On Thu, Jun 02, 2005 at 12:18:07PM -0700, "Hal Finney" wrote:
> There is a particularly interesting and surprising difference that I
> am aware of between the MWI (many-worlds interpretation of quantum
> mechanics) and more general multiverse models like Tegmark's and
> especially Schmidhuber's.  

I know there will always be differences in terminology usage, but I'll
stick with the convention of Multiverse to mean Tegmark Level 3
ensemble (ie the MWI ensemble) and Plenitude for any of the level 4
ensembles (Tegmark, Schmidhuber etc)

> 
> However, one piece is missing.  Although Everett showed that the
> universe would, in effect, split and create separate observers who would
> observe separate outcomes, the question remains of how that relates to
> probability.  The traditional quantum wave function collapse postulate
> not only says that we will observe a random outcome, it also tells what
> the probability of each possibility will be, based on what is called
> Born's rule.
> 
> Deriving Born's rule from Everett's analysis has been difficult.  In fact,
> it has been "solved" many times over the years, but none of the proposed
> solutions has really been satisfactory, which is why it keeps getting
> solved all over again.  It is easy to show that the universe will split
> and observers will appear to observe random outcomes; it is hard to show
> that the most likely outcomes are the ones most likely to be observed.

I was not aware of the Born rule having been derived multiple times
(although I'm not too suprised if that is the case). Do you have any
references? The Born rule is one of the things I derive in my "Why
Occam's paper".

I'd also be interested to know why my derivation is not
satisfactory. I received very little criticism of my work - I'm hungry
for more.

My derivation depends primarily on the "Projection postulate",
which is essentially describes how the Multiverse splits in the 1st
person perspective. I call it a postulate, because whilst it might be
derivable, there will be some other assumption needed in the
derivation. There is always a matter of taste in choice of axioms - so
long as equivalence pertains, this is not a problem.

It also depends on the Kolmogorov probability axioms, which I simply
take to be a definition of probability.


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