Since −1 < β < 1, it follows −∞ < ζ < ∞. From the relation between ζ and β, positive rapidity ζ > 0 is motion along the positive directions of the xx ′ axes, zero rapidity ζ = 0 is no relative motion, while negative rapidity ζ < 0 is relative motion along the negative directions of the xx ′ axes.