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. Since speed is constant, all you can change is wavelength/frequency. If you try to add speed, you instead add energy, which increases frequency or shortens wavelength.
E = hc / λ
where
Here, the ground is becoming shaky for me. You're asking a good question; why. Maybe all we can find out is how. From what I understand, we have piles of solid evidence that the speed of light is constant. These observations confirmed a theoretical prediction made by special relativity, which can be summarized by ...
So it seems that
But again, this is shaky ground for me. I'll be happy to read corrections.