On 10/20/2025 7:23 PM, Alan Grayson wrote:
On Monday, October 20, 2025 at 3:18:21 AM UTC-6 Alan Grayson wrote:
On Sunday, October 19, 2025 at 6:15:35 AM UTC-6 Alan Grayson wrote:
The greatest mathematicians tried
to prove Euclid's 5th postulate
from the other four, and failed;
and the greatest physicists have
tried to dervive Born's rule from
the postulates of QM, and
failed;, except for Brent Meeker
in the latter case. You claimed
it in the negative, by claiming
that without collapse, Born's
rule would fail in some world of
the MWI. An assertion is just
that, an assertion. Can you prove
it using mathematics? AG
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
*You seem very close to proving that the no-collapse
interpretation, aka MWI, gives very wrong results, but I see no
interest in publishing it. Why not expand your argument and
publish it? AG*
*Any particular reason you labeled second column as bc? AG *
Yes, it's an abbreviation.?
*What does bc stand for? AG *
Sorry, I don't quite understand your
example? What has this to-do with
collapse of the wf and the MWI? Where
is collapse implied or not? How is
Born's rule applied when the wf is
discrete? AG
You wrote, "...claiming that without
collapse,/Born's rule would fail in
some world of the MWI/....Can you prove
it using mathematics?" So I showed
that in MWI, which is without collapse,
6 out of 16 experimenters will observe
p=0.5 even in a case in which the Born
rule says the likelihood of p=0.5 is
0.049. Of course your challenge was
confused since it is not Born's rule
that fails. Born's rule is well
supported by thousands if not millions
of experiments. Rather it is that MWI
fails...unless it includes a weighting
to enforce the Born rule. But as Bruce
points out there is no mechanism for
this. If the experiment is done to
measure the probability (with no
assumption of the Born rule) then there
are 16 possible sequences of four
measurements and 6 of them give p=0.5
and 6/16=0.375, making p=0.5 the most
likely of the four outcomes. What
this has to do with collapse of the
wave function is just that the Born
rule predicts the probabilities of what
it will collapse to. So (assuming MWI)
there are still 6 of the 16 who see 2h
and 2t but somehow those 6
experimenters have only a small weight
of some kind. Their existence is kind
of wispy and not-robust.
Brent
I didn't mean to imply that Born's rule is
violated. But what you need to do IMO, is
show how Born's rule is applied to your
assumed events as seen without collapse in
some world of the MWI. Otherwise, you just
have a set of claims without any proof of
their validity. AG
You say Born's rule will do this or that, but
you don't say exactly HOW it will do this or
that. AG
I only wrote "... the Born rule says..." and
"... the Born rule predicts..." If you don't
understand how a mathematical formula can "say"
or "predict" I can't help you.
Brent
To use Born's rule, you need a wf.
Not if you already know the probability of |1> and
|0> which values I just assumed. Do you need me to
take the square roots and write down the
corresponding wave function, 0.949|0> + 0.316|1>
*Is this wf for the biased coin? For the unbiased, I
would expect the multiplying parameters would be the same
and equal to .5. AG *
No, that would be 0.707 for each.
*
*
*How is that calculation done? TY, AG*
*Oh, I see. The square must be .05. ... Indulge me on this. When I
studied QM, we akways used S's equation to solve for the wf, and it
was always a real valued complex function. So it was simple to find
its norm using complex conjugates. But I don't know how to find the
norm for a linear sum of bras. I'd like to see how its done. AG*
Brent
What is the wf one gets from your h-t scenarios?
That is, how do you calulate Born's rule in your
scenario. Why is this so hard to understand?
For who?
if we have two ways to do the calculation, with
collapse and no-collapse in this-world, and we get
different answers, then the MWI is falsified
(assuming that Born's rule give the correct answer).
We can share the prize. AG
No because those aren't the only two possibilities.
In fact advocates of MWI also use the Born rule as a
"weight" for the various worlds, but brushing under
the rug the fact that this weight is just the
probability of that world happening. They don't like
that because they want all the worlds to happen, so
they think of it as the probability that you
experience that world...even though you experience
all of them.
Brent
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