It validly follows from Einstein's 1905 postulates that, for the entire outward and return parts of the trip, the travelling twin observes his stationary brother remaining younger, and the stationary twin observes his travelling brother remaining younger. Needless to say, this is reductio ad absurdum that forces scientists to declare the underlying premise, Einstein's 1905 constant-speed-of-light postulate, false, and abandon Einstein's relativity. In Einstein's schizophrenic world the theory can be saved by informing the scientific community that "enough strangeness occurs during the turning-around period":

http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
Introduction to Classical Mechanics With Problems and Solutions, David Morin, Cambridge University Press, Chapter 11, p. 14: "Example (Twin paradox): Twin A stays on the earth, while twin B flies quickly to a distant star and back. (...) For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox...."

Pentcho Valev