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?
Ah, yes! Here, we have at least three entities:
The crucial question is, do they move relative to each other? If they all move together at c/2, their relative speed to each other is (compared to c: very close to) zero.
So in the context of an application like GPS, you do not want your satellite to smash into Earth at c/2, but have it in a stable orbit. Which means, it's relative speed is very low. This is why I think the following is a misconception:
Since both source and target move roughly at the same speed, the signal would take roughly the same amount of time even if the speed of light could be different.
Imagine being in a train and throwing a ball in the direction of movement, and in the opposite direction. As long as you target something in/on the train, it makes no difference. Similarly, the equator light source targeting an orbiting satellite does not care how fast the combined system is moving.
On top of that, the speed of light can not be different for different observers. It is the same for everyone, in each direction, in every motion. This is where relativity deviates from classical mechanics. In classical mechanics, we can make sense of things by imagining interacting billiard balls. Their individual speeds add up when they collide. In relativity, the speed of light is fixed. Nothing adds to it or subtracts from it.
Coming back to GPS: Even at these low relative speeds, there are still relativistic effects big enough to introduce significant errors in GPS positioning. We have to account for these errors: https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity
But that example with the ball works, because everything is going at 200 km/h, while the ball is going e.g. at 205 km/h.
My understanding is that light is supposed to work differently. That it does not go at
200 km/h + cwhen fired from a train. Its speed is capped at c.That means, relative to the train going at 200 km/h, its relative speed should only be
c - 200 km/h.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!