Let's take the following scenario:
A person finds a time machine. He uses it to travel to the past, and kills his grandparents. Now because of this, his parents are never born, they do not meet, and he himself ceases to exist.
I have heard one predominant result of this murder:
Since he killed his grandparents, he doesn't exist. Therefore, he could not have gone into the past and committed the murders. Therefore, he exists. Therefore, he doesn't exist and so on, ad infinitum.
However, I think that instead of an endless loop, we would end up with an altered timeline:
Since the grandparents are dead, they no longer exist. Anything they might have done to the world in the normal timeline after their deaths doesn't happen. Time moves on, and we come to the present day. There is no boy, no parents, no grandparents. The loop doesn't happen, because the grandparents are already dead. It doesn't matter that the boy isn't there to kill them again.
So which would be a more accurate expectation? Or is there a third option that I'm missing completely?
I am looking for answers from a purely physics perspective.