Miss Gulch WW of East?

Is Miss Gulch actually the Wicked Witch of the East and the ruby slippers are how she is able to travel between the real world and the world of Oz? We see her transform into the witch during the tornado and never see her alive again when Dorothy returns from Oz. The WW of the West could be her twin sister which is why they look the same. The slippers also are proven at the end to be the means by which Dorothy can return to the real world.