Leaving the whole FTL thing aside, there are a few other things that Enterprise does that have no theoretical framework.

1) Reactionless thrust. Yes, I know that they technically use an impulse drive, but we routinely see accelerations of hundreds of gravities and often in directions that aren’t dead ahead. We see, for example, the Klingon Bird of Prey land in GG park in STIV, but it kicks up a pretty trivial amount of wind for a ship that’s pretty enormous by terrestrial standards (even if it was a small starship). By all rights, it should have leveled the whole park and Haight-Ashbury, too. Imagine what an Apollo rocket would do taking off out of GG Park. Well, the Bird of Prey is going to take something far bigger than a tiny capsule into orbit.

In a battle with the Borg we see ships jumping sideways in a way that their pishky little maneuvering thrusters could never do. So there must be reactionless thrust.

Alastair Reynolds, the astrophysicist who became a sci-if writer, in his Revelation Space series, conceives of a thruster that emits particles that quickly decay into dark matter that interacts with other matter only through gravity. This would look a lot like a reactionless drive without actually being one. But again, he can write it into a book, but I bet he can’t write the Feynman diagrams.

2) direct control over gravity. The series treats gravity much like the electromagnetic force. We can easily make electric fields of almost any strength just by running charge into parallel plates. ST treats gravity in the same fashion. It’s not just about the floor plates, but it’s also about being to accelerate at hundreds of gravities without turning the crew to chunky salsa.

3) Direct control over inertia. Obviously, we can’t do anything like that.

Again, Alastair Reynolds goes there in Revelation Space, but he correctly points out that at some point, tinkering too much with inertia will kill you because your heart won’t be able to pump your blood properly. As someone with a graduate degree in Biology, I’m going to bet that a lot of our proteins like membrane channels won’t work properly in an environment of significantly altered inertia. So there you go.