Why is the speed of light constant and independent from the observer?
The philosophy department is down the hall. ;)
Well, it's constant if you stick to inertial reference frames whose coordinates are related to one another by the Lorentz transformation, and relativity predicts (and all the evidence suggests) that the fundamental laws of physics all have the property of "Lorentz invariance" which means they obey the same equations when written in any inertial coordiante system of this type. There's nothing stopping you from using a non-inertial coordinate system where light's speed is different, though.
As for "why", it depends what you're asking...given inertial frames related by the Lorentz transformation, it's easy to show that anything with a coordinate velocity of c in one inertial frame will have a coordinate velocity of c in any other inertial frame. But as to why the the laws of physics are invariant under the Lorentz transformation in the first place, like ZikZak says that seems to be more of philosophical question.
I wouldn't say it's a philosophical question. Philosophy doesn't seem to have anything to do with it (unless you're going to study the meaning of the word "why" or something like that). The only thing that could answer it is another theory of physics. Of course, if we ever find a theory that answers that question, it would give us a new set of "why?" questions.
It's philosophical in the sense that if Lorentz-invariance is part of the most fundamental laws (the final 'Theory of Everything') rather than being derivable from more fundamental laws, then "why are the laws of physics Lorentz-invariant" is just a subset of the general question "why are the laws of physics what they are", which obviously cannot be answered by physics and therefore is a metaphysical question (for example, one answer might be 'because God chose them that way', another might be 'because all mathematically describable universes exist as Platonic forms, and are perceived as real by any intelligent beings that evolve within them').
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