In school, I was taught that the speed of light is constant, in the sense that if you shoot a laser off of a train going 200 km/h, it still just goes at a speed of c=299,792,458 m/s, not at c + 200 km/h.
What confuses me about this, is that we're constantly on a metaphorical train:
The Earth is spinning and going around the sun. The solar system is going around the Milky Way. And the Milky Way is flying through the universe, too.
Let's call the sum of those speeds v_train.
So, presumably if you shoot a laser into the direction that we're traveling, it would arrive at the destination as if it was going at 299,792,458 m/s - v_train.
The light is traveling at a fixed speed of c, but its target moves away at a speed of v_train.
This seems like it would have absolutely wild implications.
Do I misunderstand something? Or is v_train so small compared to c that we generally ignore it?
Yes. Maybe a key point is to think about "speed relative to what?". Maybe we like to think about speed relative to an objective, unmoving, unchanging background. Sort of like the big stage on which the universe plays. Like a level in a video game, where each object has absolute coordinates and velocities relative to 'the universe itself'.
But in reality, we have no such thing. Or it depends on what we define as that background.
How exactly? I invite you to work out the details, make a geometry sketch.
Yes, we can use the speed of light to define a vector. For example, 1 light year is such a vector. Or 1 light second. Ah no, those are merely 1-dimensional distances. We surely can construct 3-dimensional vectors from them, though. But what is this vector's null rotation? And where is the origin of our coordinate system? A vector can be rotated and translated arbitrarily, and still be the same vector.