*** Are We All Nuts? ***

Wow there's a veritable physics lesson going on here, cool lol.

I'll just add that everything hfjacinto said regarding special relativity is based on only 2 assumptions:

1) The speed of light is finite, and the same for any (inertial*) reference frame. Translation: No matter how fast you're moving the speed of light is always constant. So you can never go just a tad slower than c and "see" the light going ahead slightly faster.
2) All physical laws are the same for all observers/inertial reference frames.

Note that invariance of time wasn't an assumption, as Newton had thought! Which gives rise to a lot of interesting phenomena/paradoxes most of which have been verified experimentally.

*inertial just means you're not accelerating = not changing your speed or direction.