I was just wondering about the line that nothing can surpass the speed of light but if we try to observe it from an accelerating frame.
Does reference frame have any effect on light?
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So you're thinking of light propagating according to Newtons laws and the Galilean transforms. However for objects travelling at a significant portion of the speed of light or $c$, you need to actually use Special Relativity. One of the two postulates of special relativity, from which it is built from, is that $c$ is the exact same to all observers, ie invariant. So no matter the acceleration or speed of an object, they will always see light moving at the speed $c$.
And then this is where it becomes really crazy, the way that it is possible that everyone sees the exact same speed of light is due to time dilation and length contraction which are consequences of special relativity!