Lesson 5 - Length Contraction
We have seen in the previous lessons that the time experienced by an observers depends upon their speed, now let us examine what happens to a spatial dimension, the length of the observer.
Let A be an observer, and suppose that observers B and C are the two ends of a rod traveling at velocity v, and the k-factor is k. Suppose that B and C determine that the rod has length L.
Let B start emitting light when B and A meet, and stop when C and A meet. Then B has been emitting light for a time L/v. That means that the distance between B and A according to A is
And since this is the time when A and C meet, A claims the rods length is (k - 1/k)c/2v L. Since ( k-1/k ) > v/c, B and C see themselves closer together than A does. This is known as length contraction.
