On 10/22/2025 12:56 AM, Alan Grayson wrote:
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*
Did you miss the part about MWI advocates using the Born rule in their
interpretation? Without it, the MWI is the same as the Born rule when
p=0.5, no matter what the Schroedinger equation says p is. It's what
MWI advocates dismiss as "branch counting".
Brent
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