New research by quantum physics infers that it may be possible, in theory, to time travel. However, the scientists believe that one could only go back in time.
LOST had a bad mix of time travel events. Did the frozen donkey wheel create the time travel episodes? Or was it the containment field from the Swan station? Or was it all a red herring by the writers?
The island's "rules" lacked clear continuity. In the Star Trek universe, Gene Roddenberry set down a specific set of rules, including science fiction elements, which carried the series through to today. LOST's showrunners did not take the time or have the patience to forge a realistic, compelling and believable sci-fi doctrine.
The weird science is explained by the strange electromagnetics of the island, inferring that those island experiences are in a different sequence in time and space. When Sayid gets the radio working, they hear a radio broadcast from the 1940s. When Sayid, Frank and Desmond left the island, they experienced events in a different sequence. When Desmond survived the Swan implosion, he began seeing future events. When the freighter doctor's corpse washed up on shore, it was out of sequence with the real time on the freighter (where he was still alive).
In the orientation film for the Orchid station, scientists talked about the island allowing DHARMA to conduct experiments to move rabbits ahead in time and in space. When Ben and Locke turned the frozen donkey wheel under the Orchid station, they found themselves 10 months in the future in a desert halfway around the world.
When the survivors left behind after Ben's wheel turning
experienced a time travel change, there was a blinding purple flash
(similar to when the Hatch imploded). After Locke fixed the wheel, there
was one last flash, but this time the flash was bright white, rather
than purple. In all instances, the travelers experienced severe head
pain, most likely caused by the extremely loud noise occurring during
People who weren't affected by the time travel appeared to be
unaware of the blinding flash and loud noise. For example, Danielle
didn't react to or mention the noise or light before Jin disappeared,
and when he reappeared in her future, she thought Jin was sick because
he disappeared.) It was the inconsistent treatment of people in the same situation which left the story weak and confused. There was no justification for allowing only certain people on the island to time skip while others did not.
For there to be a rational explanation for the differences in time travel on individuals, one must take into consideration that it may not have been time travel at all. How one experiences the passage of time is through consciousness and memory. If one can take an individual and alter, through mind control or neurologic drugs, their consciousness and memories, one could instill false memories including false time. It get backs to the possibility that much of LOST's story is not based in reality, but in the altered mind, memories or subconscious of the characters.