Along these lines...
here's a quote from my favorite paper on the Twin Paradox/Clock Effect :
"First, is it reasonable to say that
it is during his acceleration at C
that twin 2 suddenly loses time or age, and that
this loss at C causes the final age difference at B?
The answer is "no."
It is just as unreasonable to blame the acceleration at C
for the total age difference of the twins
as it would be,
in the case of a triangle ACB in the ordinary Euclidean plane,
to say that the larger length of the path ACB,
as compared to the straight path AB,
is caused by a sudden gain of length at the corner C."
The Clock Paradox in Relativity Theory
Alfred Schild,
The American Mathematical Monthly, Vol. 66, No. 1 (Jan., 1959) (pp. 1-18)
http://www.jstor.org/pss/2309916
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\begin{picture}(100,140)(0,0)<br />
\unitlength 1mm<br />
\qbezier(0,0)(0,0)(0,100)\put(0,0){A}<br />
\qbezier(0,0)(0,0)(30,50)\put(30,50){C}<br />
\qbezier(30,50)(30,50)(0,100)\put(0,100){B}<br />
\end{picture}<br />
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