Quantum non-sameness of the configurations from moment to moment, and quantum absolute equality of “the same sorts of particles in the same arrangement” are both illustrative as extremes, but the question looks much simpler to me. Since I have every reason to suppose “the me of me” is informational, I can simply apply what I know of information: that it exists as patterns independent of a particular substrate, and that it can be copied and still be the original. If I’m copied then the two mes will start diverging and become distinguishable, but neither has a stronger claim.
Quantum non-sameness of the configurations from moment to moment, and quantum absolute equality of “the same sorts of particles in the same arrangement” are both illustrative as extremes, but the question looks much simpler to me. Since I have every reason to suppose “the me of me” is informational, I can simply apply what I know of information: that it exists as patterns independent of a particular substrate, and that it can be copied and still be the original. If I’m copied then the two mes will start diverging and become distinguishable, but neither has a stronger claim.