Anything beyond Mars (which they are building a spaceship to travel to) is going to involve some hand-wave... because we don't have it working. Although there is a matter of plausibility. For me the more plausible methods of faster than light travel are teleportation. Not wizard teleportation of course, probably something more complex. Say using gravity (which apparently can out pace light because it doesn't actually travel, not sure) to transmit information about something's physical configuration and then reconstruct it at the destination sight at 0.00001:0.00001 scale.

Still all sorts of problems with it of course, many in areas of study I have only scratched, but it sounds better than just going faster than physics seems to say we can.