I think the question of immortality is basically semantics. If you are copying your brain in real time, the copied brain has no idea it's not actually the physical brain. It's existence is simultaneous and identical. It is as validly you as you are.
The instant it separates, it becomes a different being, but if it only separates when the physical shell ceases to exist, then it was you at that moment, and then it continues to be you after that moment has passed.
The thing people fail to consider is that we are not our physical shell. The physical shell merely simulates the thing we conceptualize as the self. That's why we can even conceive of doing something like transferring our mind into a computer, because the mind exists as a separate entity from the body.
Imaginate shadow cast on the wall. If someone else moves their hand in and starts casting the exact same shadow, and then we remove our hand from that shadow, the shadow exists continuously throughout. We are not the hand, we are the shadow.
The instant it separates, it becomes a different being, but if it only separates when the physical shell ceases to exist, then it was you at that moment, and then it continues to be you after that moment has passed.
The thing people fail to consider is that we are not our physical shell. The physical shell merely simulates the thing we conceptualize as the self. That's why we can even conceive of doing something like transferring our mind into a computer, because the mind exists as a separate entity from the body.
Imaginate shadow cast on the wall. If someone else moves their hand in and starts casting the exact same shadow, and then we remove our hand from that shadow, the shadow exists continuously throughout. We are not the hand, we are the shadow.