Twin Paradox

The twins are five years old when one of then is sent off in a spaceship that travels nearly the speed of light and the other remains on spaceship Earth. After 50 years Earth time the spaceship returns. The twins greet each other and compare their experiences. We know that the twin who experiences accelerations will age slower and return to Earth much younger than 55 years old. Precisely how does the general theory of relativity explain the aging of the twin during accelerations?

Answer

Both special theory of relativity (STR) and general theory of relativity (GTR) explanations for the aging of the space-traveling twin should be considered. If by the STR we consider inertial reference frames only and ignore any accelerations experienced by the space traveler, a symmetry would exist between the two frames, and the twins must both age at the same rate. Therefore, the accelerations experienced by the space traveler make the difference in the aging.

One can handle these accelerations in the STR or in the GTR. Some people argue that this twin paradox problem requires only the STR because there is no curved space-time in the problem that is, both twins can be considered to be in a flat space-time because no gravitational accelerations near a mass are necessary. Then one would handle the accelerations for the space-traveler twin in terms of STR calculations, perhaps via the velocity parameter technique. A true GTR problem, by contrast, would require the physics of the curved metrics near a massive body.

The solution of the twin paradox using the GTR relies on clocks ticking slower in a gravitational potential near a mass. The clock at a far distance from the mass ticks at its fastest rate and, if brought closer to the mass, begins to tick slower and slower. Therefore a person closer to the massive body, where the gravitational acceleration is greater, ages slower.

In cases where the acceleration of a spaceship can be approximated by an equivalent gravitational acceleration that is, using the Equivalence Principle we can expect the traveling clock to tick slower during the acceleration. And that behavior is why the traveling twin ages less. As seen by a third observer at rest with respect to the stars and the stay-at-home twin, the clock on the spaceship is changing its rate of ticking during the accelerations.