What if a spaceship traveling through the vacuum of space at 290,000,000 m/s turns on a pair of headlights. What would be the speed of the light waves produced, in meters per second, in relation to the spaceship(as measured by its crew)? In relation to a stationary observer (as measured by the observer)? In relation to a spaceship heading in the opposite direction at the same speed (as measured by its crew)?
The speed of light, according to an authority, is 299,792,458 m/s.
Let's round that to 300,000,000 m/s simply for our convenience.
To the observers in the spaceship, the light from their headlamps would appear to travel 300,000,000 m/s.
That's because the spaceship and everything in it are shortened by their speed. So it still looks like 300,000,00 m/s to them, because the meter stick they're measuring it with is shorter than it would be if they were standing still.
I have one for you to think about. If that spaceship were the ONLY thing in the entire universe, would it be moving or not? How would you know?
< How would you know? >
You wouldn't be able to tell your speed, because speed is a valid concept only when it's relative* to another object. You could be able to know you were "moving" if you accelerated... because you would still have inertia.
* Imagine you're in a train car going down the track at 60 mph. You start walking at 3 mph in the direction of travel. What is your speed? Before you answer, remember that the earth under the train is moving about 1,000 mph... toward the east While we're at it, let's take into account the speed that the planet is moving in its orbit around the sun, about 67,000 mph. The point is, speed is relative, dependent on comparison with something else.