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I recall reading (sorry, can't cite the source) that the time dilation in
the spacecraft is a result of its acceleration, which the stationary earth
does not experience. The idea being that the spacecraft and the earth are
not two different reference frames moving away or towards one another at a
constant velocity. One is an accelerated frame (at least at some point on
the voyage) and the other is not.
So what is the actual, copper-bottomed, good to go, widely accepted
explanation for the twin paradox?