The paradox of the twin paradox is that everybody, even Einsteinians, know that actually it involves an absurdity, and yet, for more than a century, no convincing demonstration of the absurdity has been proposed (reductio ad absurdum does not seem to work). It is always easy to show that the traveling twin remains younger, and always impossible to show that the stationary twin remains younger, as if the principle of relativity vanishes any time one starts pondering on the issue. The mystery can be dispelled by analyzing the following text:

http://www.amazon.com/Relativity-Its.../dp/0486406768
Banesh Hoffmann, Relativity and Its Roots, p. 105: "In one case your clock is checked against two of mine, while in the other case my clock is checked against two of yours, and this permits us each to find without contradiction that the other's clocks go more slowly than his own."

This means that the slowness of the stationary twin's clock (or the youthfulness of the stationary twin) can only be demonstrated if this clock can be checked against two of the clocks of the traveling twin. However, in the traditional twin paradox scenario, the traveling twin is not endowed with two spatially separated locations where his two clocks can be placed. Accordingly, in this scenario, only the youthfulness of the traveling twin is visible. The youthfulness of the stationary twin is there, predicted by special relativity (so we do have an absurdity), but remains invisible because the tool that makes it visible - more than one clock possessed by the traveling twin - is implicitly forbidden.

In the second scenario below the youthfulness of the stationary twin (more precisely, the slowness of the stationary clock) is visible:

A train is at rest and a clock is moving to and fro between two (stationary) clocks situated at the front and back ends of the train. This is the traditional relativistic scenario - special relativity predicts that the moving clock runs slower than (lags behind) the two stationary clocks on the train.

In a complementary scenario, the single clock is on the ground, at rest, but the train is moving to and fro so that the stationary clock on the ground effectively commutes between the front and back ends of the train. Now special relativity predicts that the single stationary clock on the ground runs slower than (lags behind) the two clocks on the moving train.

Pentcho Valev