Twin's Paradox

The Twin's Paradox is a classic problem concerning apparant violations of Special Relativity, which posits that no privileged frames of reference exist in the universe with regards to motion.

The basic idea is this: one of a pair of twins blasts off on a spaceship and accelerates to near light-speed, travels around some nearby stars, and then returns to find his sibling greatly aged due to time dilation. The question is, if there are no privileged frames of reference, why does only one of the twins age? Couldn't the twin who was travelling say that he was at rest, and it was his sibling that was in motion?

The correct Lorentz transformations are provided by including General Relativity, since accelerating objects reside in warped spacetime, and must take that into account to fully describe their frames of reference. The paradox results from only taking differences in the twins' positions into account, and not their respective local spacetime curvatures.