First off, the car is traveling *faster* than the speed of light. Second, the theory of relativity states that the headlights are in your reference frame (if you are in the car). Think of it this way. If you’re on a train and you jump up and you’re no longer anchored to the train, do you end up a few feet back by the time you land because the train is going faster than you? You don’t, because you’re still in the reference frame of the train. Same for the theoretical headlights. There’s a classical physics demo where the prof shoots a ball straight up out of a model train. The ball maintains its speed along the x/y axis, which was the speed of the train and whatever acceleration it gained along the z axis from the propellant that launched it in the air. It will maintain all of that unless a force acts on it. In this case, the force is gravity, so you go up, decelerate, stop, come down. If no other force acts on the ball, the speed along the x/y axis remains the same and the ball will trace out a parabola and end exactly where it started from (same for you from the reference frame of an observer because from your reference frame, you just go up and then back down). Anyway, the headlights. They’ll go out in front of the car for the same reasons. Unless you’re an observer, and then you have a different reference frame. But now also consider that nothing goes faster than the speed of light. So whatever multiverse you’re in (and it isn’t ours) might have completely different laws of physics.
You can see how this all can become a mindfuck to think about.
