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You can prove time dilations, but to do it you need acceleration/decelerations to create that 'twin experiment'. Using solely uniform motion it becomes impossible, as far as I know, to prove a 'twin experiment', as you can't 'get back' to earth to compare the result.
Haven't seen that one Damocles But how do they coordinate their clocks? In a co moving frame it's fairly easy to do so, you just bounce a light signal - A to B - (it bouncing back to A), B set his clock at null receiving it. The signal bounces back to A who just have to split it into two, to get the time it took to reach B, then setting his clock to that number. But here you have A inertial, B at 0.99, then meeting C at 0.95. then both (A and C) transferring their readings to each other, simultaneously?It seems difficult to do that one? But it would be sweet if it worked.