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While correct it requires that you ignore what happens during the
The key point is that when the traveller transfers his
timekeeping from the outbound observer to the inbound
observer, there is a radical disagreement as to
what they think the "current" time is back home. We
can understand this just by glancing at the spacetime
diagram: Look at the the red line (toward 8:00) from
the turnaround point and see where it crosses the
green vertical axis (which is the worldline of the
stay-at-home twin). Then look at the blue line (toward
10:00) from the turnaround point and see where it
crosses the the green axis. These two crossing points
are radically different.
Note that we do not need to worry about what Gee forces
the traveller is subjected to during the turnaround.
That doesn't matter. No matter how he accomplishes
the turnaround, he must transfer from one timekeeping
system to the other, and must therefore incur the
disgreement as to the "current" time back home.
To complete the analysis, you need to take into account
the time dilatation of the red and blue observers
relative to the green observer, but that's relatively
routine.