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.

## Advertising

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. -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------

**
pgpfSbPCT44fg.pgp**

*Description:* PGP signature