When Haruka, Yuu and their friends decided to go ghost hunting, they had no idea the "ghosts" they'd find would turn their lives upside down. Black-clad and wielding quantum powers, these knights from the future are after an artifact of immense power that they hope will save their dimension from destruction: the Dragon Torque; and Haruka seems to be the key. As factions within the knights violently disagree on how to proceed, Haruka and the gang are caught up in a fight with the Shangri La, in an existential battle where fates of entire universes are decided.
In the early 21st century, insectoid organisms are invading the galaxy, searching for new stars to house their young. Mankind's only defense lies with space cadets such as Takaya Noriko, daughter of a celebrated admiral killed in battle, and Amano Kazumi, the top of her class. With their skill and the power of the mecha known as GunBuster, the girls must help fight to protect the galaxy from total annihilation...
Gunbuster and Noein are character driven stories set against a background of science. While the main plot concerns itself with fundamental physics concepts like special relativity and quantum mechanics, the greater dramatic impact lies in the relationships and personal lifes of the cast.
Isaac Asimov once said, "sci-fi is not a kind of fiction, but a wide-spread genre that includes many genres in itself" and this two series prove him right. Noein and Gunbuster are equal parts hard science fiction and slice of life, so anyone who likes either should enjoy both.
Welcome to a world in which memories can be transferred from body to body; old painful memories can be removed and replaced with new ones, and the poor sell their bodies to the rich to survive. Waking up one day, Kaiba finds himself in a strange place with no memories of his past and a mysterious hole in his chest; the only clue as to his identity is a locket with a picture of a girl hanging from his neck. Armed with this token, Kaiba must now travel across the galaxy to discover who he is and what the girl in the locket means to him; however, his journey will bring him into contact with many people whose lives have been tragically affected by the manipulation of memories. All too soon it becomes clear that something is very wrong with this world…
Yuki is a disaffected middle school boy who has no dreams or goals in life; in fact, the only thing he has is his diary. Writing down everything he observes and documenting every thought, the young boy uses it as an outlet for his imagination. One morning, however, Yuki wakes up to find his cell phone filled with diary entries for the next ninety days. Thinking nothing of it, he continues his morning until he begins to realize that everything on his phone is rapidly coming to pass, and it isn't just mere coincidence. Now, Yuki suddenly finds himself thrust into a survival game against other future diary owners to become the new Lord of Time.
Both of these anime feature heavy reliance on understanding of causailty and time travel - albeit more relied upon in Noein.
Mirai Nikki includes the linear theory in which when you go back in time you and your past exist in the same spacetime, being able to create a "new future" in which you can both cause and interact with, as well as interact with your past self - something that would clearly cause a paradox, but that's neither here nor there...
Noein uses the theory where there are multiple parallel universes existing at the same time in the same space but out of phase, so as to remain separate. One can visit the paralell world - be it in the future or the past - and can only interact with the surroundings or oneself if in phase with the parallel universe.
If you can understand one you will understand the other.
Although the worlds of heaven and earth used to exist as one, they are now seperated by the boundaries of time and space. As the towers of heaven begin to fall, Munto, the magical king, descends to earth in a seemingly futile attempt to find the chosen one who can stop the worlds from being destroyed.
Munto and Noein are masterfully directed features that exploit a similar premise for all it's worth. Both juggle parallel stories about the daily life of children and an otherworldly apocalyptic battle that, in lesser hands, would have collapsed under their own weight. The other selling point is the visuals. Both features are highlighted by stylized animation, lavish designs and excellent storyboarding.
If you're looking for something creative, both in plotting and design, Noein and Munto are for you.
Ayato Kamina may seem like an average boy in a devastated world, but after being captured by TERRA, a military organization set on saving the world from the Mu, an alien race set on "tuning" the world, he realizes he is an instrument in deciding the fate of humanity and piloting RahXephon. Not only is Ayato the only person who can control the mecha, but he also has a terrible fate of his own. Holding onto memories of his old life and grasping to keep his own humanity, he must struggle in this new world and realize his true potential with RahXephon.
Noen and Rahxephon where somewhat similar, but the problem is I'm not sure why. Well there was this time travel theme thing, but that is definitely not the only similarity. If you seen one you should check the other and find out yourself what makes them similar.
P.S. In both cases its not exactly time travel, but shhhhh don't tell anyone.