Can FTL communication avoid causality paradoxes with a preferred reference frame?

[Ich]

As far as I understand, FTL communication (or instantaneous communication) is impossible because one cannot define what "instantaneous" means, so you run into problems.
What if there were some kind of sub-/hyperspace with an absolutlely defined time and instantaneous messaging? Do the paradoxes still arise when communication is happening always instantaneous wrt this hypothetic preferred frame?
Does such a possibility violate some known laws of physics, or is it just that there is absolutely no evidence for it?

 

[Nugatory]

As far as I understand, FTL communication (or instantaneous communication) is impossible because one cannot define what "instantaneous" means, so you run into problems.

That's not quite right. The problem is that...

What if there were some kind of sub-/hyperspace with an absolutlely defined time and instantaneous messaging? Do the paradoxes still arise when communication is happening always instantaneous wrt this hypothetic preferred frame?
Does such a possibility violate some known laws of physics, or is it just that there is absolutely no evidence for it?

The problem lies with relationship between the events "message sent" and "message received". If the message arrives before a light signal could have made it from sender to receiver, then there will be some observer for whom the receive event happens before the sending event - and this observer will be able to prevent the message from being sent. For example, they could wait until the message is received and then destroy the transmitter before the message is sent (Google for "tachyonic antitelephone" to see how this might be done).

This contradiction is inherent in the relationship between the sending event and the receiving event, so we cannot make the contradiction go away just by choosing some more clever way of delivering the message - no matter how it is sent, if it arrives before a flash of light would, we are stuck.
The technical term for events related in this way is "spacelike-separated"; events that are always ordered with causes happening before effects are said to be "timelike-separated". Googling for those terms will bring up a flood of good writeups.