Simpler forms of life are technically immortal. It is nearly impossible for a human being to be immortal, to the best of my knowledge no matter how advanced we get. If you think of capturing all your life's memory in a microchip and install it to a computer, still it will never be You as a whole.
I believe your sense of being is illusionary and dynamic. 'You' are constantly changing at least to minor degrees, based on your thoughts inputs, behaviors and the memories you recently accessed. You aren't exactly the same person you were a few seconds ago. If you were some how duplicated atom for atom, relative position for relative position, and the duplicate placed next to the original you would still immediately start to diverge into two similar but different people. One would think who is this person who looks just like me to my right, and the other would think who is this person who looks just like me to my left.... Now you have had different thoughts and the divergence has already started.
As someone who has technically died essentially no heart beats (well just 3 or 4) for 3 minutes, then put in a coma for a week. I have personal evidence that ones own reality is just an hallucination/interpretation, by your brain, based on your current sensory inputs, and when there are no inputs it can continue fabricating a 'reality' without them, that you can't distinguish from your 'normal reality, and your normal sense of self'. My medical chart says I'm brain damaged, but it seems to have survived the hard rebooted quiet well. I have managed to publish 8 scientific papers since then. Here's a link to a presentation(Sept 2023)/publication of mine (Feb 2022). That I feel will be quite influential. It's based on an old idea of mine (1998) which would have never been published if I'd died.
Presentation Is the cell a digitally controlled system
I know you can't check the accuracy of a ruler using the same ruler) but I feel I'm the same person as I ever was, but I'm not. Perhaps I'm Erwin Schrödinger biochemist and quantum entangled Phil is in the totally opposite configuration :-)) However, I and my behavior have changed and my attitude to life has changed, so I'm not the same person.... it is only my memories that convince me I am the same person. This experience left with an irrational feeling of invulnerability. I always try to make what I believe to be is the most ethically correct decision at the time if possible. I'm still not 100% sure I'm not still in a coma somewhere, and this is all an illusion within an illusion, but now it would be apparently 8 years in length. BTW I'm an atheist.
Philip G Penketh thanks for sharing your belief and experience. Duplication of each cell in our body could be something similar to bacterial division. But the product might be similar to an identical clone. Then again I think that would not be the same "person" even when exposed to the same events in life.