A study or proposal was carried out about time travel. Someone in east asia said that it was impossible to go forwards or backwards in time. They brought up that they can't tell if photons can move faster than "c." I read that the closer you move to the speed of "c" the further you'll excel forward in time. My question is that if an object is moving at x m/sec and throws off a beam of light; wouldn't that beam of light be moving at c + the velocity of the oject?
No, the speed of the beam & of light would be equal to c in any case (in vacuum).