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. It is counterintuitive, but correct.
The magnitude of v_train does not affect the speed of light coming in from, or going out in different directions. c simply is constant to all observers, regardless if and how they are moving.
Light emitted or absorbed by a train will always have the speed of c, not c + v_train. Even if that train moves nearly at the speed of light itself.
However, v_train affects wavelength, or color. Light coming in from the front will be more blue, and light coming in from the back will be more red (see 'red shift' in the context of distant galaxies). Geometry will warp. But light will always move at the speed of light.
Sounds as if the fun begins here. Of what implications are you thinking?
Doesn't that mean the speed of light is a universal reference frame? If you made an ideal wavelength detector that precisely captured wavelength, and emitted a light source of exactly 1 constant wavelength, the pointed 2 of the detectors at it on opposite sides, wouldn't the tiny differences in wavelength represent a vector of movement in that axis relative to all of space where the speed of light is constant? Make 3 of those on x, y, and z axes, and don't you have an absolute vector of movement in our entire spatial universe?
Somewhat yes. There are no unmoving objects in space, but recently scientists have measured redshift differences from distant stars to calculate very accurately their distance and how it evolves over time. This enabled them to detect gravity waves at a galactic scale, effectively turning the entire galaxy in a gravity telescope.
You're looking for an absolute standard vector, to measure absolute velocities?
Yes, I think you can make one. It's not even hard. But how can you tell wether you are moving, or wether it is moving?
Imagine all the possible ways this vector can be in, and move through space. For all of those, you measure the same speed of light. But for each of those, you measure a different wavelength, based on it's relative speed (and due to the universe expanding, distance) to you.
Now you can tell your relative distance and speed to any of these vectors. Like we do with other astronomical objects.
If you want to get rid of relativeness, and achieve absoluteness, you have to subjectively define which reference frame is your rest frame.
I guess that makes sense, but I was always struck by the assertion that there is no absolute reference frame for our universe. If the speed of light in a vacuum is a constant speed, that always struck me as incompatible in my head because the speed of light itself would define an absolute reference frame. I'm certainly not trying to assert anything, and I assume I'm just not understanding it properly, but a universe wide constant that can be used to define a vector feels like it could be used to establish a zero coordinate. If you could establish three points that are not moving relative to each other and measure their universal velocities, a difference between the three axes of velocity could point to a spherical center point.
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.
So is the speed of light constant because light is a particle and a wave? And when the particle moves at a constant speed the change in speed/energie is achived by a modulation of the wave?
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.
Well, to massively simplify all of this, let's assume the Earth is moving in the direction of the North Pole at
c/2.That means, if you're at the equator and send a signal to a satellite over the North Pole, it's going to take twice as long as a signal sent across the same distance from the equator outwards.
That feels like it would be quite relevant for GPS.
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!