This is a statement asked by the comedian Steven Wright that this author will attempt to answer.
First, what is the speed of light. It is a constant at which a photon travels from one point to another. This rate of travel is universally known as 299,792,458 meters per second. A photon travels at this rate through the vacuum of space without any impedance. Since a photon has no weight it can also be thought to maintain this speed even within dense atmospheres.
Now the summarization of special relativity and how it answers the above question. Remember first that movement is relative. If we are in a moving vehicle and jump we do not, all of a sudden, fly backwards. We are moving relative to the speed of the vehicle we are in. Therefore, comes the first possible way to explain the question. Since the car is moving at the speed of light the photons projected from the head lights would be moving at this same relative speed before being projected out into space. Therefore, of course the lights would work, because there actual speed would be the speed of light plus the speed of light that they throw off. Another explanation could be no they do not work. The speed of light is a constant. If something reaches this speed a photon could not individually exceed that speed and so would not exit the lamp. Relativity basically means that we see things relative to our position. Movement in these terms is a concept based on position. We could say that we do not move, but the universe moves around us and be totally justified, despite the scientific evidence. Relativity would then have us believe that the car could move at the speed of light and have its head lights shine, or not. It depends on your perspective. If you are in the car moving quickly along, you possibly perceive no movement. Therefore, because there is no relative movement the photons would exit the head lights.
It can be stated in several different ways, and intelligently argued, but the fact is that no one knows because we haven’t gone that fast yet.
A few inane facts.
A car can reach a rate exceeding the speed of sound (343 meter per second) but is still 874,030 times slower than a photon.
A photon is a particle with no apparent mass. It has the characteristics of both a particle and a wave.
There are two theories of relativity. Special relativity has to do with movement and general relativity speculates on gravity.