On 2/7/2020 5:53 PM, Bruce Kellett wrote:
On Sat, Feb 8, 2020 at 12:23 PM 'Brent Meeker' via Everything List
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On 2/7/2020 2:16 PM, Bruce Kellett wrote:
The point of Kent's argument is that in MWI where all outcomes
occur, you will get the same set of sequences of results whatever
the intrinsic probabilities might be. So you cannot use data from
any one sequence to test a hypothesis about the probabilities:
the sequences obtained are independent of any underlying
probability measure.
Why not? Most copies of me will see sequences with approximately
equal numbers of H and T.
You are making the mistake that many commentators make: you are
thinking of the distribution over the set of all possible sequences,
and then assuming that we sample at random from this set. But that is
not how experiments are done. We run the experiment N times and obtain
some sequence of results. We then use the data so obtained to compare
with our theory. There is no random selection from the set of all
possible sequences. In fact, in MWI, there is one observer for every
possible sequence, and we have to consider what each of them, in
isolation, will conclude. Many will see the Born rule disconfirmed.
But in the limit of large N those who see the rule disconfirmed will be
small.
In fact we do use data from one sequence, which ever one our
accelerator produces, even though the theory we're testing
predicts that all sequences are possible. But we don't compare
sequences; we compare statistics on the sequences and compare
those to predicted probabilities.
That is just a fantasy made up to get out of a difficulty. That is not
how science proceeds.
I beg to differ. Who compares sequences of double photon production at
the LHC? The data I see is always derived statistics.
Of course, if many-worlds is correct and every possible outcome occurs
for every trial, then given the probability deduced from one set of N
trials, we can always attempt to confirm this result by doing another
set of trials. The problem is that the second set of trials is quite
like to give a different result from the first. That also would count
as a disconfirmation of the theory.
How is that different than in a single world. Sequences in
probabilistic experiments give different results. We don't count that
as disconfirmation because we look at the statistics and say, "Oh that
doesn't agree with the Kellet experiment, but it's well within the
confidence bounds, so they both confirm the theory."
Whether sequences are independent of "underlying probabilities" is
a different problem. First, one can't legitimately assume
underlying probabilities when trying to justify the existence of a
probability measure.
In the first instance, we are not trying to justify the existence of a
probability measure. We are trying to see if experimental data can
confirm a particular theory.
Second, the simple way to postulate a measure is just counting
branches, which means that there must be many repetitions of the
same sequence on different branches in order to realize
probability values that aren't integer ratios
Branch counting has a bad reputation as a basis for a probability
measure. One problem, as Wallace for instance points out, is that the
number of branches is never well-defined, so no clear count is available.
Right. The number has to be essentially infinite in order that
irrational probabilities can be represented. But it can't be actually
countably infinite because then that creates the problem of defining a
measure over infinitely many integers. So it seems it must be bigger
than any number ever measured, but not infinite.
There are other problems, which have led to the abandonment of this
approach to probability.
I'm not aware of any other problems...aside from the mere extravagance
and lack of function of MWI.
Brent
Bruce
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