The “twin paradox” corresponds to the situation where two twins begin at rest in an inertial reference frame, one of them takes a journey, normally very fast and to a distant place, and then returns to the twin at rest. The “twin paradox” evokes the idea that each twin would say that it should be the other who is younger because of their relative motion. A complete resolution of the paradox corresponds to the calculation of the elapsed proper time of each twin, by each twin, and the subsequent observation that they actually get the same answer, that the travelling twin is indeedthe younger twin. Acceleration has a role to play; indeed, if one tries to calculate the age difference from the point of the view of the travelling twin, then the role of the acceleration is crucial and cannot be dismissed. In this tutorial, we show in complete and pedagogical detail, how to do the necessary calculations according to each twin using simple transformations of coordinates.
Variational finite-difference representation of the kinetic energy operator