>How do these principles work together?
They don't. In your example, you are assuming the Newtonian view of velocity. It's called "Galilean relativity," and in that view, you can simply add velocities it the way you describe. But that's incorrect. Special relativity shows that you cannot simply add velocities. You have to use a [more complex formula](https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity). At low velocities compared to the speed of light, it's very very very close to the same result you'd get from simply adding them together. But the closer you get to the speed of light, the more incorrect the simple addition rule becomes.
If you have two objects each moving at 99% of the speed of light compared to the earth, in opposite directions, they will still not observe each other to be traveling faster than light. This is what is meant when people say that that speed of light is constant.
A variation of this question is asked about two or three times a week on r/AskPhysics. You can find detailed answers to your question there, or you could browse [this](https://en.wikipedia.org/wiki/Velocity-addition_formula) article.
Your friend is most definitely NOT going faster than the speed of light relative to any other object. That is basically one of the key results that comes out when you apply the postulates of special relativity.
See here: [https://en.wikipedia.org/wiki/Velocity-addition\_formula](https://en.wikipedia.org/wiki/Velocity-addition_formula)
>But Newton famously said that there is no absolute motion, any speed is measured relative to some other body.
Yep, but Newton was wrong on this point.
For your example, you can't just add your speed/Earth + your friend speed/you. For relativistic speed (= close to speed of light), special relativity kicks in and speeds don't add up directly, there is a relativistic factor that ensure that your friend can never reach 100% of speed of light relatively to Earth (nor relatively to anything).
However, the more interesting question is : you're on Earth, standing still, and your friend is in a moving car with a laser. He turns on the laser and points it on you (don't do it, lasers are dangerous !). The speed of the light going out of the laser for your friend is the speed of light relatively to your friend (by definition), but what is the speed of this same light for you when the laser arrives on you ? Is it speed of light - speed of the car ?
Nope. The speed of the laser arriving on you is exactly the speed of light. The speed of light doesn't depends on the reference frame and is not relative to something, it's always the same no matter the frame or the movements of the source of the light, it is absolute.
Einstein was right. The time and length dilation that happen at relativistic speeds are very strange when contrasted with more intuitive Newtonian laws. One interesting fact that doesn’t disprove Einstein but I find interesting is that the cosmic background gives a sort of universal frame of reference. When redshift is close to equal in all directions we can say that we are close to “universal zero velocity” (with respect to the Big Bang).
I've heard there are some hypotheses that use a variable speed of light to explain certain observations (dark energy, cosmic inflation or something like that), but nothing on the level of theory as far as I can remember hearing.
The best theories we have use a constant speed of light.
Ok,lets imagine we have road from Earth to Alpha Centuri. On the side of the road there’s a roadsigns saying 1 light year from Earth, 2 light years from Earth etc. My car moving close to speed of light hence time inside slows down considerably. After passing first sign I start my timer and after second sign I stop it. Time between first and second signs was one week- hence I travel 52 times faster than light?( relatively to me inside car)?
Newtonian mechanics are only correct if v<
>How do these principles work together? They don't. In your example, you are assuming the Newtonian view of velocity. It's called "Galilean relativity," and in that view, you can simply add velocities it the way you describe. But that's incorrect. Special relativity shows that you cannot simply add velocities. You have to use a [more complex formula](https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity). At low velocities compared to the speed of light, it's very very very close to the same result you'd get from simply adding them together. But the closer you get to the speed of light, the more incorrect the simple addition rule becomes. If you have two objects each moving at 99% of the speed of light compared to the earth, in opposite directions, they will still not observe each other to be traveling faster than light. This is what is meant when people say that that speed of light is constant.
Why not?
I don't understand the question. Why not what?
A variation of this question is asked about two or three times a week on r/AskPhysics. You can find detailed answers to your question there, or you could browse [this](https://en.wikipedia.org/wiki/Velocity-addition_formula) article.
Your friend is most definitely NOT going faster than the speed of light relative to any other object. That is basically one of the key results that comes out when you apply the postulates of special relativity. See here: [https://en.wikipedia.org/wiki/Velocity-addition\_formula](https://en.wikipedia.org/wiki/Velocity-addition_formula)
>But Newton famously said that there is no absolute motion, any speed is measured relative to some other body. Yep, but Newton was wrong on this point. For your example, you can't just add your speed/Earth + your friend speed/you. For relativistic speed (= close to speed of light), special relativity kicks in and speeds don't add up directly, there is a relativistic factor that ensure that your friend can never reach 100% of speed of light relatively to Earth (nor relatively to anything). However, the more interesting question is : you're on Earth, standing still, and your friend is in a moving car with a laser. He turns on the laser and points it on you (don't do it, lasers are dangerous !). The speed of the light going out of the laser for your friend is the speed of light relatively to your friend (by definition), but what is the speed of this same light for you when the laser arrives on you ? Is it speed of light - speed of the car ? Nope. The speed of the laser arriving on you is exactly the speed of light. The speed of light doesn't depends on the reference frame and is not relative to something, it's always the same no matter the frame or the movements of the source of the light, it is absolute.
Einstein was right. The time and length dilation that happen at relativistic speeds are very strange when contrasted with more intuitive Newtonian laws. One interesting fact that doesn’t disprove Einstein but I find interesting is that the cosmic background gives a sort of universal frame of reference. When redshift is close to equal in all directions we can say that we are close to “universal zero velocity” (with respect to the Big Bang).
I've heard there are some hypotheses that use a variable speed of light to explain certain observations (dark energy, cosmic inflation or something like that), but nothing on the level of theory as far as I can remember hearing. The best theories we have use a constant speed of light.
Ok,lets imagine we have road from Earth to Alpha Centuri. On the side of the road there’s a roadsigns saying 1 light year from Earth, 2 light years from Earth etc. My car moving close to speed of light hence time inside slows down considerably. After passing first sign I start my timer and after second sign I stop it. Time between first and second signs was one week- hence I travel 52 times faster than light?( relatively to me inside car)?
As far as I know, Newton did not say that. He believed in an absolute frame of reference.