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In Newtonian mechanics, by the following two assumptions:
(i) The time is absolute.
(ii) The length is absolute.
it is easy find the relations betweem two coordinate systems with uniform motion respect to each other (galilean transformations). Then is not complicated to prove that two inertial frames (i.e. two coordinate systems where holds the law of inertia) must move with constant velocity relative to each other.
In order to find the real relations between two inertial frames, in special relativity should assume the principle of constancy of the velocity of light. My question is:
Why two inertial frames of reference (in special relativity) moves with constant velocity relative to each other?
We only prove it in the context of Newtonian mechanics!