I'm a non-physicist so pls pardon this dumb question. (Maybe one of you high school physics teachers could use this to puzzle your students?)
Say we're at big hard pan desert. A referee fires a gun and two cars on either side of him take off in opposite directions, each reaching a speed of 80mph. Relative to the man, they are both going 80mph away from him. But when the two cars look back toward each other, they can easily see (or measure by sonar) the other car receding at 160mph.
Now say we're at some point in outer space and, when the referee gives the signal, two star ships start off in opposite directions, each reaching a speed of 80% of the speed of light (.8c). Now, the referee can see (using the red shift I guess) both ships receding at this speed. But what happens when the ships look back toward each other? Presumably they can't be receding from each other at 1.6c (.8c+.8c). If they shine a light beam back toward each other, could the crew on each ship ever even see the light beam from the other ship? It is really hard for me to conceive this situation. I know that the ships can not be exceeding light speed even relative to each other, and I guess this fact must somehow be reconciled by time, although I can't conceive exactly how.
On another point, I've never been able to comprehend cosmologists when they say the Big Bang never originated in a certain point in space. Maybe it is the word "bang," which implies an explosion, and indeed they say the entire universe was condensed into a space smaller than an atom, right? I don't understand how you can have an explosion which does not originate in a specific point in space.
