Why does the group act on the right on the principal bundle?
In many textbooks, in fact all textbooks I've seen, the fiberwise group action on the principal bundle is on the right. It seems to me that left actions and right actions are essentially the same. Then why do people keep acting on the right for the principal bundle, while acting on the left for many other cases? Is it because one might want to consider the possible additional left action on the bundle?