The light from the headlights is travelling at the speed of light anyway, so I would’ve thought that of course you’d see the headlights What you might be meaning is, if a car, for example, was travelling at the speed of light with its headlights on, and if you were an observer stood in front of the car, would you still see the headlights? Again, I don’t see why not. Light travels at around 186,000 miles per second and we always see it under normal conditions. So if the lights are on a vehicle travelling at 186,000 miles per second, then surely we should still see the lights Maybe someone with a physics degree could clarify