I figure I'm going to get ridiculed for this question, and maybe deservedly so. The sensor images and eyewitness accounts from the Naval Aviators released last year of unexplained aerial phenomena support a claim that the craft maneuvered in a way that 'defied physics.' After observing the imagery it appears that 'defied physics' means that the craft can make changes in trajectory that are impossible unless they found a way to 'zero' out their momentum, and make instant changes in direction and velocity. For the sake of argument, if they could do this, could they travel faster than light?
The standard physics answers are that there is no way to cancel out your momentum and no reasonable way to travel faster than light.
I would expect either that the observers are mistaken in what they saw, or there is an mundane explanation. But without better information, it is hard to say. I wouldn't take explanations such as aliens, particularly aliens with physics that contradicts known laws, seriously without some evidence that they exist. Seeing something that we cannot explain is just evidence that we don't understand what is going on. It is a far stretch to say that something impossible must be going on.
I won't ridicule you for your question - you are obviously trying to find out a sensible explanation. Nor down vote. But sorry, I don't have answers along the lines of what you have been hearing. There are good reasons to be skeptical. People have looked for ways to travel faster than light.
For example, Alcubierre drives are a theoretical way to do it. But they are really just mathematical games. They are a solution to Einstein's field equations that exhibit faster than light travel. To build one would require matter with negative mass. There is no reason to suppose such matter exists and good reasons to suppose it doesn't. Loosely, if you give me antigravity, I will give you faster than light travel.