If relativity holds, than faster-than-light travel would allow for time travel into the past. However, some claim that if all FTL travel used only one frame of reference, there could be no temporal paradoxes such as going into your own past and preventing the journey from happening in the first place. This is an interesting solution because I don't want time travel in my universe. However, I want to know whether some kind of "jump" travel can be made logically consistent with our physics.
I'm not the most experienced with physics, but some potential problems I've seen so far are:
Quantum field theory has problems with any fields that allow for faster-than-light particles (as a discussion in the comments in the first answer to the first question notes)
Conservation of energy, linear momentum, and angular momentum (Jason W. Hinson makes an argument that angular momentum, in particular, cannot be conserved with this kind of travel, would Noether's theorem mean in that case rotational invariance does not hold, and would that cause big problems?)
Is travelling in one preferred frame even possible?
There may be other problems I do not know about. What I want to know is not whether this "jump drive" is possible in our actual universe(it probably is not) but whether these problems can be overcome and a mathematically consistent set of rules created that allows for a universe with this faster-than-light travel while preventing temporal paradoxes and allowing for most phenomena to be similar to our universe(with stars, planets, life, and so on).
Edit: This question may seem similar to the one in the first link, but the difference is there seem to be some problems with the answers listed there that I have so far not found solutions to. What I want now is either information on how to get around these problems or an explanation of why no consistent set of rules can be created to do that.