In theory of relativity all relations are derived based on one observer in a moving frame relative to another frame. How statistically relevant it is to make conclusions based on just one observer? Who told it is valid?

I don't quite recognize relativity in what you're saying. Relativity tells us that an experiment in one inertial (non-accelerating) frame will look the same in any other inertial frame (that part also applies to Newtonian physics) and that the speed of light (in a vacuum) is the same in all inertial frames. (That part is a departure form Newtonian physics.) Relativity also tells us how to translate velocities, times, etc. between different inertial frames, and it gives an answer that's different from the Newtonian one. But the evidence for relativity has nothing to do with picking some one observer and giving that observer special status. On the contrary: that would go completely against the point of relativity. Further, there's no question of drawing experimental conclusions of whatever sort based on just one observer. Rather, what relativity says is that whichever observer performs an experiment, his/her state of inertial motion won't affect the physics. Whether the evidence from the observer's experiment is strong enough to let us draw general conclusions is a separate question, and one that has nothing to do with the theory of relativity.

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