Question: If two cars somehow had infinite energy and were travelling at the speed of light. Say one had a head start. If one of them had a headlamp system that was already turned on, could it illuminate on the back of the other car?
In theory yes it could, the speed of light is independent of how fast the cars are moving, it shouldn’t matter if they are moving at 10 miles an hour or 671 million miles an hour because they are in the same frame of reference. Was that the answer you were expecting?
This is exactly the kind of question that Albert Einstein spent a long time thinking about, one of his famous “thought experiments”! In fact, it was his thinking about standing on a train going very fast and shining a torch that helped him think of his theory of relativity! (He realised that the light from the torch must still be going at the speed of light, regardless of how fast the train was going).
You’ve spotted the problem with your question already – you say “somehow had infinite energy”. This is of course not possible, there is only a finite amount of energy in the universe!!! In particular, anything with mass cannot travel at the speed of light.
Try thinking about this – imagine I have a torch and two mirrors, traveling on a train. I shine the torch, and I set a stopclock to beep every time the light bounces off a mirror, I now have a “clock”! If I am on the train, my clock will tick at a certain rate – the distance directly between the mirrors divided by the speed of light. But now imagine somebody watching the train from the platform. The distance the light travels looks longer, since it not only bounces directly between the mirrors, but it looks like it is going sideways. The ‘ticks’ sound further apart. This means time is slower on the train than on the platform…. 🙂 weird huh!