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Sometimes it is stated that General Relativity is inevitably needed
in the analysis of the twin paradox. Hestenes (1990) discusses how
this misconception was initiated by Einstein himself! Hestenes goes
on and states that "he may have harbored some misconceptions of his
own relativity". Interesting indeed.
...
As long as the analysis is entirely done from the point of view of
the stay at home twin there is no paradox.
Special relativity can not be used to
analyze the problem from the point of view of the moving twin
because part
of the time he is not at a constant speed.
General relativity supplies the
pieces needed to complete the analysis from the point of view of the
moving twin's acceleration.
Unfortunately getting students to understand this is often fairly
difficult.
Students will routinely apply equations such as
x=X0 + V0 t + 1/2 a t^2 in situations where the acceleration
changes. In other words they do not recognize that equations are
only applicable under certain conditions.
The idea that an equation is only valid in certain ranges or when
the constants are indeed constant is a difficult concept. Similarly
the equations of special relativity are not applicable during the
moving twin's acceleration.