Well, Ms. Hawking clearly stated that there was time travel. Also, the producers have also stated that time travel is involved, and that it may not be in the standard way people are thinking about time travel (i.e., people on spaceships flying through wormholes to the other side and then seeing mirror images of themselves. It is time travel nonetheless, meaning the ability of a person to observe another point in time, while being armed with facts that you still have that come from the past or present). It is one thing to time travel with no knowledge of the past or present, it is quite another to move from one dimension to the next, armed with facts that you know will happen or have happened to complicate your journey even more!
The case for "Mind Time Travel" has been clearly represented in this show and there have been multiple cases of characters and writers supporting this theory. Being able to observe (and alter) events that occurred in a different time has been shown and you can believe your eyes, the show is telling you what they are doing, whether you want to believe it or not.
Some examples:
-Ms. Klugh- "have you ever seen Walt in a place he was not supposed to be in?"
-Walt appearing and reappearing in places where he wasn't originally.
-The whole "Jacob" incident (appeared to be a mind time traveler from another era, that was 'trapped' in a dimension he clearly didn't belong in or want to be in)
-almost the entire episode of Desmonds experiences in "Flashes Before Your Eyes" (which, by the way, the writers were quoted as saying after this episode that this was a major piece of how the show will be explained going forward)
-the concept of 'flash forwards' and 'flashbacks' as a major vehicle for the show
-the whispers, which are possibly travelers who are trapped or are observing from afar 'in between' two worlds
-Cooper who mysteriously ends up on the island, with some lame excuse (If you actually believe he was "kidnapped" and transported to the island on a sub, you really need to watch the show more closely)
-"Only fools are enslaved by time and space" as a major talking point from the wacky 'Room 23' video
-the island as a Pandora's box metaphor (not really a metaphor)- 'whatever you wish for you can get' (explains how Cooper and other things have come to the island, the island that 'can't be seen by God himself'
-Cindy's proclamation to Jack in the cage "We're here to watch"
-The new revelation from the spoiler for Season 4 [spoiler](don't read if you don't want to be spoiled) from Dark UFO
Posted by DarkUFO Episode 4.02 will be called "Confirmed Dead".
If they are dead, how can they be alive? Because they are dead in one time thread, but alive in another[/spoiler]