On Tuesday, October 21, 2025 at 2:35:05 PM UTC-6 Brent Meeker wrote:
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
*Since you're a master of plots, how difficult would it be to produce three
plots of the double slit experiment, with as many single events as you deem
suitable? First plot would simulate the result of the experiment; the
second would demonstrate the prediction using the collapse model; and the
third would simulate the no-collapse model. Before we allow the
many-worlders to confuse the issue, let's see if the no collapse model make
the predictive cut in THIS WORLD. AG*
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