Nothing special would happen, accordingto Newtonian Physics. But this is not actually so. Relativity says otherwise. And the fact is that peculiar things happen even when you are travelling at speeds below light-speed. But these are practically unnoticeable. The faster you travel, the slower your time goes, and the shorter your lengths become, according to an observer standing still. But you on the other hand would see these same efects happen to the observer, because, according to you, the observer is the one who is moving, while you are not.
