I really like sci fi settings where there is one major leap of physics that has ramifications across the rest of the setting.
Mass Effect is my prime example with the discovery of mass effect fields that allow the manipulation of how much mass things have. This is the basis for local interstellar travel after using a mass relay, as the mass of the ship is reduced for acceleration greater than the speed of light. Artificial gravity is created by increasing the mass of the floor. Guns work by electromagnetically accelerating bullets through a reduced mass field for greater acceleration, while shields work by emitting repulsive mass effect fields.
In The Expanse, the only technological breakthrough that doesn’t feel like a natural extension of modern technology is the Epstein Drive. The only thing it does is make propulsion engines fuel efficient enough that they can burn nonstop between destinations, which allows a ship to constantly accelerate to its destination instead of reaching a maximum velocity then floating the rest of the way there. It cuts down travel times between planets from months/years to weeks, and allows the society presented to exist.








In my own made up worlds I often imagine FTL works by moving between the 2nd and 3rd dimensions. 3D is “flattened” in such a way that point A (where you start) and point B (where you want to be) are at the same point of the now 2D universe. During the transition back to 3D, points A and B go back to their original positions, but you are now at point B.