I’ve been watching the TV series Pantheon and I really like it, but this tiny aspect is something I can’t quite grasp. So these people have their minds uploaded to the cloud - and they make a point to state that they’re still “them” - alive, real, authentic. But would it really be like that? The process is brain mapping, so essentially they just make a perfect clone of your brain/mind and run it digitally. But it’s still just a simulation. A perfect clone is still just a clone. The original person is gone. I don’t see the “continuity” aspect.
I suppose it really depends on figuring out what consciousness really is.
If we’re talking about pure digital information then nothing is actually moved, it’s just copied and written to a new location. From the perspective of the new mind, continuity would be preserved and it would think it had simply changed places. The old mind (if it survives the scanning/transfer process) would still be outside the simulation and see a new copy of itself in there.
On the other hand, if consciousness is some kind of understandable phenomena, with even more sci-fi tech we might be able to simply scoop it out and put it somewhere else. In that case it would be the same person.