Ways to save Emma that contradict the whole premise of this movie
The idea that you cant change the past is just ridiculous and contradicts itself in a situation where you can go back to visit the past. By going back in time you already change what did happen ( even if a little ), so you already successfully did affect the present.
You never actually know the past, you only observe it form one point, by this simple fact we can create infinite scenarios in which saving emma is possible and in which she can both die and survive.
1. Go back in time and give the younger Alexander design for the time machine
This way we remove Emma from the equation allowing for her to be saved without braking the original loop.
2. Kidnapping Emma into the future
Emma still goes missing but survives, we dont break any rules the movie introduced
3. Go back in time, kill the robber, take his place, use blanks/poison
Another option that allows us to keep everything as it was, but let Emma survive, Alexander still has a reason to make the time machine since he dosnt know she didnt really die.
4. Go into the future, get tech advanced enough to revive someone who died form a bullet wound
Another option that allows her to both die and survive, we brake no rules of this movie.
You could go on like this for a long time, only shows how bad the script for this movie was.
Honestly everything about this movie was idiotic, i wont even go into teh second half of this flick.