On Sun, Aug 21, 2005 at 06:12:54PM -0700, Brent Meeker wrote:
>
> I've haven't read your derivation, but I've read quant-ph/0505059 by VAn
> Esch which is a proof that the Born Rule is independent of Everett's MWI
> and cannot be derived from it.
>
> How do you avoid Van Esch's counter example.
>
> Brent Meeker
I'm not sure its that relevant - I don't derive the Born rule from
Everett MWI per se, but rather from assumption that 1st person
experience should appear as the result of an evolutionary process. I
actually use Lewontin's criteria for evolution - I have an improved
explanation of this in appendix B of my draft book, although
technically it is identical to the FoPL paper.
Another way of viewing this topic is that the Multiverse (or MWI) is a
3rd person description, whereas the Born rule is a 1st person
property. So it is not surprising that the two are independent.
Looking at the paper, Esch proposes an alternative projection postulate
that weights all possible alternatives equally, ie it is equivalent to
the usual PP provided that the state vector is restricted to the set
of vectors \psi such that
<\psi|P_i|\psi> = 1/n_\psi or 0.
Let \psi' = \sum_i P_i\phi, for any vector \phi, and let
\psi=\psi'/\sqrt{<\psi',\psi>}, so this set if not empty.
This is a kind of all or nothing approach to \psi - \psi contains only
information about whether x_i is possible, or impossible, but doesn't
contain any shades of gray. It is saying, in other words, that White
Rabbit universes are just as likely as well ordered one - something
that contradicts the previous section on the white rabbit problem.
Instead, I assume that \psi does contain information about the
liklihood of each branch, and once you compute what this is, the usual
Born rule follows.
Cheers
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Received on Sun Aug 21 2005 - 22:43:45 PDT