How is the theme of the supernatural used in the play?

The Inspector’s name, though explicitly spelled “Goole” in the play, is often interpreted through an alternative spelling: “ghoul.” The Inspector, it seems, is not a “real” Brumley police inspector, and Priestley provides no answer as to whether we should believe his claim that he has nothing to do with Eva Smith. What are we to make of the police inspector who rings to announce his arrival at the end of the play? Is the original Inspector, perhaps, a ghost? What forces are at work in the play to make the Birlings really accept their responsibility and guilt?