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

From: Fred Chen <flipsu5.domain.name.hidden>
Date: Sat, 12 Feb 2000 23:37:19 -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 Sat Feb 12 2000 - 23:41:14 PST