I personally subscribe to the Many Worlds theory regarding time travel. Beyond that, my layman's view of things would make me suspect that true sci-fi-esque time travel isn't possible for anything other than elementary particles.
Why we think there’s a Multiverse, not just our Universe – Starts With A Bang
I'm too lazy to read that, but it's probably the same as my "forked quantum reality" concept. basically, there's infinite distinct realities that represent each outcome of a random chance (does an electron go left or right = poof! 2 new quantum realities).
Michael Crichton's novel Timeline used this approach (then ignored it later).
The premise being, if you COULD travel back in time, you are in an alternate quantum reality from the original that you experieced/came from. So the original reality where you were not present from the future exists and YOU experienced that (or descended from it).
Now you travel back in time, and that creates a NEW quantum reality. the current YOU and the Chrono-Native inhabitants of this NEW quantum reality experience whatever it is you and they experience (like the fun of trying to kill/protect Hitler). Let's say you're successful.
To the Chrono-Natives, they experience a world where Hitler died at your hands. To you, assuming you stay there, you watch the world experience a different sequence of reactionary events to Hitler's death. But that doesn't erase your memory of your past experience (or time spent in history class) of your original Quantum reality. If you hang out long enough, you'll get to see if this Quantum Reality's version of you gets concieved and watch you grow up (or not, if it turns out your mom marries somebody who wouldn't have existed if the Holocaust happened).
This is how Quantum physics guys explain away the paradox of killing your grandpa before your dad was born.
The time traveller is the observer. He witnessed or descended from a timeline where his grandpa concieved his dad in his Quantum Reality of Origin.
Going back in time, isn't going back in the QR of Origin. It's shifting to a new QR set in the past. You whack Gramps in THAT QR. If you then hop to the future, you are moving back to your Origin QR or the future position of this new QR. You don't cease to be because YOU were born in your Origin QR, not this new one where an equivalent you doesn't get made.
By travelling back in time, you BECOME the initiating choice factor for a new Quantum Reality. because there's the original reality where you were NOT present in 1940 Berlin, and the new reality where you just appeared from nowhere in 1940 Berlin.
there's probably more sciency details, but that's my basic understanding of Quantum physics and multiple realities. A few sci-fi authors have played with this idea, like Crighton, and Neil Stephenson if I recall.