Hafele and Keating in a fictious gravitational field

Abstract

The so called twin paradox is described in every special relativity (SR) textbook. Obviously, an exact calculation requires the application of the general theory of relativity (GR) but, thanks to some simplifying hypotheses concerning the acceleration and deceleration phases, even in SR it is possible to find the correct solution and that is "the twin who goes on space travel is the one who, returning to Earth, finds the aged brother." In a curved spacetime, instead, we have the algebraic sum between a kinematic and a gravitational effect. What happens in the presence of a gravitational field is, for example, well described by Hafele and Keating's experiment and, in this case, it may happen that the traveling brother can grow older than his brother at rest. Continuing in this pedagogical tradition, we consider the Hafele and Keating experiment in a fictious gravitational field of a rotating frame. The equality of the results between curved spacetime of a real gravitational field and flat spacetime of a fictitious one, in our opinion, is interesting to emphasize even today the great genius of Einstein and that is "inertia is gravity in disguise".