On 23-04-2022 03:44, Bruce Kellett wrote:
On Sat, Apr 23, 2022 at 11:18 AM George Kahrimanis
<gekah...@gmail.com> wrote:
On Friday, April 22, 2022 at 1:54:36 AM UTC+3 Bruce wrote:
we now know that MWI is inconsistent with any sensible
interpretation of probability; strict MWI is inconsistent with the
Born rule.
Dittos!!! At least, mostly.
What do you mean "we now know"? Any citations, pretty please?
This has been argued by people like Adrian Kent and David Albert. See
Albert's "Mindscape" discussion with Sean Carroll, for example. Or
Kent's contribution to the volume "Many Worlds? Everett, Quantum
Theory, and Reality" (Oxford, 2010).
In claiming that MWI is inconsistent with the Born rule, I point to
the fact that MWI insists that every outcome occurs (in different
branches) on every trial.
This in itself cannot possibly lead to a problem, because we may let Mr.
DATA from Star Trek do experiments with two possible outcomes with
probabilities of 1/3 and 2/3. After each experiment where MR. DATA does
n trials, we reset Mr. DATA's internal state to that just before the
first experiment. For Mr. DATA every outcome for the n trials occurs and
yet there is no contradiction with the notion of probabilities here. At
least, while one may invoke a problem here like in the Sleeping Beauty
paradox, this is then really an issue within the realm of probability
theory, it has nothing whatsoever to do with the MWI.
This means that for the state
a|0> + b|1>
there is a branch with result |0> and another branch with result |1>
for every trial, independent of the coefficients a and b. The Born
rule, on the other hand, says that the probability of obtaining |0> is
|a|^2, and the probability of obtaining |1> is |b|^2. (Note that there
is no branching with the application of the Born rule -- there is just
one result, obtained with the specified probability.)
Whether or not there is branching is independent of assuming the Born
rule.
Over N trials,
strict MWI (one example of each result, on different branches) implies
that the relative frequency of |0> and |1> results tends to 0.5 for
the majority of branches, regardless of the coefficients a and b.
Whereas the Born rule says the the proportion of |0> results, for
example, will tend to |a|^2 for large N. (Recall that |a|^2 + |b|^2 =
1). For general and and b, these predictions are incompatible. So MWI
is inconsistent with the Born rule.
That's MWI with branch counting instead of the Born rule, which is
indeed not the same as QM without collapse.
Saibal
Bruce
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