Thank you for the posts. I have posted it again with some improvement and the paragraph.
My theory is related to Daniel’s statements on and about the island and on Desmond experiences: I assume that the island is travelling in time because it is moving faster than light.
At the end of this long argomentation about the physics of the island, I will explain why, as someone else does, I think that Mrs. Hawking works with the MIB, to make sure that only the alternate reality remains, and the original timeline cheases to exist.
First of all, (in "Confirmed Dead") Daniel paid attention to the Island's unique physical properties, observing that the scattering of light on the Island seemed unusual.
It recalled me the idea of the velocity of light, that is assumed to be the faster velocity permitted by physics laws.
At the same time if we assume that faster then light travel could exist, then faster than light travel is equivalent to time travel, as you can read here:
http://www.theculture.org/rich/sharpblue/archives/000089.html
The first and most convincing proof that in the show the island is travelling faster than light is Daniel's timing experiment.
I'll resume it here:
First the beacon was mounted by Daniel on a tripod with a clock on it.
Regina was asked by the physicist to launch a "payload" from the freighter.
Regina did so and began counting down the geographic arrival of the payload in rapid 5-kilometer-steps, starting with 40 km. But when she reached zero, the rocket had not reached the beacon. Regina said that it was "weird" while Daniel responded that it was "far more than weird".
The rocket did eventually arrive a while later.
Daniel compared the time on a digital clock from the rocket with the one from the tripod he had set at the beginning of the experiment and saw that they were different by 31 minutes, 18 seconds. The clock from the rocket stated 03:16:23, while the clock of Daniel stated 02:45:03.
Daniel commented that the result was "not good".
This experiment could easily recall some of Einstein statements.
In his famous work on special relativity in 1905, Albert Einstein predicted that when two clocks were brought together and synchronized, and then one was moved away and brought back, the clock which had undergone the travelling would be found to be lagging behind the clock which had stayed put.
Einstein considered this to be a natural consequence of special relativity, not a paradox as some suggested.
As for the clocks on the show then, Daniel’s clock was slower than the other, so it must have been the clock moving very fast, back and forward, despite seeming to be still, fixed on the ground of the island. That’s why I think that the island is physically moving through space, and faster than light.
As I said, the result of a faster than light travel is equivalent to time travel. Regina and Daniel could simultaneously talk, maybe because the island is moving through space, but at such a velocity that exceeds the velocity of light, causing time travel (I’m not really sure about the physical explanation of that).
Just after this experiment Daniel must have understood that the island was moving faster than light, as he must have expected it to do, probably due the massive amount of energy that is contained in the “pocket” underground.
He maybe knows about it from Mr. Widmore, who sent him on that mission, or maybe he as gained this knowledge during his studies in Ann Arbour in the seventies, (because I assume that these events already really affected this temporal line).
Daniel said that the experiments results were “far more than weird” because the faster then light movement of the island is something challenging the classical laws of Physics and implies the dismissing of the law of causality, as I will discuss further.
Then we have another proof: the death of the doctor of the freighter.
On day 97 on the Island, his body washed ashore, with his throat slit and stitched facial wound.
Daniel contacted the freighter asking what has happened to the doctor. Bernard decoded Omar's response which stated that the doctor was fine, and Daniel was very disappointed of them knowing it.
This could not be only because of the so called “time difference” between the Island and the freighter.
It is an important violation of the causality.
The Doctor can’t be dead if he hasn’t already been murdered by Keamy.
This is only possible because inside the “circle” of the island the time is affected by the faster then light movement, hence a consequence could manifest inside the circle even before the materialization of his own cause outside the circle.
I'm speaking about a “circle” because immediately after Ben turns the frozen wheel, a loud noise is heard and a flash lights up the sky above all the survivors who are still on the island and the island vanished for those who are on the Freighter and on the helicopter. On the Zodiac, Daniel, noting that they can still see the island, says that the raft "must have been inside the radius." Speaking about a radius implies that there is some kind of circle that includes the island, and that is moving faster than light and travelling in time.
So the faster then light movement of the island makes the time in the island behave in a different way than it is in the rest of the world, causing some paradox, similar to the twin paradox of physics.
In physics, the twin paradox is a thought experiment in special relativity, that now is proved to be real, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth.
That’s why, in my opinion, Daniel, travelling in time and being around 2002 on the island, talks to Desmond out of the hatch and asks him to go and find his mother, and simultaneously the 2007 Desmond wakes up on his boat and remembers this as a memory of his past: because in that precise moment on the island the time is moving slower than on the rest of the world, so the simultaneous connection in the real world would be with the 2007 Desmond.
At that time, around five years previous, Daniel wondered whether it would be useful to talk with Desmond, and first he was thinking that it wasn’t, preventing Sawyer to talk with him; at this time Daniel was convinced that time is like a street; "people can move forward on that street, they can move in reverse, but they can not ever create a new street. If someone tries to do anything different, they will fail every time".
His famous statement was: “Whatever happened, happened.” And I’m pretty sure that this was his mother's (Mrs hawking's) idea.
But then Daniel looked at his journal, and he changed his mind- Maybe he noticed his notes and remembered all about Desmond time skipping to 1996; then he decided to talk with him. In that occasion Daniel told him that "the rules don't apply" to him, that he is “uniquely and miraculously special”. Maybe the rules which Daniel is thinking about are related to the fact that time travel trough faster than light travel could be very dangerous, and could cause the death of the person who proves it.
Daniel himself have suffered serious consequences (as we thought) after years of time-travel experiments, but they may also be the consequences of his previous time skipping on the island, so that he had lost his memory and skills after his journey to the island and his skipping back and forward time. I say so because in some moments he recalled bits and pieces of his past experience on the island, that’s why on 2004 he cried and became upset looking at the fake Oceanic wreckage discovered under the water.
Now, Daniel looks at his journal and remembers that Desmond has already experienced time travelling, he has met him at Oxford and changed the chain of events, and he has found his own constant in Penny, so he knows that he could afford an experience like having a memory from the future and making things happening in his present, changing the chain of events. This really changes Desmond future, as we will talk about later.
The “incident” caused by the Losties on 1977 could have discharged the island energy and make it travel trough time again, resetting everything that was linked to the island after 2004 (outside world timing) making in this alternate reality the island to be submerged by water. So Charlotte, Daniel, Charlie, and everyone are not dead, because everything that happened in the island after 1997 was prevented to be by the bomb.
But at the same time, the "incident" didn’t prevent the island to still be there, in an alternate reality reuniting 1977 Losties with the others survivors of Ajira flight.
But we don’t know still what is it the actual timing of the island in this timeline. We know from Widmore words that in the outside world is 2007, because Desmond had been shot by Ben, and he has a son and he and Penny are safe, so the original timeline still exist; but we don’t know nothing about the exact island timing at that point.
So maybe after the “incident” the island that isn’t under water is continuing to come back in time, or time travelling, because of her own faster then light movement produced by her own magnetic energy.
Could be that the energy must be discharged again in some way, or people linked with the island could somehow dead in the simultaneous timing of the real world.
That’s maybe why Mr. Widmore had brought Desmond on the island on external world 2007, claiming that if Desmond doesn’t make the “sacrifice” that he is asking him “for the sake of all of them”, Penny, his son and everyone will be gone forever.
That’s because actions on the island could affect the “simultaneous” future of the rest of the world, because they are happening before in the particular time-space of the island moving faster then light. So, if Desmond doesn’t do the discharging of the fail-safe key again, surviving, in the real world he wouldn’t be able to have a son with Penny.
So it is possible that the action that they do in the present of the island affect the ones that happen to them in the real space and time, in the original timeline.
But if the “incident” on the island has created a different chain of event where the plane doesn’t crash and safely lands in LA, we see that Msr. Hawking knows a lot in both, and in the alternate reality she knows that this two alternate reality could mix with each other.
Could be that she knows that Desmond's travelling between this two timeline using faster then light travel is creating what she calls "a violation". If in the real world faster then light travel implies causality violation, as I said before, this may be exactly the violation that Heloise Hawking was referring to speaking to Desmond travelling in her 2004 alternate reality.
Desmond travelling faster then light implies him travelling from the timing of the island (that is still not clear to us, but it is likely to be slower then the other) to his own alternate 2004 timing, in the reality that appears only after the first "incident".
I’m sure that Desmond is only one, and he is travelling between the two realities; the proof is that he fainted in front of Penny and then he wake up again on the island, so he is not living two "lives" or "realities", but just one, and he is of course making some “violation”, as Heloise stated to him.
Maybe Heloise knows that at that at some point he will marry Penny and have a son with her even in this alternate reality, but she knows also that he is not “ready” to accomplish his path, or that he is not suppose to have knowledge of the alternate reality.
So she tries again to stop him, as she has done before, in “Flashes before your eyes”; could be that she, living for a long time on the island, and being connected with Jacob (or with the Man In Black, who knows?), had know the important role of Desmond, and has interfered with his life many time, even previously, when Desmond enters the Convent, cause we know that she is a friend of Brother Wallace, because she is with him in a photograph on his desk, remember?
My guess is that she wanted to use Desmond to prevent the death of his own son in the alternate reality, maybe following the instruction of Jacob or of the MIB.
Could be that she shifted to the MIB side, having been told from him that she will have her son back.
Actually it makes sense to me, because this is the strategy that the MIB always uses: temping people telling them that they will meet again their beloved lost. Maybe the plan of the MIB is to make the alternate reality the unique reality, and doesn't make it to annihilate running into the other one, at some point.
My opinion is that Mr. Hawking was using Desmond all the time to accomplish her (or the MIB) plan, and preventing her son to die by her hand.
When she went visiting Desmond at the hospital she stated that “for the first time in a long time she does not know what will happen next” because Ben, travelling trough time and violating the rules, had shot Desmond, and this was not suppose to happen in that reality.
Desmond was so important to Mr. Widmore because he is the only that could discharge the island again, and to her because she was feeling sorry about the fact of Desmond being in the harbour looking for her, and not being safe sailing in the see. I think that after Daniel's death the path of Mrs. Hawking and that of Mr. Widmore split for good: she desided to help the Losties detonating the Hydrogen bomb to reset their timeline and prevent his son to be killed by her; he decided to do everything possible for the "sake" of the island, as he always states.
That's why she hit him when he says "he was also my son". Because is she didn't help them to reaching the bomb, then his son will be gone forever; now instead, there is an alternate reality, of which they both are aware, where is son is fine and follows his path. So I think that now Mrs. Hawking is working to annihilate the original timeline, as the MIB maybe wants, while Mr. Widmore is working on mantainig the original timeline where the island is safe and it's not underwater. Even if it signifies doing some "sacrifices" like loosing his son, his daughter's love, and risking the life of the husband of her daughter.
So now I bet that we have Widmore and Jacob (through his truly candidate, Hurley) working to mantain the original timeline on one side, and the MIB and Mrs Hawking, with the alternate reality on the other. I'm not sure which one I would like to win, actually.
Finally, both Ben and Mr. Widmore, and indirectly Mrs Hawking, referred to the rules. That Widmore left the Island regularly and had a daughter with an outsider, was considered by Ben against the rules. Killing Ben’s daughter was considered by Ben a change in the rules made by Widmore, so he decided to broke the rules himself, turning the Frozen wheel, and travelling back in time to 2005 and makes Sayid kill a large number of people off the island; then he broke the rules again when he came back to the Island after turning the Frozen wheel.
Maybe the “rules” are that you cannot kill anyone in the outside world, neither on the island, because this could cause a "violation" in time course and it could make things happen in a way that it’s unpredictable to any one, due maybe to "course corrections".