This is the subject of tonight's episode 4.14 of Fringe. Once, again, in at least two ways. The proximate way is a video which has been recorded over, but which, in Walter's lab, can be optically penetrated to reveal something of the original. The deeper way concerns the story with which we have been grappling all season - the relationship of Peter to the Olivia and Walter of this world.
I've been saying, all along, that this world, in which Peter did not exist after he drowned as a boy (or, more accurately, the Peter of this world died of a serious illness, the Peter who drowned was alternate Peter being brought back to this world) - but this world in which there was no adult Peter, but to which adult Peter returned, was really the world of Fringe for the first three seasons.
Olivia was coming to believe that. So was Peter. And one of the Eternal Bald Observers confirms this - I would say, beyond any doubt - when he asks at the beginning of this episode why September "did not erase the lingering traces of Peter Bishop from this time line"? For how else could there be "lingering traces" if this world now on our screens was not in fact the same world of the first three seasons, except with Peter's existence yanked out of it?
Alas, this does not yet yield a happy ending for Olivia and Peter - by the end of the episode and all that Peter and Olivia have been through, Peter concludes that the Olivia in front of him is not the right Olivia - not his. Peter is especially influenced by finding out about Henry, the son he had with Fauxlivia, which shows him the profound consequences of being with the wrong Olivia. But he's completely wrong, I'd say, about the Olivia in front of him not being his - certainly this conflicts with what the EBO said above.
In additional to this Shakespearean twist, we also learned a lot about the EBOs and some answers about the very basis of Fringe in this episode. The Observers are humans from the distant future. They're here to observe their beginnings - their emergence from us - which apparently spring from Henry, the son Peter and Olivia are supposed to have, but did not, because of Fauxlivia and the war of the realities triggered by Walter's kidnapping Peter. We further learn that Walternate would have hit upon the cure for Peter's illness himself, had not September accidentally distracted him at the wrong moment. This in turn led Walter to go across to the alternate reality to kidnap Peter, to save him, which was the action that got all of Fringe going.
September has been trying to set things right ever since - this presumably being Peter from the other side (the Peter we know) with our Olivia. (The rest of the Observers want to set things right, too, but they see things differently from September. I wonder what they think of the current Olivia, who has now remembered Peter?) Tonight was thus a big step forward in our knowledge, but backward in the two getting together. But Fringe is itself a palimpsest, and it's just a matter of peeling away enough false surfaces to get to this truth.
... Fringe 4.2: Better and Worse Selves ... Fringe 4.3: Sanity and Son ... Fringe 4.4: Peter's Back, Ectoplasm, and McLuhan ... Fringe 4.5: Double Return ... Fringe 4.6: Time Slips ... Fringe 4.7: The Invisible Man ... Fringe 4.8: The Ramifications of Transformed Alternate Realities ... Fringe 4.9: Elizabeth ... Fringe 4.10: Deceit and Future Vision ... Fringe 4.11: Alternate Astrid ... Fringe 4.12: Double Westfield / Single Olivia ... Fringe 4.13: Tea and Telepathy