On 10/27/2025 5:28 AM, smitra wrote:
On 13-10-2025 03:56, Alan Grayson wrote:
Correct me if I'm mistaken, but as far as I know the wf has never been
observed; only the observations of the system it represents. This
being the case, in a large number of trials. Born's rulle will be
satisfied regardless of which interpretation an observer affirms;
either the MWI with no collapse of the wf, or Copenhagen with collapse
of the wf. That is, since we can only observe the statistical results
of an experiment from a this-world perspective, and we see that Born's
rule is satisfied, so I don't see how it can be argued that the rule
fails to be satisfied if the MWI is assumed. I think the same can be
said about the other worlds assumed by the MWI, namely, that IF we
could measure their results, the rule would likewise be satisfied.AG
I've scanned through part of this thread, so perhaps someone has
already said what I'm going to say here. A special case of the Born
rule is when measuring an observable A when the state is in an
eigenstate of A. In that case you find the eigenvalue of A for that
eigenstate the system is already in with 100% certainty. We can then
exploit this fact to try to set up an experiment to verify the Born
rule as a quantum experiment where the outcome is either 0
corresponding to the Born rule being falsified and 1 corresponding to
the Born rule being verified. If we can then come up with such an
observable for testring the Born rule, then if the Born rule is true,
any quantum state should be an eigenstate with eigenvalue 1.
The problem here is that we can only ever do a finite number of
measurements and we don't have a sharp rejection or verification of
the Born rule. And there are then always exceptional states where the
statistics will start to agree with the Born rule arbitrarily late. We
can at most write down for any arbitrary integer an observable for
repeating an experiment N times in a quantum coherent way where each
individual measurement doesn't collapse the wavefunction (e.g.
measurement conducted by a quantum computer and stored in that quantum
computer), and only at the end we perform a measurement on the entire
statistics stored in the quantum computer.
Suppose we set things up such that there is qubit that will take the
value 1 if the hypothesis that the Born rule is false is ruled out at
99% confidence level. Then that qubit will be in a superposition of 1
and 0 and with N very large, the amplitude for 0 will be extremely
small. But the amplitude for 0 will only become zero in the limit of N
to infinity.
So, there is still a problem here, but at heart this is actually a
problem with the very concept of probability, which is not well
defined in physical contexts where one can only ever do a finite
number of measurements:
https://www.youtube.com/watch?v=wfzSE4Hoxbc&t=1036s
Saibal
But that's a completely general problem with all of science. No theory
is ever proven true. It may be proven false or restricted in its domain
of application, but however much evidence is found in its favor, it is
not proven true. That's why there's interest in using Bayes's theorem
to quantify the degree of confidence we should ascribe to a theory. It
uses probability as "degree of justified belief". It has nothing to do
with frequencies and limits at infinity.
The problem with MWI is that, in 1 or 0 test sequence, the branching
structure produces numbers of observers with a binomial distribution of
p=0.5 no matter the probability in the Born rule, P. The Born rule is
satisfied for the QM predicted probability, but not by the branch
counting. This is mathematically and empirically consistent. But to me
it is seems philosophically inconsistent.
In an experiment with P=0.9 the branches consistent with this will have
the most weight, but the branches consistent with p=0.5 will be much
more numerous but of low weight. In Copenhagen they simply have a low
probability of being the one existent branch, but what are we to make of
their existence in MWI? /Almost all/ physicists will be getting the
wrong answer.../but that's OK because they have "low weight"!/ Their
existence is /thin/ in some sense? What does having "low weight"
mean. If it's a probability, as assumed in it's calculation, what is it
a probability /of/? If is a probability of happening, then a low value
means it probably didn't happen...not that it happened /thinly/.
Brent
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