I'm trying to define "identity"... Let's write x~y if SAS's x and y (possibly in different universes) have the same identity. I propose that this relation must be reflexive, symmetric and transitive. This neatly partitions all SAS's into equivalence classes, and we have no ambiguity working out whether any two SAS's across the multi-verse have the same identity.
Consider an SAS x that splits into x1, x2 (in child universes under MWI). We assume x~x1 and x~x2. By symmetry and transitivity we deduce x1~x2. So this definition of identity is maintained across independent child universes. This is at odds with the following concept of identity... > I am, for all practical purposes, one > and only one specific configuration of atoms in a specific > universe. I could never say that ' I ' is ALL the copies, since I > NEVER experience what the other copies experience It seems necessary to distinguish between a definition of identity and the set of memories within an SAS at a given moment. Is it possible that over long periods of time, the environment can affect an SAS to such an extent that SAS's in different universe that are suppose to have the same identity actually have very little in common? What happens if we "splice" two SAS's (including their memories)? It seems to me that the concept of identity is not fundamental to physics. It's useful for classification purposes as long as one doesn't stretch it too far and expose its lack of precision. This reminds me of the problem of defining the word "species". Although a useful concept for zoologists it is not well defined. For example there are cases where (animals in region) A can mate with B, B can mate with C, but A can't mate with C. - David