On 2/7/2020 3:07 AM, Bruce Kellett wrote:
On Fri, Feb 7, 2020 at 9:54 PM Lawrence Crowell
<[email protected]
<mailto:[email protected]>> 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. 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.
Brent
Bruce
An observer might see their branch as having sufficient randomness
to be a Bayesian prior, but to derive a full theory these outlier
branches with the appearance of structure have to be eliminated.
This is not a devastating blow to MWI, but it is a limitation on
its explanatory power. Of course with statistical physics we have
these logarithms and the rest and such slop tends to be "washed
out" for large enough sample space.
No matter how hard we try it is tough to make this all epistemic,
say Bayesian etc, or ontological with frequentist statistics.
LC
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