One of the criticisms of no-collapse theories has always bothered me. Some people say that the mystery of non-determinism in conventional interpretations of QM is replaced by an equally baffling mystery in no-collapse theories: why do I end up in *this* branch rather than some other?

The critics understand, I presume, that observers end up in all branches asking themselves this question. But they still seem to think there is some mystery about the process, something that needs to be explained. I don't see what the mystery is. We have often considered thought experiments involving duplicating machines, which show the same phenomenon. A man walks into a duplicating machine and two men walk out, each having equal claim to being the original. Both ask this question: "Why did I end up as *this* person instead of the other one?" Is that a question which needs an answer? A question to which there can be any answer? I don't see it. Each copy is guaranteed in advance to be a continuation of the original. There is no mystery, nothing which needs to be explained, in the fact that each copy exists and has separate consciousness. Traditionally, no-collapse models were also criticized on two other grounds. (I will ignore the complaint that the theory is inparsimonious in its creation of multiple universes, because IMO this is more than made up for by the simplicity of the theory. Algorithmic complexity theory teaches us that it is the size of the program that counts, not the size of the data, and that is the measure we have used on this list.) One complaint is the non-uniqueness of the basis vectors for the decomposition. I think it is generally agreed today that this is solved because in practice only one basis will give the vanishing of off-diagonal elements in the density matrix, which corresponds to causally independent worlds. Ultimately this is due to the unexplained fact that the laws of physics have a built-in concept of positional locality. Locality manifests itself in the dynamics of QM in such a way that natural basis vectors correspond to well defined positions of macroscopic objects. I think the paper of Tegmark's we discussed last month developed this idea in more detail. The other critique is that the measure and probability functions are introduced on a somewhat ad hoc basis. I think this is still a valid criticism. We need to find some way to explain the MWI measure in similar terms to how Schmidhuber explains it in the multiverse model. He uses the universal measure (sometimes), which can naturally be interpreted as being proportional to the fraction of all countably-infinite size programs which create the universe in question. That is a very natural and powerful explanation for measure, but nothing similar exists for the MWI. If there were an explanation for the MWI branch measures in terms of a similar argument then I think this problem would be solved as well. Hal