What is the twin paradox?

Answer 1

The twin paradox is the following: if there are two twins on Earth, let's call them A and B, and B flies away and comes back at nearly the speed of light, then A has aged more than B. This occurs in A's reference frame. The paradox comes in to play when you look at the exact same situation in B's frame of reference. In this case, B sees A travel away at nearly the speed of light and come back, so therefore one would think that B would have aged more than A in B's reference frame. Relativity states that all inertial reference frames of a given situation produce the same result, yet by switching frames of reference for the above problem we get two different results, A being older in one and B being older in the other.

This paradox is resolvable, however, through the use of general relativity, as opposed to just special relativity, in the following way: For both twins to start out stationary and then have only one of them go away and come back, only one of them could have actually been acted upon by an applied force; in fact, three applied forces: one to get going, one to turn around, and one to stop. Let's say B is the twin who was acted upon by these forces. Special relativity, then, is sufficient to explain the above result in A's reference frame, since no applied force acted upon A, and A remained stationary. Special relativity is not sufficient to explain the above result from B's reference frame, however, since B was the one who had the forces acted upon them, yet A was the one to move.

General relativity gets around this problem by introducing the concept that any result obtained from a measurement made by a uniformly accelerating observer in the absence of a gravitational field, is equivalent to that of a stationary observer in the presence of a uniform gravitational field. By setting twin B stationary and introducing homogeneous gravitational fields that result in twin A's acceleration away from B, the acceleration necessary to turn A around, and the acceleration necessary to stop A when they get back, the calculation for the difference in how much each twin aged results in what we had initially found from above; that twin A has still aged more than twin B.