On 10/20/2025 10:52 PM, Alan Grayson wrote:
Sure. Consider a sequence of n=4 Bernoulli trials. Let
h be the number of heads. Then we can make a table of
the number of all possible sequences bc with exactly h
heads and with the corresponding observed proportion h/n
h bc h/n
0 1 0.0
1 4 0.25
2 6 0.5
3 4 0.75
4 1 1.0
So each possible sequence will correspond to one of
Everett's worlds. For example hhht and hthh belong to
the fourth line h=3. There are sixteen possible
sequences, so there will be sixteen worlds and a
fraction 6/16=0.3125 will exhibit a prob(h)~0.5.
But suppose it was an unfair coin, loaded so that the
probability of tails was 0.9. The possible sequences
are the same, but now we can apply the Born rule and
calculate probabilities for the various sequences, as
follows:
h bc h/n prob
0 1 0.0 0.656
1 4 0.25 0.292
2 6 0.5 0.049
3 4 0.75 0.003
4 1 1.0 0.000
So most of the observers will get empirical answers
that differ drastically from the Born rule values. The
six worlds that observe 0.5 will be off by a factor of
1.8. And notice the error only becomes greater as longer
test sequences are used. The number of sequences peak
more sharply around 0.5 while the the Born values peak
more sharply around 0.9.
Brent
*By the above paragraph, it seems you've already
falsified the MWI, except that you could claim that's
what no-collapse yields in this-world. I don't see any
reason for claiming each sequence is observed in
different worlds. AG*
There's no unique sequence "in this world" because there's no
unique "this world" in MWI.
Brent
*
*
*IMO this is ridiculous. How can you disprove the MWI when you accept
its foolish claim of many worlds? All that's required is to show that
the no-collapse hypothesis gives wrong results compared to Born's rule
in the only world you know for sure, THIS-WORLD. AG*
The no collapse hypothesis gives wrong results in some worlds and not in
others. The problem is how you assign probabilities to these worlds.
MWI advocates use the Born rule to assign probabilities to the different
branches and so produce /an interpretation empirically identical/ to the
neo-Copenhagen interpretation. I think it fails in the sense that it
can produce many observers, even a majority, existing in low probability
branches who cannot know they are in low probability branches and so are
deceived by their observations into falsifying QM. MWI dismisses them
as low probability even though they are numerous. Copenhagen says "low
probability" means they likely don't exist. So it is a philosophical
disagreement about the meaning of applied probability.
Brent
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