However, every such diagram I’ve ever seen shows the source and observer of that signal in relative motion. I can understand that if two observers are in relative motion, then they can disagree on whether two events are simultaneous or not. This would set a limit on how fast information could travel between them without having a signal go backwards in time. But I don’t see how to create such a paradoxical reference frame between two observers who are in zero relative motion to each other. As far as I can see, if they are in the same reference frame then information could travel between them at infinite speed.

You could invoke a third observer in motion relative to the first two. But that only creates a paradox if it can “see” the world line of the signal moving between the first two. If you presumed that any attempt to intercept the signal midway destroyed the information, like in quantum theory, then I don’t see where an backwards-in-time reference frame could arise. (Inspired by the proposed light theory post which hypothesizes that light doesn’t really “exist” between it’s source and destination.)

2

This is correct. In one reference frame, you could have instantaneous communication without causality paradoxes. The implication of having instaneous communication is that either that reference frame is special, or causality is broken.

If there is nothing special about that reference frame, then two other observers in zero relative motion, but in relative motion to the first pair, could perform the same instantaneous communication in their frame of reference. This is what would allow communication back in time.

If the second pair can’t have instantaneous communication, then there is something special about the first frame of reference. It would be a preferred frame of reference, the only one where instaneous communication is possible. If you assume that observers in relative motion to the preferred frame could still attempt instaneous communication, but that it would be instaneous in the preferred frame rather than theirs, then by careful measuremnts, the second pair could determine their absolute velocity with respect to the preferred frame.

So, in short, instaneous communication breaks something, but not necessarily causality.