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Fridge Horror: Vox spent thousands of years alone in the underground ruins completely alone, save for one Eloi who managed to escape the Morlocks. We then see that the Eloi died of old age and until Alex showed up, Vox was probably going to spend eternity in the same room as his only friend's corpse, all the while unable to bury him.
Fridge Logic: If the Morlocks can no longer go in the sunlight, how come the raiding party took place in the middle of the day? The only explanation is that the Uber-Morlocks as albinos aren't capable of returning to the surface and they're keeping the other castes underground on purpose.
He can't go back and save his girlfriend because then he'd have no reason to go back and save her. Then at the end of the film he goes to a bad future, then goes back in time and prevents it which he can do because... ?
He couldn't save his girlfriend because it would remove his reason for creating the time machine, but could stop that future from occurring because he was just observing it.
But remember that he wouldn't be able to observe it in the future if he prevented it from happening in the first place. The same effect, only the other way round.
Ah, but! Saving his fiancée in the past would be an action that affects his present. Observing one possible future where he is a temporal outsider, then going back a bit before that to change it is a different thing entirely. He can't change his past, but he can change the future. If his fiancée hadn't died, he wouldn't have built the time machine or used it like he did, so she would've died, so he would've saved her, so she would've died, and so on. Paradox. However, once he has access to the time machine he's free to travel to the future, see how it goes, then travel back and change it in whatever way he wishes so long as it doesn't affect anything that happened to him before he first turned on the time machine. Everything before he activated the time machine is immutable because if things were different, the time machine wouldn't have come to exist. Everything after that is free game because nothing in the future is essential to the creation and operation of the machine.
Although Fridge Horror sets in when you realise that without the Uber-Morlock's influence, he states that the Morlocks would exhaust the food supply in a matter of months... which looks very much the Morlock-Future Alexander found himself in. And we know they have other colonies. invoked
But then he fixed it all with a big time explosion. Time explosions are special; they can destroy all Morlock colonies simultaneously without affecting the geology enough to dislodge the precious Eloi towns precariously stuck to the sides of precipices. Time explosions are funny that way.
He wiped out the Morlock colony that lost the Uber-Morlock that he killed. The others have their own Ubers, so they won't exhaust the food. Simple.
He couldn't save his girlfriend because then he would be creating a paradox, however he can influence the future because he's from the past and the time machine itself gives him greater insight on what will happen as well as how to stop and/or change it.