I'll be the first to admit that I don't know jack about relativity, so this might come across as a bit ignorant but "if you move faster than an arbitery set of light particles, you travel through time" sounds a bit silly.
I mean, if someone flies in that direction on sub-light for six days and I catch up in ten minutes using FTL, that doesn't mean I travelled through time. It's no different than catching up with someone who walked away by jogging. I got where they are faster than they did by moving at greater speeds.
Talking about perception or frames of reference... I'm pretty sure physics work exactly the same regardless of whether you're looking at them or not. Assuming that the universe stops doing something when you stop paying attention to it sounds like a child's sort of logic, where people can't see you if you cover your eyes.
The world around you doesn't give a fuck if you're looking or not. It's doing it's thing and it's going to continue to do so.
In a comic-book world, however, that shit doesn't fly at all. "Goes fast" is a cosmic force and time-travel is explicitly a part of it's gimmick.