You're in your pimped out rocket ship traveling at the speed of light, and get too far from the sun so it gets pretty dark. You decide to turn on your headlights. Does the light go twice the speed of light or does it pool up around your headlights?
No. If you are moving at the speed of light you become light, so this scenario is not possible. But if it somehow was possible, the speed of light would not increase 2 fold. Due to the nature of light, no matter what speed your are traveling, the speed of light will remain constant. Like if you are driving your car 60 km/hr with the headlights on, the lights in your headlights aren't moving the speed of light (3.0x10^8 m/sec) plus the 60 km/hr your driving, they are just moving the speed of light.
At the speed of light you would be not moving physically inside you ship so you could never turn on the headlights. If you were just below the speed of light you would see beams going forward normally. An outside observer near the rear of the ship would see beams severely red shifted. An observer in front of the ship would see beams severely blue shifted
When you want to discuss the light velocity. It has two values. The phase velocity and group velocity. The group velocity that is the velocity of the information carried. Phase velocity can be any where between 0 and infinity. But the group velocity will be always less than c. In vacuum both velocities are the same. We need to distinguish these two velocites.
Nope, neither of those things. Light has one speed, the speed of light regardless of the reference frame or what it's doing. So if you're going almost light speed U = kC < C and shine a head light V = C, the total speed of that headlight when observed from a static reference frame is W = (U + V)/(1 + UV/C^2) = (k + 1)C/(1 + kCC/C^2) = C. The speed of light, that's all. QED. How's that happen? Space and time adjust to keep the speed of light at and only at C...period. That's one of the basic findings that led to the special theory of relativity in 1905.
