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, the speed of light is exactly the same in all directions.
This is a very important and counterintuitive finding, most famously verified by the 1887 Michelson-Morley experiment.
It wasn't explained until Einstein developed special relativity in 1905.
But it's not proven to be the same in all directions.
"The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed (or "two-way" speed of light) from the source to a mirror (or other method of reflection) and back again to detector. Albert Einstein chose a synchronization convention (see Einstein synchronization) that made the one-way speed equal to the two-way speed."
See this for detailed references.
https://en.m.wikipedia.org/wiki/One-way_speed_of_light
The issue being that you're sending a beam of light to a mirror and seeing the time it takes to take a round trip. It could be faster going to or faster coming back, we don't know. We just know how fast it went there and back again.
And if you were to send a detector and try to beam light to it, you run into clock synchronization issues - i.e. the time registered on the far away detector is no longer in sync with the one on the point of origin. Want to sync it remotely? Send a signal at the speed of light to tell it the new time, but that depends on the speed of light in that direction, so it may very well remain out if sync. Does the sync happen instantaneously? Claim your Nobel, you just found something faster than light. Plus any sort of issues if you decided to beam the signal back (speed of light, again) from the detector instead of transporting it back and reading it.
Right, yeah, if the whole system is moving in the direction of the light being sent, it would take longer to get there, while the mirrored light would be faster, ultimately zeroing out until its back at the origin.
Sometimes, I feel like we need more blind physicists. Those wouldn't be horribly confused when they cannot detect things along the way.