Our protagonist (I'll call her Juni, although in my mind it was never Juni but some human girl) had a little brother, who drowned when she was young. When she's a bit older she meets a scientist who's working on time travel. She realizes this could be her chance to saver her brother, and starts working with the scientist. Eventually they get there, and Juni volunteers to use the time machine to travel to the past for the first time, to the day her brother died. Unfortunately, there are some calibration errors and Juni ends up being sent to a time long before humans even existed. This is where the actual level starts.
The machine isn't perfect when it comes to spacial precision so the return portals aren't exactly where you arrive, but when you enter a portal you arrive exactly in the same place. This was obviously made to fit the game better, but I was even gonna make a book about all the rules and have it in the game :P
Then there's the whole level, and you go to the future. When you arrive, you realize that something horrible must have happened, because everything is deserted and seems to have been abandoned in a long time, even though only a couple years have passed. But when Juni comes back, she doesn't mention it to the professor and gives him the charged power core.
(I actually had all this pretty much ready to go but removed it completely because I wasn't happy with it anymore. Kinda wish it was here in this version now.)
Now this was the only part that I never got to do at all, the endings (except for the alien one):
Ending 1:
With the charged power core, Juni can travel to the past again, this time with a better calibrated machine, and try to save her brother. She arrives at night, passes by her house, maybe sees herself asleep if you explore, etc. She gets to the river, which has a bridge over it instead of the boat we see in the present, her brother is there, sitting on the rail. When Juni steps on the old bridge, her brother is startled and falls in the river. Juni jumps in to save him, and ends up accidental jumping through the return portal. Wow, this part sounds stupid now that I'm typing it all out. So basically Juni kills her own brother in a Terminator 1-like turn of events, triggering the events in the game in a cool/cliché time loop. Also for some reason she can't try to do it again.
Ending 2:
The alien ending present in the game, unlockable in the future when you're supposed to get the charged power core. You talk to some aliens who are there to keep you from messing with the space-time continuum, they give you the option to live in that virtual world where you didn't kill your own brother, and she would be unaware of it, so its kind of real. You need 2 of the keys to get this ending.
Ending 3:
After getting the charged power core, instead of going back to the scientist you visit an angel-like figure who offers you a cool power (the eye). This somehow lets you save your brother, didn't really get to decide how. You need the other 2 keys to get this ending.
Ending 4:
After getting the charged power core from the future, you return to the present and destroy the power core that's still charging (this would mean that the charged power core couldn't exist). Apparently, this is a single timeline world, so the universe collapses in on itself. You talk to God, who is pretty pissed off at you. He starts making a new universe, without Juni in it, and you just chill with him.