We usually heard that speed of light in vacuum $c$ remains same no matter how observer is moving?
I am wondering whether is it taken as a postulate or a proven phenomenon that $c$ is constant irrespective of observer's speed?
Answer
I am wondering whether is it taken as a postulate or a proven phenomenon that c is constant irrespective of observer's speed?
Either one. Both.
Einstein took it as a postulate in his 1905 paper on special relativity. From it, he proved various things about space and time.
The frame-independence of $c$ is also experimentally supported. This is what the Michelson-Morley experiment showed (although it was not interpreted correctly until much later).
You can also take other postulates for special relativity, describing the symmetry properties of space and time. In this case the constancy of $c$ becomes a theorem rather than an axiom. From a modern point of view, this approach makes more sense than Einstein's 1905 axiomatization, which puts light in a special role and defines $c$ as the speed of light. Nowadays we know that light is just one of several fields, and $c$ is not the speed of light but rather a conversion factor between space and time units. The symmetry approach goes back to W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972, and can be found in various other modern presentations, such as this one or my own.
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