Walter's theory is that this is an iteration of Peter -- he stops himself short of saying "my son" -- from yet another universe. "Walter, people from other universes don't just show up in your dreams," says Olivia, like that's some kind of RULE or something, and an agitated Walter says Broyles asked for his theory but Walter never said it was flawless.
Broyles wants to know how this "Peter Bishop" got here and how he has all this classified information on all of them, and Walter glumly acknowledges that the best way for him to ask Peter. But he's not sure he's the best suited for it. Except for the fact Peter won't talk to anyone else. Wait, have they tried torture? Why haven't they tried torture? Just to see if anything shakes loose! Olivia says they'll be right aside, so if whenever Walter wants to leave he can, which is kind of funny given that he doesn't want to go in in the first place but that's not an option.
So into the holding cell, where Peter greets Walter warmly and Walter can barely make eye contact. Walter sits down at the table, opposite Peter, and slowly lifts his eyes. "You don't who I am, do you?" asks Peter, and Walter shakes his head. Peter says he knows this is confusing for Walter, but something's happened and he needs Walter's help. Walter says he'll try and Peter starts rambling on about the two universes, with both dying. Olivia, Astrid and Broyles are in the observation room, watching through the two-way mirror. "How does he know all this?" asks Olivia. Sssshhhh! That's what Walter's in there to find out! You're missing all the awkward reconnection!
It's when Peter starts talking about Walter building the Peter-powered machine that's a bridge between the two universes that he loses Walter. "There is a machine, but I didn't build it. I don't know who you are, what your agenda is, or why you claim to be my son," he says, somewhat angrily.
So now Peter starts talking about the Brief History of Dying Peters, and discovers from Walter that Peter 2.0 drowned in Reiden Lake. He's confused: "The Observer didn't pull us out of the lake that night? Well, that must be it, Walter." In the observation room, Astrid says, "What's an Observer?" Broyles looks at her -- does he have some idea and he just hasn't revealed it yet, like when he revealed it to Olivia?
Anyway, Peter's babbling on about how he was supposed to die that night, but since he didn't, he became a paradox and had to be "deleted" for the worlds to heal. This, naturally, raises more questions than it answers, like if he's already dead in both universes, how is he back?