If time travel exists, then it cannot be a simple rewind of the universe's tape. Because if that was the case, then rewinding the tape to a time that your father was not born would mean that you will also not be born, and thus there wouldn't be any time travel, since neither you nor anyone else would be able to witness it.
Thus, in order for time travel to work, it means to rewind the tape and add yourself to the tape at a moment you did not exist before. Thus, if you killed your father, your replica wouldn't be born, but you wouldn't stop to exist.
Therefore, the whole 'grandfather paradox' is not a paradox at all: if time travel exists, then you would simply exist in a universe where a replica of you will exist or not, depending on how events play out.
Not so fast - who says you become a "replica" in the first place? Assuming time travel replicates things, then yes, what you said holds true.
But as I understand it you don't replicate, your time just loops back on itself. So looping back to a time before you were born and killing your father would create a paradox.
You seem to have not understood what I said. I did not say time travel would replicate anything.
You would simply be transferred to the past, without any connection to the outcome of that past.
I.e. Let's say that you are transferred back in the 50s and you go kill your father before you were born. Then nothing will happen, there would be no paradox, you will continue to exist in that universe.
Thus, in order for time travel to work, it means to rewind the tape and add yourself to the tape at a moment you did not exist before. Thus, if you killed your father, your replica wouldn't be born, but you wouldn't stop to exist.
Therefore, the whole 'grandfather paradox' is not a paradox at all: if time travel exists, then you would simply exist in a universe where a replica of you will exist or not, depending on how events play out.