 Max von Laue (1911, 1913) elaborated on Langevin's explanation.Using Hermann Minkowski's spacetime formalism, Laue went on to demonstrate that the world lines of the inertially moving bodies maximize the proper time elapsed between two events.He also wrote that the asymmetric aging is completely accounted for by the fact that the astronaut twin travels in two separate frames , while the Earth twin remains in one frame, and the time of acceleration can be made arbitrarily small compared with the time of inertial motion.