On 2/11/2020 4:16 AM, Bruno Marchal wrote:
On 7 Feb 2020, at 12:07, Bruce Kellett <[email protected]
<mailto:[email protected]>> 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.
Each individual sequence of head/tail would also occur with
probability, in the corresponding WM scenario, and in the coin tossing
experience.
In the MWI, what you describe is what has motivated the introduction
of a frequency operator, and that is the right thing to do in QM. I
think you might confuse the first person and the third person points
of view, in the WM-scenario and in the MWI (which is coherent with
your non-mechanist stance).
What is a frequency operator? Your WM thought experiment models a case
in which the probabilities are equal. MWI seems implausible if it
splits into two worlds when P(W)=P(M)=0.5 but splits into a thousand
worlds when P(W)=0.501 and P(M)=0.499.
Brent
Bruno
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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