Peter dreams he's in a park with Olivia, watching Walter on the swings. They agree that this is the perfect day, and kiss. But it has to end, she says; you can't ignore the problem. What's the problem? He is.
He wakes up in his cell at Fringe HQ as Olivia arrives. Something's going on with time - something maybe related to Peter's sudden appearance. Shortly before he arrived, the Fringe team experienced time anomalies too.
At a Boston apartment building, a time bubble has burst, leaving part of the place scorched in a perfect circle, as though by fire. Lincoln says that there was a fire here four years ago. Broyles tells Olivia to have Walter run tests on Peter immediately. Olivia says Walter refuses to do anything involving Peter, but Broyles insists that Walter's job is to investigate Fringe events - like Peter.
At Harvard, Walter declares that "the subject" is not causing the time-related phenomenon and storms off, telling Olivia he'll be in his bedroom. Peter is surprised that Walter lives in the lab.
Peter thinks his return somehow damaged the space-time continuum, and these anomalies will probably get worse. Olivia says that all the time slips are within a 40-mile radius of downtown Boston. She also tells him about Walter's visions and Peter showing up in her dreams. How's that possible? He tells her to believe whatever she likes, but this is where he's supposed to be. Maybe she and Walter saw echoes of the other timeline.
Some teenagers are nearly flattened when a train suddenly emerges from a time bubble at a crossing. While investigating, Peter experiences time jumps, shifting between the crossing and being in the SUV with Olivia and Lincoln. The railroad line was decommissioned four years ago, and Peter finds heightened levels of neutron radiation. That means somebody's causing these time events.
Elsewhere, a man named Raymond watches his wife, Kate, write equations in a notebook. She asks him some mundane questions. He looks at his watch, counting down from 59 seconds. She breaks her pencil, and he hands her a red marker as she says she's getting closer to success. He kisses her when the countdown ends . . . and suddenly she's in a different room. She struggles to remember him.
At Harvard, Peter and Lincoln mark four time-bubble events on a map, and Walter abruptly notes that snails, nautilus shells, and rams' horns all have something in common: Fibonacci's golden spiral. He draws a spiral connecting the points, saying the source of the events must be in the center, in Brookline.
That's where Kate and Raymond live. In the basement, Raymond types the new part of her equation into a computer. He flips a switch; machinery hums, and a clock counts down from 47 minutes. Upstairs, Kate's working on the equation again, using the red pen. She asks Raymond the same questions as before.
As the team canvasses Brookline, Peter asks Olivia about her dreams. Did she feel anything for him? Puzzled, she says you're a stranger, so what would I feel?
The FBI and police gather outside as Raymond shows his machine to a bewildered Kate. He built it from her work - it took almost three years, but time chambers are possible! She needs to complete the equation so they can keep the chamber open indefinitely. Confused, she asks what year it is. In here, it's 2007. Outside, it's 2011.
An agent approaches their front door. He walks unknowingly into a time bubble and is vaporized.
Walter determines that the time bubble around the house is the source of the anomalies; it's much deadlier than the others, which were merely echoes. Peter says a mobile Faraday cage would block the electromagnetic field long enough for him to go in and turn off whatever's causing this. Though disgruntled, Walter builds it. Meanwhile, Lincoln realizes that a time bubble will emerge in a tunnel under the river, which didn't exist four years ago. He leaves to help the police evacuate.
Kate asks why Raymond has done this. Distraught, he says, "I lost you, Kate." Outside, Broyles tells Olivia that Raymond's an electrical engineer, and Kate's a professor emeritus of theoretical physics. She retired three years ago, due to early onset Alzheimer's.
Peter puts on Walter's Faraday harness and enters the bubble. Kate informs Raymond that she's solved the problem but hasn't written it down yet. Peter goes into the basement, and Raymond whacks him with a baseball bat! He comes to and hears Raymond say the machine didn't work until three days ago. Peter confronts them, and they agree to shut down the machine, which is causing time displacement. Privately, the pair emotionally discuss her illness. Raymond just wants to repay Kate for all she's done for him. She reluctantly starts finishing the equation.
Raymond turns off the machine, and Kate reverts to her 2011 state. Later, Raymond discovers she scribbled out the equation and left a note: "How you repay me . . . Just love me. And live your life . . ."
At HQ, Peter tells Broyles how Raymond's machine started working three days ago - when Peter arrived. Now he thinks he's really in the wrong place. He has to figure out how to get home. Broyles informs him that Walter owns a house on the Harvard campus.
Olivia takes Peter to the same home he and Walter shared, once upon another timeline. She smiles and says, I was important to you, wasn't I? I mean, the other version of me. He says yeah, she was - she is. Olivia hopes he gets back to her. Me too, says Peter. She leaves him alone in the house.