Recalling that the interval along a line of simultaneity is the distance in the associated reference frame, we reach the astonishing conclusion that even though the object associated with the curved w...Recalling that the interval along a line of simultaneity is the distance in the associated reference frame, we reach the astonishing conclusion that even though the object associated with the curved world line in Figure \PageIndex6: is accelerating away from the origin, it always remains the same distance (in its own frame) from the origin.