The largest particle collider we have access to isn't the LHC, its the atmosphere, and we've seen a significant number of collisions that suggest the particles that caused them moved faster than should be possible. So fast and close to the speed of light, that the mostly empty void of space should slow them down(call it friction, if you feel like that term is appropriate for a subatomic scale.)
Even if Superluminal speed was possible, you'd eventually have to stop using it, as you'd be travelling increasingly further backwards in time, until you'd reach all the way back to before the universe was cold enough to allow for deionisation, turning you any everything else into plasma.