Differential aging from acceleration, an explicit formula

Abstract

We consider a clock 'paradox' framework where an observer leaves an inertial frame, is accelerated and after an arbitrary trip comes back. We discuss a simple equation that gives, in the 1+1 dimensional case, an explicit relation between the time elapsed on the inertial frame and the acceleration measured by the accelerating observer during the trip. A non-closed trip with respect to an inertial frame appears closed with respect to another suitable inertial frame. Using this observation we define the differential aging as a function of proper time and show that it is non-decreasing. The reconstruction problem of special relativity is also discussed showing that its, at least numerical, solution would allow the construction of an 'inertial clock'.