Given your clone is a perfectly mirrored copy of yourself down to the lowest physical level (whatever that means), then breaking symmetry would violate the homogeneity or isotropy of physics. I don’t know where the physics literature stands on the likelihood of that happening (even though certainly we don’t see macroscopic violations).
Of course, it might be an atom-by-atom copy is not a copy down to the lowest physical level, in which case trivially you can get eventual asymmetry. I mean, it doesn’t even make complete sense to say “atom-by-atom copy” in the language of quantum mechanics, since you can’t be arbitrarily certain about the position and velocity of each atom. Maybe saying something like “the quantum state function of the whole room is perfectly symmetric in this specific way”. I think then (if that is indeed the lowest physical level) the function will remain symmetric forever, but maybe in some universes you and your copy end up in different places? That is, the symmetry would happen at another level in this example: across universes, and not necessarily inside each single universe?
It might also be there is no lowest physical level, just unending complexity all the way down (this had a philosophical name which I now forget).
Given your clone is a perfectly mirrored copy of yourself down to the lowest physical level (whatever that means), then breaking symmetry would violate the homogeneity or isotropy of physics. I don’t know where the physics literature stands on the likelihood of that happening (even though certainly we don’t see macroscopic violations).
Of course, it might be an atom-by-atom copy is not a copy down to the lowest physical level, in which case trivially you can get eventual asymmetry. I mean, it doesn’t even make complete sense to say “atom-by-atom copy” in the language of quantum mechanics, since you can’t be arbitrarily certain about the position and velocity of each atom. Maybe saying something like “the quantum state function of the whole room is perfectly symmetric in this specific way”. I think then (if that is indeed the lowest physical level) the function will remain symmetric forever, but maybe in some universes you and your copy end up in different places? That is, the symmetry would happen at another level in this example: across universes, and not necessarily inside each single universe?
It might also be there is no lowest physical level, just unending complexity all the way down (this had a philosophical name which I now forget).