As far as I'm concerned, everything that has a beginning must have an end - the universe, solar systems, the earth itself, and pretty much any other physical entity, to my knowledge. We would certainly gain the ability to become 'immortal' as that would obviously fall under the (only) category of 'everything', but fundamentally, the practice of then biologically instituting 'immortality' would be in direct contradiction to the natural path of birth --> death found in all other universal entities. I have absolutely no doubt that we will be able to extend our lifetimes to incredible lengths, but I question the morality of living forever when even the universe is supposed to end. Unless we can travel outside of our universe, I'm pretty sure we eventually won't be 'immortal'. The concept only exists as long as we are unable to absolutely refute it; I have attempted to refute it here, although I will admit that I'm unlikely to have been completely successful.