Re: AUH/MWI/UDA (Was: Everything is Just a Memory)

From: Fred Chen <flipsu5.domain.name.hidden>
Date: Sat, 12 Feb 2000 21:02:31 -0800

Alastair, your discussion below is interesting:

Alastair Malcolm wrote:

> ----- Original Message -----
> From: Fred Chen <flipsu5.domain.name.hidden>
>
> > Can it be argued that the "simplicity" (of QM interpretation,
> computational
> > implementation) of MWI gives it a larger measure among other
> possibilities? Or
> > is it the large number of worlds generated by MWI splittings that would do
> this?
>
> Russell's paper implies simplicity alone is sufficient, but in case it is
> not totally watertight (I am not competent to fully assess this), here is a
> (pretty Heath-Robinson) argument showing how splittings might conceivably
> contribute:
>
> Suppose the minimum functional bit string length for a specification of
> Everett many worlds is n.

Here is the first interesting point. I haven't finished rereading Russell's
Occam Razor paper to my complete understanding, but from what I understand
Russell argues that mathematically QM gives the greatest measure for SAS's.
However, I am still not sure where the MWI of QM (i.e., actual splittings)
explicitly fits in.

> Then we are comparing the measure of SAS's of all
> combinations/interpretations of bits up to n. (Bits above n could 'multiply
> up' whatever has been specified below n either via different possible
> interpretations, different 'don't care' bit combinations, or direct
> 'multiplier' bit-string segments, dependent (at least partly) on the
> particular version of the AUH chosen. Effectively these factors above n
> 'cancel through' for all different combinations/interpretations of the first
> n bits, and so can be ignored.)
>
> Now, in order to 'out-measure' Everett, a theory would have to produce the
> complexity needed for SAS's well *within* the n bits, so that the surplus
> bits can be used to outnumber the worlds/SAS's produced in the splittings of
> Everett's theory, or else it must itself produce Everett-like splittings
> (and SAS's) with less than n bits (that is, with greater simplicity than
> Everett). There is little indication where such a theory could possibly come
> from.

Here is where I think things can potentially get messy. There is nothing
forbidding splittings (Everett or other) into an infinite number of branches, as
long as the ratio of branches follows the expected a priori probability (e.g.,
50% for a single coin toss). In fact, within the AUH, this case should dominate
those universes where finite splittings occur.

>
>
> But if there were some theory of similar simplicity to Everett specifying
> SAS's in a single world (say something approaching a good old-fashioned
> all-Newtonian universe), then it would be the Everett splittings themselves
> that would be responsible for the dominant measure (and explain why we see
> interference fringes).

> Alastair

Without Everett splittings, you can still have an infinite number of
"pre-existing" copies of the single world. The ratio of copies corresponding to
different outcomes (e.g., heads or tails) should still be the same as in
Everett's MWI.

Fred
Received on Sun Feb 13 2000 - 23:59:09 PST