Consider two reference frames S and S'. For observers in each of the reference frames an event has space-time coordinates of (x, y, z, t) in frame S and (x', y', z', t') in frame S'. Assuming time is measured the same in all reference frames, if we require x = x' when t = 0, then the relation between the space-time coordinates of the same event observed from the reference frames S' and S, which are moving at a relative velocity u in the x direction, is: