Differential aging from acceleration: An explicit formula

Minguzzi, E.

doi:doi:10.1119/1.1924490

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American Journal of Physics -- September 2005 -- Volume 73, Issue 9, pp. 876

Differential aging from acceleration: An explicit formula

E. Minguzzi^1,2

¹Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, E-37008 Salamanca, Spain
²INFN, Piazza dei Caprettari 70, I-00186 Roma, Italy

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We consider a clock paradox where an observer leaves an inertial frame, is accelerated, and after an arbitrary trip returns. We discuss a simple equation that gives an explicit relation in 1+1 dimensions between the time elapsed in 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. We use this observation to define the differential aging as a function of proper time. The reconstruction problem of special relativity is discussed and it is shown that its solution would allow the construction of an inertial clock. © 2005 American Association of Physics Teachers.