In my last theory "Desmond and Changing the Future" I included Dr. Chang as one of the people who may time travel to 2007, but that was a mistake because obviously Dr. Chang needed to have been present in Dharma, post-incident to create the Swan orientation video.
Also, I'd like to add an addition to my theory:
The Fail-Safe
When Sayid & Jack found Jughead, they removed the core, and it was the core that was detonated at the Swan site in the final episode of Season 5. The rest of Jughead was still a working bomb, so I think Radzinsky and Dr. Chang found the rest of Jughead and sealed it up behind the wall of concrete inside the Swan Station. Then they rigged the fail-safe key to detonate the rest of Jughead in case the button wasn't pushed. The effects of not pushing the button were equal to that of Radzinsky's original drilling into the pocket of energy. When Desmond turned the fail-safe key at the end of Season 2, this was equal to Juliet detonating the Jughead core at the end of Season 5. When Desmond turned the fail-safe key we know he time traveled (at least in his consciousness), so the same happened to Jack, Kate, Hurley, & Sayid. Instead of actual time traveling (via the Orchid), they consciousness traveled like Desmond, except instead of Desmond waking up naked in the jung! le because his body had never left the island, just his mind, they actually died. That's right, I think that Jack, Kate, Hurley, & Sayid all really died (just like Alpert said they did) when Jughead exploded, but they also consciousness traveled. And not to 2007, like I originally said in my last theory, because one can only consciousness travel back in time to one's own consciousness, so I think they went back to the Ajira Flight to the point right after they originally time jumped. So somewhere in the events of 2007 with Sun and Ben and Fake Locke are hiding Jack, Kate, Hurley & Sayid. I'm amending my last theory, not to include Juliet, Sawyer or Miles in that because they weren't originally on 316. Juliet most likely died because of her close proximity to the explosion and Sawyer & Miles stayed on the island with Dharma.
Also, I'd like to add an addition to my theory:
The Fail-Safe
When Sayid & Jack found Jughead, they removed the core, and it was the core that was detonated at the Swan site in the final episode of Season 5. The rest of Jughead was still a working bomb, so I think Radzinsky and Dr. Chang found the rest of Jughead and sealed it up behind the wall of concrete inside the Swan Station. Then they rigged the fail-safe key to detonate the rest of Jughead in case the button wasn't pushed. The effects of not pushing the button were equal to that of Radzinsky's original drilling into the pocket of energy. When Desmond turned the fail-safe key at the end of Season 2, this was equal to Juliet detonating the Jughead core at the end of Season 5. When Desmond turned the fail-safe key we know he time traveled (at least in his consciousness), so the same happened to Jack, Kate, Hurley, & Sayid. Instead of actual time traveling (via the Orchid), they consciousness traveled like Desmond, except instead of Desmond waking up naked in the jung! le because his body had never left the island, just his mind, they actually died. That's right, I think that Jack, Kate, Hurley, & Sayid all really died (just like Alpert said they did) when Jughead exploded, but they also consciousness traveled. And not to 2007, like I originally said in my last theory, because one can only consciousness travel back in time to one's own consciousness, so I think they went back to the Ajira Flight to the point right after they originally time jumped. So somewhere in the events of 2007 with Sun and Ben and Fake Locke are hiding Jack, Kate, Hurley & Sayid. I'm amending my last theory, not to include Juliet, Sawyer or Miles in that because they weren't originally on 316. Juliet most likely died because of her close proximity to the explosion and Sawyer & Miles stayed on the island with Dharma.