There are an interesting series of answers to this here:
You are in a space ship traveling at the speed of light. You turn on the headlights. What happens to that light? | Answerbag
Here's one that I found most plausible..
You are on a train. That train is traveling at the speed of light. You are facing a wall on the train. You turn on a flashlight; Low and Behold! There is the beam of light on the wall! Why? Because the train is traveling at the speed of light WITH you, as is the flashlight.
Take the same example, and shine the light facing the wall towards the �engine� of the train (That is to say, the �front� of the train) and low and behold, the beam of light is on the wall at the front of the train! Why? Because the train is traveling WITH you, as is the flashlight.
Now, let�s turn on the headlights of this train. What do you know? The headlights are projecting light ahead! Why? Because the headlights are moving with the train!
This can easily be proven in a much more minor scale of speed and using mass. Next time you are in the car flying down the highway, flip a coin. The coin does not go shooting out the back window; it goes up and then comes down. Why? Because the coin is traveling WITH you in the car.
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