You ever feel like paleontologists are going to go extinct, like the dinosaurs they hunt for, just because... they found them all?
Short answer, it's physically impossible, but if you could actually get to the speed of light, the universe would end before you could check. Speed of light = infinite time dialation; time of the outside universe would essentially stop and the universe would appear to end quicker than that toy submarine imploded on the way to the Titanic.
Why does everyone in post-apocalyptic TV shows/Movies have clothes that aren't worn out and how does everyone have clothes that fit them perfectly? I'd think that at least that if they were wearing their original pre-doomsday clothes, they'd all be baggy now due to less food.