From MangaHelpers:

When Takuma was a kid, he had an experience involving a mysterious light, but he eventually believed, as all the adults he had told, that it never really happened. He figured he must have gotten reality and imagination mixed up. Now he's a college student, and he has a crush on a philosophy student. One day, a young girl named Sora collides with him from the sky. She seems to have some connection with his past, and claims she is here to expose the lie of the world. In fact, Takuma feels like he can remember two worlds, one where he and the philosophy student were dating, and the current one where they are merely acquaintances. Could it be that the other world is not his imagination, and someone is warping the world for their own ends? [tethysdust]