On 24-04-2022 03:16, Bruce Kellett wrote:
On Sat, Apr 23, 2022 at 6:55 PM smitra <smi...@zonnet.nl> wrote:
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,
But it does lead to a problem. As explained below.
because we may let Mr.
DATA from Star Trek do experiments with two possible outcomes with
probabilities of 1/3 and 2/3.
A moment's thought should make it clear to you that this is not
possible. If both possibilities are realized, it cannot be the case
that one has twice the probability of the other. In the long run, if
both are realized they have equal probabilities of 1/2.
The probabilities do not have to be 1/2. Suppose one million people
participate in a lottery such that there will be exactly one winner. The
probability that one given person will win, is then one in a million.
Suppose now that we create one million people using a machine and then
organize such a lottery. The probability that one given newly created
person will win is then also one in a million. The machine can be
adjusted to create any set of persons we like, it can create one million
identical persons, or almost identical persons, or totally different
persons. If we then create one million almost identical persons, the
probability is still one one in a million. This means that the limit of
identical persons, the probability will be one in a million.
Why would the probability suddenly become 1/2 if the machine is set to
create exactly identical persons while the probability would be one in a
million if we create persons that are almost, but not quite identical?
After each experiment where MR. DATA does
n trials, we reset Mr. DATA's internal state to that just before the
first experiment.
Why would you want to reset his internal state to that of just before
the experiment?
Without resetting the different experiments are not identical to Mr.
DATA as he would remember the previous experiments.
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.
The Sleeping Beauty paradox is of no conceivable relevance to the
argument.
The argument in favor of equal probabilities that leads to that paradox
is the same as used here.
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.
You can't have branching with unequal probabilities for the formation
of each branch when both branches are certainly formed.
As explained above, there is no problem whatsoever with getting to
unequal probabilities when all outcomes happen with certainty.
So if the Born
rule gives unequal probabilities for the results, you cannot form a
single branch for each result at the same time as satisfying the Born
rule. You can (by fiat) give your branches different weights, but such
weights are not probabilities.
There is no reason why every branch should have the same probability.
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.
There is no branch counting involved. As usual, you seek to raise red
herrings in an attempt to divert attention from the logic of the
argument as presented.
Assuming that each branch has equal probability = branch counting.
The probabilities for each result in Everettian
QM do not, in general, agree with the Born rule, as has been pointed
out by Kent and Albert among others.
Based on a branch counting argument. It's true that attempts to derive
the Born rule have not been successful and can be criticized. But if we
take the MWI to be QM without collapse then there is no tension
whatsoever with that and the Born rule.
Saibal
Bruce
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