New Discoveries

Sure. A faster than light drive presupposes a new paradigm but that is not why sf writers deploy FTL drives. Usually, they are just exploiting a convenient cliche to move their characters around on an otherwise impossible galactic scale. 

It is impossible to predict a new theory. If an author, pre-Einstein, had written that there was going to be a new theory called "relativity," then he would have predicted the name but not the content of that theory whereas, if he had stated the content, then he would have made, not predicted, the theory. An sf writer can convey the sense of discovery but can only guess at what new discoveries there might be. In James Blish's The Quincunx Of Time, his characters receive messages from many future periods with mutually incompatible and incomprehensible paradigms.

Poul Anderson conveys the sense of new discoveries in his fictional introduction to "The Three-Cornered Wheel" where someone called Vance Hall points out that it had been thought:

that power could not be extracted from atomic nuclei until uranium fission was discovered;

that energy projectors/ray guns were impractical until lasers were invented;

that accelerating spaceships must expel mass until artificial gravity fields were generated;

that light speed could not be surpassed until the quantum hyperjump was found.

Thus, Anderson does make anti-gravity and FTL seem like up-coming stages in a current process. 

He presents several distinct FTL scenarios, e.g.:

the quantum hyperdrive in the Technic History, of course;

the superlight drive and civilization clusters in After Doomsday;

the interstellar and intergalactic space jump in World Without Stars.