# FTL communication and paradoxes with local causality

I have Yet Another Question about FTL communication, causality and sending a message into your past. I've read this article and this excellent answer and I understand why it's possible to find a reference frame from which a given effect may appear to precede its cause. However, I haven't been able to make the mental leap from that to being able to meaningfully send information backwards in time.

Here's where the article ends:

As you can see, the light from the phone call reception arrives well before the light from the placing of the phone call. Again: causality is violated. ...

If you could travel or communicate FTL, you can time travel, or at least communicate backwards in time. And that would be troubling - and doesn't seem to be the Universe we live in.

Assume that FTL communication has some constant non-zero travel time associated with it - it's not instantaneous (i.e. $$1s / LY$$). An observer $$O$$ traveling at relativistic speeds will see the phone call from $$A$$ to $$B$$ arrive at $$B$$ before they see the call being made. But even if they were told of its arrival at FTL speeds, by the time they could turn around and send a message to $$A$$ and have it arrive, it's too late for $$A$$ to act on it.

So from the perspective of $$O$$, they may be sending "Don't call $$B$$" message back into $$A$$'s past, trying to create a paradox, but it won't arrive in $$A$$'s past, from $$A$$'s perspective, and thus no paradox. Even from $$O$$'s perspective, they will observe $$A$$ placing the original call before they observe $$A$$ receiving their "don't call" message - it just might not happen until after $$A$$ sends a FTL message back saying "why did you say that?"

From a fourth perspective ($$O'$$), the "Don't call $$B$$" message may arrive before $$O$$ sends it (even if the notice from $$B$$ to $$O$$ hasn't happened for $$O'$$ yet), but in that frame they would still see it arrive after $$A$$ makes the original call.

Put another way: as best as I can understand it, it may be possible to observe a causality violation, but there is no way to meaningfully affect it, and there is no way to cause one to appear in your reference frame.

What am I missing that leads to an actual paradox, or taking advantage of the causality violation in any way?

• FWIW, I've also tried to read the Wikipedia article on the tachyonic antitelephone, but I can't follow it well enough to know what I'm missing. – Bobson Apr 23 at 6:56