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?
Or 195 km/h. The point is, the ball is moving relative to the train (at 5 km/h). As long as this movement is perfectly constant (no acceleration / deceleration), the overall speed is entirely irrelevant. You can throw a ball the same way at -200 km/h, 0 km/h or a million km/h. Note there is no difference between the system being in motion and being in rest. And you can throw it in any direction, including in movement direction and the opposite. As long as the overall speed remains constant.
Similarly, for the system of equator light source and orbiting satellite, it does not matter how fast this system moves, and in which direction. Or even if it moves at all. So even in classical physics, ~~light~~ classical cannon balls would reach the North Pole and South Pole in the same time.
This feature (N/S reachable in the same time) does not change in relativistic physics. It adds another, equally self-sufficient reason: Light has the same speed in all directions, regardless of relative speeds.
c is not capped at c, but fixed at c. Light always moves at c, for every observer. Regardless of relative speeds between observer and light source, light will always travel at exactly c.
Man, I hate how it sounds like you're contradicting yourself. As if you've somehow gotten extremely confused by my questions or hit your head or something.
Someone else posted this video: https://www.pbs.org/video/pbs-space-time-speed-light-not-about-light/
At least for me personally, that explanation made it click better that we're not talking about traditional speed, but rather about a general propagation speed limit for causality.
I certainly don't understand the implications yet, but I feel like I just have to think about it and re-read everyone's responses a few times over.
Thanks a ton for your help!