In the new season of Lost (stop reading now if you haven't watched through the sixth season premiere yet and don't want to be spoiled), the writers have introduced a new storytelling device. The first three seasons filled out the backstories of the characters by means of alternating between the current story and flashbacks, usually from before the characters were on the island, focusing on a different character each episode. The fourth season changed the device to flashforwards. The main story continued where it had left off the previous season, but in most episodes it alternated with what happens to some of the characters after they leave the island. At the end of the season in the main story, we see the events that lead up to them leaving the island.
The fifth season splits in two pieces. For the first half of the season, we have the continuation of the characters who remain on the island, as their location in time becomes unstable, and they shift from one time period to another across various periods in the history of the island. This is alternated with the characters who left the island, as they move toward returning. Mid-season, we see those characters arriving, and the time-shifts end. The characters who had remained on the online got stuck in 1974, and the characters who returned to the island have arrived, some of them in 2007, three years after they had left, and some in 1977, three years after their compatriots had arrived in the past. At the very end of season five, we see them initiating a plan to try to change the past and prevent themselves from ever having arrived on the island. The fifth season ends as it looks as if they have achieved what they intended, but we see no effects from it.
Now the sixth season has begun, and the new storytelling device is neither time travel, flashbacks, or flashforwards. They're calling it flash-sideways. One storyline involves the original characters in the aftermath of their plan. They seem to be in an unchanged timeline, back in 2007, where they will presumably meet up with the other characters who arrived on the island in 2007 as planned. The new storytelling device adds a story about people who look just like the characters we already know but who have led very different lives, as if the world has been different since 1977. The plane doesn't crash. The island seems to be underwater. We see small differences, some of them attributable to the island's demise in 1977. Hurley is lucky rather than unlucky. John Locke isn't depressed, and he at least seems to indicate that he went on the walkabout. Jack is nervous and Rose calm. Charlie is suicidal rather than just addicted. Desmond is on the plane rather than on the island pushing the button. Some characters who were on the plane are not there now (e.g. Boone couldn't get Shannon to come back with him). I'm guessing that some of the slight differences in personality or life-path are due to Jacob not meeting up with some of the characters (whatever it is he did to them by touching them), and some from other aspects of the island being changed (the numbers not being broadcast for Hurley to encounter them, the island not being there to be found by Desmond or maybe even Charles Widmore not being alive to send him on his trip to begin with).
What seems to have happened (and I'm guessing we might end up being surprised to find out something else is actually going on, judging my the executive producers' cryptic comments about this) is that the time-traveling characters did something in 1977 that didn't change anything in their own timeline but did cause a different timeline to take a different path. This sort of fits with what J.J. Abrams and his associates have done with time travel in another franchise, namely the latest Star Trek film. The time-traveling characters in that movie traveled back to the past and changed it. But the past they changed wasn't their own past. It was the past of a different reality. That's the similarity, but there's a big difference with Lost. The world Nimoy-Spock ends up in is another reality, the changed one. He's there with his alternate-past self. In Lost, the characters don't see any change whatsoever, even though they're present when they presumably cause the change. So the cause of the change is in their reality, and it has an effect in a different reality that they never enter. The Star Trek version involved the time-travelers simply going to an alternate world and causing the different path of history in that other world, while their past remained the same without them in it.
The problem with the Star Trek way of doing it is that all time travel would have to be really just alternate-reality travel in the cases when it seems to be past-changing, but then why would some time travel be that and others be going to your own past (the ones where you don't change anything)? Why would events after you arrive (i.e. whether you change anything) determine whether you went to another world, when you've already been wherever you are the whole time before those events? So it must be that all time travel is alternate-reality travel to avoid such a problem.
The Lost way of doing avoids that problem, because you go to your own past, but anything you do that you might think changes anything has no changing effects in your own reality but does in the other one. The problem now is that something you do in one reality causes a different reality to have a different history, when nothing in its own timeline causes the difference. But if you don't actually do anything different from what had ever occurred all along in your own reality, why does an action you don't even do have an effect that makes the other timeline different? So something's really confused if the story the writers want us to believe is really the explanation for the flash-sideways.
Robert Orci explains the rationale for treating time travel as alternate-universe travel in this interview, which I've commented on previously. He rightly opposed the idea of changing the past. Damon Lindelof, who worked on that film with him, is one of the two executive producers of Lost who run the show (and both projects are under J.J. Abrams' ultimate leadership). Damon Lindelof and Carlton Cuse have said several times that they opposed time travel stories with paradoxes, and presumably they mean the kind caused by changing the past. Here is one instance from Lindelof:
We're not going to tell you that we're against bending the time-space continuum. We are very for it. Carlton and I are PRO time-space continuum bending! But we're ANTI-paradox. Paradox creates issues. In Heroes, Masi Oka's character travels back from the future to say, ''You must prevent New York from being destroyed.'' But if they prevent New York from being destroyed, Masi Oka can never travel back from the future to warn you, because Future Hiro no longer exists. Right? So when we start having those conversations at Lost, we go, ''This show is already confusing enough as it is.'' To actually have characters traveling through time has to be handled very deftly.That sounds to me as if they're committed to having stories that don't change the past despite allowing travel to the past (which must be what they mean by bending time). That does in fact seem consistent with everything they've done in the show so far with genuine time travel. Anything time-traveling characters do is something that always had happened that way. The only possible exceptions are the few instances of consciousness-time-traveling, but even in those the small variations are explicitly said to change nothing, since attempts to change things fail to make a significant change (and they were pretty much done with those before they got to the genuine time travel, so they may have solidified their view more fully by then, and it's also possible that those instances of consciousness-time-travel that had slight changes to the past were travel to alternate timelines anyway).