On 2/7/2020 2:16 PM, Bruce Kellett wrote:
On Sat, Feb 8, 2020 at 6:45 AM 'Brent Meeker' via Everything List
<everything-list@googlegroups.com
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On 2/7/2020 3:07 AM, Bruce Kellett wrote:
On Fri, Feb 7, 2020 at 9:54 PM Lawrence Crowell
<goldenfieldquaterni...@gmail.com
<mailto:goldenfieldquaterni...@gmail.com>> wrote:
On Thursday, February 6, 2020 at 10:59:27 PM UTC-6, Bruce wrote:
This argument from Kent completely destroys Everett's
attempt to derive the Born rule from his many-worlds
approach to quantum mechanics. In fact, it totally
undermines most attempts to derive the Born rule from any
branching theory, and undermines attempts to justify
ignoring branches on which the Born rule weights are
disconfirmed. In the many-worlds case, recall, all
observers are aware that other observers with other data
must exist, but each is led to construct a spurious
measure of importance that favours their own observations
against the others', and this leads to an obvious
absurdity. In the one-world case, observers treat what
actually happened as important, and ignore what didn't
happen: this doesn't lead to the same difficulty.
Bruce
This appears to argue that observers in a branch are limited
in their ability to take the results of their branch as a
Bayesian prior. This limitation occurs for the coin flip case
where some combinations have a high degree of structure. Say
all heads or a repeated sequence of heads and tails with some
structure, or apparent structure. For large N though these
are a diminishing measure.
I don't think you have fully come to terms with Kent's argument.
How do you determine the measure on the observed outcomes? The
argument that such 'outlier' sequences are of small measure fails
at the first hurdle, because all sequences have equal measure --
all are equally likely. In fact, all occur with unit probability
in MWI.
In practice one doesn't look for a measure on specific outcomes
sequences because you're testing a theory that only predicts one
probability. You flip coins to test whether P(heads)=0.5 which
you can confirm or refute without even knowing the sequences.
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. 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.
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. 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
Brent
It might be that every sequence you get by flipping is in the form
HTHTHTHTHTHTHT... which would support P(H)=0.5. It would be a
different world than ours, possibly with different physics; but
that would be a matter of testing a different theory.
One of the problems with MWI is that can't seem to explain
probability without sneaking in some equivalent concept. The
obvious version of MWI would be branch counting in which every
measurement-like event produces an enormous number of branches and
the number of branches with spin UP relative to the number with
spin DOWN gives the odds of spin UP. A meta-physical difficulty
is the all the spin UP branches are identical and so by Leibniz's
identity of indiscernibles are really only one; but maybe this
inapplicable since the measure involves lots of environment that
would make it discernible.
That seems to be rather beside the point.
Bruce
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