On 11/08/2017 7:13 pm, Bruno Marchal wrote:
On 11 Aug 2017, at 02:11, Bruce Kellett wrote:
On 11/08/2017 9:45 am, Stathis Papaioannou wrote:
"What will I see tomorrow?" is meaningful and does not contain any
false propositions. Humans who are fully aware that there will be
multiple copies understand the question and can use it consistently,
and as I have tried to demonstrate even animals have an instinctive
understanding of it. Probabilities can be consistently calculated
using the assumption that I will experience being one and only one
of the multiple future copies, and these probabilities can be used
to plan for the future and to run successful business ventures. If
you still insist it is gibberish that calls into question your usage
of the word "gibberish ".
Not everyone will be successful in this scenario. No matter how mane
duplications cycles are gone through, there will always be one
individual at the end who has not received any reward at all (he has
never seen Washington :-)). This is the problem of "monster
sequences" that is so troublesome for understanding probability in
Everett QM.
? You might elaborate. It looks like the white rabbit problem.
It has nothing to do with the white rabbit problem. In the duplication
model, each iteration gives W and M, each with unit probability. This is
a trivial consequence of the fact that there is a person created in W
and in M every time, so we know in advance that these occur necessarily.
So after N iterations of the duplication (each person is re-duplicated
on each iteration) so there are 2^N sequences after N iterations. One of
these sequences will be N occurrences of M, and one will be N
occurrences of W. So the prediction of the person with N occurrences of
M, based on induction from his past experiences, will be M, with p =1.
Similarly, for the person with N occurrences of W, his prediction will
be p(W) = 1. People from other sequences predict W or M with varying
probabilities. Very few actually predict p(W) = p(M) = 1/2.
In the duplication scenario, the third person view enables one to put a
natural measure over these sequences -- just by counting the number of
sequences with particular relative frequencies. The low measure
(probability) sequences are those known as "monster sequences" in
Everett QM, and they can be seen to be of small measure in the classical
duplication scenario.
The problem in QM is that no external observer is possible. A
probabilistic interpretation then becomes problematic because we cannot
count over all the sequences: we only have the one sequence that we
actually observe, and we can have no way of knowing whether or not what
we have observed is a "monster sequence". This gives rise to the
question as to whether observation can ever be a reliable guide for
determining the underlying probabilities -- how can we use any sequence
of observed results as a test of some theory? The sequence we have
observed might, for all we know, be some 'monster sequence' of very low
probability.
The problem is usually circumvented by assuming a probabilistic model
from the start, but that is imposed from the outside and does not arise
from the theory itself. Deutsch and Wallace get around the problem in
this way -- they assume at the outset that small amplitudes correspond
to small probabilities, so monster sequences are assumed to be very
unlikely, and observed frequencies are assumed to converge towards the
true underlying probabilities. But then, this convergence is not
uniform, or even necessarily monotonic: the best one can say is that
observed frequencies tend to converge only /in probability/ to the true
probabilities. Hence there is circularity inherent in any such approach
to probability in Everett QM, where every outcome occurs with
probability equal to one. Deutsch and Wallace do not avoid this
circularity in their attempts to derive the Born Rule.
I see the problem with mechanism, (indeed that is the result of the
UDA: there is a measure on first person experience problem), but in
Everett the problem is solved by Feynman phase randomization, itself
justifiable from Gleason theorem. Then the math of self-reference
shows that, very possibly, Gleason theorem will probably solve the
classical case too, given that we find quantum logics at the place needed.
Everett does not solve the measure problem, or give any non-circular
account of probability in QM: Feynman phase randomization is a possible
solution to white rabbits, but it has nothing to do with the origin of
probabilities.
Gleason's theorem does not avoid the circularity problem either. All
that Gleason's theorem demonstrates is that for space of greater than
two dimensions, any viable probabilistic interpretation has to accord
with the Born Rule. But that does not demonstrate that one can actually
have a probabilistic interpretation in the many worlds case. Zurek is
quite dismissive of Gleason's theorem because, as he says, it assumes
the additivity of probabilities, rather than deriving this result from
within the theory. You have to show that results in QM give a model that
satisfies probability axioms, such as those of Kolmogorov -- one can't
just assume from the start that these axioms apply. This is one of the
main strengths of Zurek's 'envariance' approach, based as it is on the
symmetries of in entanglement -- he does not have to assume a measure
(probability) or probability axioms, he derives them from entanglement.
Are-you defending John Clark? That would be nice! He convinces nobody
since years, and some helps might be handy.
I think that John does have a point -- the prediction of probabilities
different from unity is possible only in a third person overview of the
situation. The prediction p(M) = p(W) = 1 is all that the set up
actually allows one to conclude prior to the duplication.
Are you telling us that P(W) ≠ P(M) ≠ 1/2. What do *you* expect when
pushing the button in Helsinki?
I expect to die, to be 'cut', according to the protocol. The guys in W
and M are two new persons, and neither was around in H to make any
prediction whatsoever.
Bruce
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