<P> In special relativity, time dilation is most simply described in circumstances where relative velocity is unchanging . Nevertheless, the Lorentz equations allow one to calculate proper time and movement in space for the simple case of a spaceship which is applied with a force per unit mass, relative to some reference object in uniform (i.e. constant velocity) motion, equal to g throughout the period of measurement . </P> <P> Let t be the time in an inertial frame subsequently called the rest frame . Let x be a spatial coordinate, and let the direction of the constant acceleration as well as the spaceship's velocity (relative to the rest frame) be parallel to the x-axis . Assuming the spaceship's position at time t = 0 being x = 0 and the velocity being v and defining the following abbreviation </P> <Dl> <Dd> γ 0 = 1 1 − v 0 2 / c 2, (\ displaystyle \ gamma _ (0) = (\ frac (1) (\ sqrt (1 - v_ (0) ^ (2) / c ^ (2)))),) </Dd> </Dl> <Dd> γ 0 = 1 1 − v 0 2 / c 2, (\ displaystyle \ gamma _ (0) = (\ frac (1) (\ sqrt (1 - v_ (0) ^ (2) / c ^ (2)))),) </Dd>

The faster you travel the slower time passes