This was nicely explored in the movie "Contact", where the protagonist, a firm atheist, went on a Journey into outer space, yet when she returned home could not prove she went anywhere. Her rationality broke down and it was shown that it didn't matter or not if she had in fact went anywhere, it was that she was given such a powerful personal experience of her own revelation, that proving it scientifically was now beyond necessity anymore.
This character is ENTj btw.