I named this thread "impossible FTL" because I think this is more of a physics question than anything to do with actually going faster than the speed of light. If this thread needs to go someplace else, please move it. This is more of a flight of fancy than anything else. I thought of it for a story, but it's a rather dumb story. So, it won't even be used for that.

In this scenario, two ships are traveling at ridiculous speeds, a high percentage of the speed of light. Let's call them "The Leader" and "The Chaser". The ships have a problem, they are pretty much the same except for the crew. They are accelerating at the same rate, so the gap between the ships cannot be closed. This chase has been going on for a long time and everyone finds it frustrating to be stymied by technology and physics.

The crew of The Leader comes to the conclusion that relativity isn't real and believe they can tap energy from outside the ship (another place, another dimension, magic, whatever.) to accelerate to FTL speeds. They are correct that they can tap that energy, but the ship can't take the acceleration and breaks up. Someone forgot to carry a one or something, I guess.

Would The Chaser momentarily feel a pull from all of that extra energy/mass coming from the other ship?