Suppose you and I have a conversation from a long distance away. We're at rest with respect to each other and communicate much faster than light. I say "How are you", and you wait a short time and say, "I'm fine thanks."
From our point of view, you were responding to my question. However, from a reference frame moving from me to you at relativistic speed, your clock is significantly ahead of mine (a relativistic effect). This means that although you thought you received the message shortly after I sent it, in this frame you didn't. You actually received the message at an earlier time (before I sent it), but you thought it was later because your clock is ahead.
From your and my point of view, the order of events is
- I say "How are you?"
- You hear me say "How are you?"
- You pause a short time.
- You say, "I'm fine thanks."
- I hear you say, "I'm fine thanks."
From the frame moving from me to you, the order of events is
- You hear me say "How are you?"
- You pause a short time.
- You say "I'm fine thanks."
- I say, "How are you?"
- I hear you say, "I'm fine thanks."
The fact that the order of events changes between reference frames is simply part of relativity, with or without faster-than-light communication. However, it seems strange in this scenario because you are responding to me. Presumably, if I had said, "Where are my car keys?", you would have chosen a different response than "I'm fine thanks." How then is it possible that you responded to my greeting before I uttered it, at least in some frame?
I'm not sure if this "violates causality", but it's unintuitive.
The difference is that in the case of wormholes, it is not certain that closed timelike curves (and thus violations of causality) actually occur, and if they occur, in which form. There are different approaches to the issue, for an interesting read (which also treats other kinds of spacetimes that potentially violate causality), see this. The general idea is that causality violations might be suppressed by quantum effects.
Best Answer
In some reference frames, your friend guesses the information and acts before you send it and in others, he guesses and acts after you send it.
But there is no causality problem since his action is caused by his guess rather than the received information.
In all reference frames, the guess precedes the action.
Now consider the actual effect of receiving the information. Perhaps a tone is sounded or a light is activated.
If the information propagates faster than $c$ from the transmitter to the receiver in some frames of reference, there are other frames of reference in which the event that the tone is sounded occurs before the event the information is transmitted, i.e., the cause and effect are reversed.
This is clear if you draw a spacetime diagram of two events, E1 and E2, with spacelike interval and note that, in some reference frames, t(E1) < t(E2) and, in others, t'(E2) < t'(E1).