On 10/25/2025 7:04 AM, Alan Grayson wrote:
On Wednesday, October 22, 2025 at 5:54:40 PM UTC-6 Brent Meeker wrote:
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
*I'm not sure I understand your comment. You seem to be claiming the
Many Worlders get the same result as the collapse model for a special
case of p=0.5. But do they get the same result in THIS-WORLD for the
double slit, which collapses to a huge number of outcomes? If not,
then the MWI does not satisfy Born's rule. AG *
When p=0.5 branch counting is the same as the Born rule. In a double
slit experiment the probability of each slit is 0.5 and all you get is
an interference pattern, no counts of this vs. that.
Brent
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