Your spaceship is traveling at 1/2*c and you approach Bob's spaceship going -1/2*c in the opposite direction. Relative to you, Bob is going the speed of light, and of course he has a giant ticking clock for all to see. From your perspective, Bob's clock looks like it is completely stopped.
1) Can you even see the clock as you approach it? It's coming at you at the same speed light propagates toward you.
2) Do all of Bob's light rays hit you at the same time when Bob passes you so that you would see a long blur/beam of where Bob has been traveling? Could it be more like a big flash because all the photons arrive at the same time, built up like a sound waves before a jet breaks the sound barrier?
3) From Bob's perspective, the light from his clock hit you long ago. Or another way to think about this: say Bob turned on a laser beam pointed at you 10 years before passing you. Bob thinks the laser finally reached you 5 years before you both pass each other. But you still don't see the light until you pass him?! It's tough to wrap my head around this. Idea?
4) Can you see Bob after he passes you? From your perspective, light would have to catch up to him in order to rebound back to you. Perhaps light coming from the side would allow you to see his moving away from you. From Bob's perspective, after you pass him his light will never reach you again because you are traveling away as fast as his light.
5) One step further: if Bob was flying at -2/3*c, is Bob's clock ticking backwards from your perspective? Would you see him pass you before you see him approaching you a mile away?
