Sean Hollyman said:
I'll try and explain it using a scenario.
So there you are, sitting on a bench and you're pretty hungry. Suddenly your future self from 2016 pops in and gives you a sandwich. Then he leaves.
So you live your life normally until 2016, and you realize this is the day that you're supposed to go back and give yourself the sandwich.
What would happen if you choose not to?
It's already happened in your past, but how can it happen if you don't go back and do it?
One of two things would happen. It depends if you're on the side of linear time or nonlinear time.
In a linear time you would suddenly no longer have the sandwich, never of eaten it, perhaps not even remember it. A good example would be, You went back in time to preserve and reconnect your left hand that you lost in a circular saw 2 years ago. You fix your past self and warn him to warn his own past self, but then he forgets 2 years later. The hand should instantaneously be gone. This might occur after the 2 years or it might take till you die thus making it impossible to save you hand in the past.
In nonlinear time you'd travel into the past and altered history. However the present that you left has already written all of that history so it will remain unchange. After you give yourself the sandwich and return, you'll return to an alternate timeline that has you eating that sandwich 2 years ago. There would also be two of you. You, the time traveler, and you the one you visited in the past, now grown 2 years to your present.
The you who traveled back in the first place has in no way consumed this sandwich as that part of history was already written when he left. However, the you in the past that has grown 2 years did consume it. Now if the past you forgets to go back into the past and give yourself a sandwich nothing should happen. That history in this new timeline has you eating the sandwich. So you don't have to go back, you'll only run into the original you giving yourself a sandwich.
It can be a little confusing, my best analogy would be writing a story with a pen, then wanting to change something. You save your original story and continue to write it without the new changes. You take out new paper and copy everything, word from word, until your first new change. Then start writing in your changes on the new paper adjusting anything that might be affected by those changes as you write. So if you were to finish your story you'd have two stories that have alternate events. Once it is written, it can not be erased, you have to start fresh.