Generalizations

Due to symmetry reasons, the previous theorem is valid in any direction in K, not only along the x-axis:

(Theorem) If an observer is moving at velocity w relative to K, then after Δt time elapsed in K, the observer's own clock will show only a corresponding Δt' = Δt · √1 – w2   / c2   .

The formula works for polygonal trajectories as well, provided that the speed is the same along all edges.

(Assumption) Any motion (of a point-like entity) can be approximated with arbitrary accuracy by polygonal motion.

This makes the formula valid for any motion of constant speed; even for circular ones as a matter of fact.

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