Show that two space-time points (0, 0, 0, 0) and(t, x = vt, 0, 0) that lie on the trajectory of an object traveling at speed v along the x-axis are separated by a distance satisfying Δ² = 0 if and only if |v| = c. Use the relativistic in variance of Δ² to show that the speed of light is the same in all reference frames. Show that if v > c then Δ² > 0, so that according to Problem 21.8,the points cannot be in causal contact.