A PBS program said that the theory of general relativity holds acceleration and gravity observationally equivalent. (Einstein's space elevator example was given.) Here is a thought experiment based on that mental picture. A "gravity switch" will make the following thought experiment easier to relate, but is not essential for it. A set of twins is brought together at a place. One of the them is set on a spaceship which starts to accelerate at a constant rate. No sooner than the ship takes off, a gravity switch is thrown on and a gravity field is created in a way that it affects only the "stationary" twin. If the strength of the spaceship's acceleration is identical to the gravitational field, then the twins will not only be speeding away at the same relative speed but also at the same "relative acceleration." That is because nobody can tell the difference between being on a spaceship accelerating away and being in a gravity field of equal strength. As the spaceship traverses the (closed) universe and ends up near where it started from (place where the other twin has been living under the gravitational field), it decelerates. As it does so, the gravity field is turned off gradually. The twins are united once again. Would they have aged differently?