Every atom is your body is supposedly replaced within a 7-year timeframe. So assuming monism, which is a hefty assumption in and of itself, it's the arrangement or interaction, not anything inherent in the matter itself, and it would seem that as long as that pattern is conserved, so are you. If a replica of you is created, it would also be you.*
As illuminated by some experience with heavy depersonalization, I think our continuity is an illusion anyway. If sentience is a natural property of certain arrangments of, or interactions between, bits of information, then it's my personal belief that we're actually just frames of discrete consciousness blended together by short-term memory - which would go hand in hand with the "specious present."
Abandon hope, all ye who enter here: ---- The rest was vaguely rational, this is not.
---- But feedback is always appreciated so I offer it up.
*At the risk of sounding insane, I'll write what "reasoning" I use to "resolve" that conundrum.
I take ( insert whatever substrate for consciousness you personally subscribe to (or like me, use the abstract notion) here) and assume that different states of that system correspond with different sets of qualia (disparate consciousness).
The aforementioned (2 paragraph ago) discrete flashes of consciousness, in this particular case, are manifest as different states of that system. Just like the number of possible images our eyes/mind can apprehend are finite (though unfathomably large), there are a finite number of states of whatever substrate you subscribe to. So just like one could calculate every sight seen throughout history or that will ever be seen by human eyes, assuming one could manipulate the consciousness-manifesting system directly, they could create every possible subjective state possible (though I'm sure, like images, there are differing resolutions, adding more complexity). These conscious states would include all the moments of my entire life, as well as yours, or any person that has or will ever exist.
Now here, we depart reason for the vagaries of cotarded's demented mind. I see myself (referring only to the current discrete snapshot, a planck time of that consciousness manifesting system, or whatever) as simply the possibility of that state. So all the 'I's I'll ever be are already sentient by possibility, regardless of whether a body ever generates the manifesting arrangement/interaction that offers them context.
Already, I disagree with that. But hey.
edit: I started this way earlier tonight, before neurocomp's post, and got distracted and forgot about it. so some of this is redundant.