Quoted: So, if a hypothetical vehicle traveling at the speed of light turns on the headlights will it exceed the speed of the light and never illuminate the front of the vehicle?
or
If two spacemen are using a vehicle that can travel at .9999999 of the speed of light and are traveling away from each other and they both turn on their headlights at the same time to illuminate the other will either of them ever see the other's headlights?
or
If two spacemen are traveling at .9995 of the speed of light and travel near a black hole will they be able to transmit images back to Earth?
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At those speeds the rules change.
As an example, if you were traveling toward someone on the ground at near light speed and shined a light toward them, the light would not hit them at almost double light speed. It would hit them at light speed, even though to the person traveling, the light would be traveling away from them at light speed. Logic says that the light should then be traveling the person's speed plus light speed, but it doesn't. The reason that this makes sense is that time is warped.
The observer on the ground would see the light from the traveler extremely blue-shifted, and even though the person was coming toward them at near light speed, the person would appear to be almost stationary.
To the person traveling at near light speed, he would observe time on the ground traveling very fast, and light coming from the ground would be extremely red-shifted.
I think I got all that right. If I didn't hopefully someone can correct it.