Why is one chunk of matter me, and all the others not me?

 I want to know, if materialism is true, why one chunk of matter is "me" and all the rest of the chunks of matter are not me. Even if you buy the whole story about something evolving that functions as if it were a me, I can still imagine a possible world physically identical to this one in which I am somebody else. So the explanation for why one chunk of matter is me, and another chunk of matter is, say, Barack Obama, can't be something about the physical world, since in a physically identical world, I'm Obama, and someone else is Reppert.