This made me think immediately of a book by Robert Monroe. I forgot which one.

He describes ways to induce out of body experiences using sound. Besides that, he uses a technique for leaving the body.

Now sometimes he describes that he turns around while leaving, and then he doesn't go through the normal out of body routine, but he awakes in a counterpart of himself in a "parallel earth", of which the history lines up for some time with our world, but has diverged. He describes different styles of transportation for example.

I will look this one up.