On 3/4/2020 6:45 PM, Bruce Kellett wrote:
On Thu, Mar 5, 2020 at 1:34 PM 'Brent Meeker' via Everything List
<everything-list@googlegroups.com
<mailto:everything-list@googlegroups.com>> wrote:
On 3/4/2020 6:18 PM, Bruce Kellett wrote:
But one cannot just assume the Born rule in this case -- one has
to use the data to verify the probabilistic predictions. And the
observers on the majority of branches will get data that
disconfirms the Born rule. (For any value of the probability, the
proportion of observers who get data consistent with this value
decreases as N becomes large.)
No, that's where I was disagreeing with you. If "consistent with"
is defined as being within some given fraction, the proportion
increases as N becomes large. If the probability of the an even
is p and q=1-p then the proportion of events in N trials within
one std-deviation of p approaches 1/e and N->oo and the width of
the one std-deviation range goes down at 1/sqrt(N). So the
distribution of values over the ensemble of observers becomes
concentrated near the expected value, i.e. is consistent with that
value.
But what is the expected value? Does that not depend on the inferred
probabilities? The probability p is not a given -- it can only be
inferred from the observed data. And different observers will infer
different values of p. Then certainly, each observer will think that
the distribution of values over the 2^N observers will be concentrated
near his inferred value of p. The trouble is that that this is true
whatever value of p the observer infers -- i.e., for whatever branch
of the ensemble he is on.
Not if the branches are unequally weighted (or numbered), as Carroll
seems to assume, and those weights (or numbers) define the probability
of the branch in accordance with the Born rule. I'm not arguing that
this doesn't have to be put in "by hand". I'm arguing it is a way of
assigning measures to the multiple worlds so that even though all the
results occur, almost all observers will find results close to the Born
rule, i.e. that self-locating uncertainty will imply the right statistics.
Brent
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