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.


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