On Mon, Feb 10, 2025 at 02:14:07PM +1100, Bruce Kellett wrote:
> On Mon, Feb 10, 2025 at 1:47 PM Russell Standish <li...@hpcoders.com.au> 
> wrote:
> 
>     On Mon, Feb 10, 2025 at 11:35:11AM +1100, Bruce Kellett wrote:
>     > On Mon, Feb 10, 2025 at 10:52 AM Russell Standish 
> <li...@hpcoders.com.au>
>     > wrote:
>     >
>     >    
>     >     >     On Mon, Feb 10, 2025 at 09:25:57AM +1100, Bruce Kellett wrote:
>     >     >     > On Mon, Feb 10, 2025 at 8:49 AM Russell Standish
>     >     >     wrote:
>     >     >     >
>     >     >     >     On Thu, Feb 06, 2025 at 11:38:52AM +1100, Bruce Kellett
>     wrote:
>     >     >     >     >
>     >     >     >     > Many worlds theory does not have any comparable way of
>     relating  probabilities
>     >     >     >     > to the properties of the wave function. In fact, if 
> all
>     possibilities are
>     >     >     >     > realized on every trial, the majority of observers 
> will
>     get results that
>     >     >     >     > contradict the Born probabilities.
>     >     >     >     >
>     >     >     >
>     >     >     >     I'm not sure what you mean by "contradict", but the
>     majority of
>     >     >     >     observers will get results that lie within one standard
>     deviation of
>     >     >     >     the expected value (ie mean) according to the
>     distribution of Born
>     >     >     >     probabilities. If this is what you mean by "contradict",
>     then you are
>     >     >     >     trivially correct, but uninteresting. If you mean the
>     above  statement
>     >     >     >     is false according to the MWI, then I'd like to know 
> why.
>     It  sure
>     >     >     >     doesn't seem so to me.
>     >     >     >
>     >     >     >
>     >     >     > It does depend on what value you take for N, the number of
>     trials. In the  limit
>     >     >     > of very large N, the law of large numbers does give the
>     result you suggest. But
>     >     >     > for intermediate values of N, MWI says that there will 
> always
>     be branches for
>     >     >     > which the ratio of successes to N falls outside any
>     reasonable error bound on
>     >     >     > the expected Born value.
>     >     >     >
>     >     >     > This problem has been noted by others, and when asked about
>     it, Carroll simply
>     >     >     > dismissed the poor suckers that get results that invalidate
>     the Born Rule as
>     >     >     > just poor unlucky suckers. Sure, in a single world system,
>     there is always a
>     >     >     > small probability that you will get anomalous results. But
>     that is always  a
>     >     >     > small probability. Whereas, in MWI, there are always such
>     branches with
>     >     >     > anomalous results, even for large N. The difference is
>     important.
>     >     >     >
>     >     >
>     >     >     Yes, but the proportion of "poor unlucky suckers" in the set 
> of
>     all
>     >     >     observers becomes vanishingly small as the number of observers
>     tend to
>     >     >     infinity.
>     >     >
>     >     >
>     >     > The number of trials does not have to tend to infinity. That is
>     just the
>     >     > frequentist mistake.
>     >     >
>     >
>     >     I wasn't talking about the number of trials, but the number of
>     >     observers. That is either astronomically large or an actual 
> infinity.
>     >
>     >
>     > There are only ever 2^N branches under consideration, so only ever 2^N
>     observers.
> 
>     These 2^N observers will be unevenly weighted. If you want to do even
>     weighting by some sort of symmetry argument, you will need to
>     subdivide more finely.
> 
> 
> And where do these weights come from?

That is another question entirely.

> If you do the construction, all 2^N
> branches arise in the same way, so they have the same weight.

This is where I disagree with you. The only way of assigning equal
weight is if there is some fundamental system symmetry that allows the
indifference principle to be applied. But by construction, that
symmetry is broken.

> 
> As I have said. I did not apply the indifference principle because the
> sequences would have equal weight simply by construction. Besides, the
> "weights" assigned to these sequences are essentially irrelevant.

I disagree.


-- 

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Dr Russell Standish                    Phone 0425 253119 (mobile)
Principal, High Performance Coders     hpco...@hpcoders.com.au
                      http://www.hpcoders.com.au
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