The more I think about it, the more I think time travel on the island is made possible by an alternate dimmension. We forget that the characters dont travel through time, the Island moves through time. When Faraday was telling the Losties (Left Behinders) that he wasnt sure if the island was traveling or they were traveling. I think at that time, the Losties were moving WITH the Island (the problem which needed to be corrected) and this is why Sawyer could see Aaron/Kate/Claire, he had a window of the other dimmension. Whereas Kate and them probably would have just heard whispers. In fact Kate and them, were not moving with the Island, or else they would have been seeing the flashing lights too. So...there are different versions of the Island, not different versions of the characters, UNLESS the characters are moving WITH the Island. The whole concept of "moving the island" is not in place, but in time. When the O6 came back, they landed on a different Island then the one Sun landed on. Hence two dimmensions, which make possible the barracks looking differently than if you were looking at it from a "one timeline" perception. This would make sense according to Hegel, who said, "history engages events as particular products of their time and space." Time and Space are not linear, they are multi-dimmensional. Heidegger, another german philosopher who studied time and space, said "Space is time, that is, time is the truth of space"
If we're talking about time travel, we cant leave out space, as space is the other side of the equation. For more on the philosophy of time and space, this is a good place to start: