I've waffled on this before. Ultimately, I don't think it matters, and we really shouldn't care whether he is actually time traveling or not. I think one way you could read it is as a story about a man suffering from severe PTSD. At this point, he's old, traumatized, and starting to lose touch with reality. His mind wanders into the past and into a future he is imagining to cope with the end of his life. That's a pretty touching story. Or maybe he was really time traveling, and really was abducted by aliens. There's no proof, so who's to say? What would be the difference anyway? From our perspective, and from Billy's perspective, the result is the same: a feeling of being "unstuck" and everything overlapping. That feeling is the whole point of the book, and I think, it's a book worth reading. If it hurts the book for you, well, so it goes.