On 2/8/2020 3:21 PM, Bruce Kellett wrote:
On Sun, Feb 9, 2020 at 9:48 AM 'Brent Meeker' via Everything List
<[email protected]
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On 2/8/2020 2:12 PM, Bruce Kellett wrote:
On Sun, Feb 9, 2020 at 6:38 AM 'Brent Meeker' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
On 2/7/2020 11:00 PM, Bruce Kellett wrote:
It is an indexical theory. The problem is that in MWI there
will always be observers who see the sequences that are
improbable according to the Born rule. This is not the case
in the single-world theory. There is no random sampling from
all possibilities in the single-world theory.
?? There's something deterministic in single-world QM? You
seem to have taken the position that MWI is not just an
interpretation, but a different theory.
That is a possibility. I do think that MWI has difficulty with
probability, and with accounting for the results of normal
observation.
That some very improbable results cannot occur in SW QM. I
think you are mistaken.
I don't know where you got the idea that I might think this.
No matter how low a probability the Born rule assigns to a
result, that result could occur on the first trial.
Yes, but in SW the probability of that is very low: in MWI the
probability for that is unity.
You keep saying that; but you're misreferencing what "that" is.
The probability of any given observer seeing the low probability
event is just that low probability. "That" isn't unity.
It is unity if the hypothesis is that every outcomes occurs for every
trial. It is not a matter of any arbitrary observer -- it is that
there is an observer who definitely sees that result.
Not "that result" = "every outcome occurs". It's that given an outcome,
there is an observer who sees it. And given an outcome there is only a
probability P(outcome_i) that you see it.
However, we seem to be in danger of going round in circles on
this, so it might be time to try a new tack.
As I said, I have difficulty understanding how the concept of
probability can make sense when all results occur in every trial.
If you have N independent repetitions of an interaction or
experiment that has n possible outcomes, the result, if every
outcome occurs every time, is a set of n^N sequences of results.
The question is "How does probability fit into such a picture?"
In any branch, when the experiment is performed, that branch is
deleted and replaced by n new branches, one for each possible
outcome of the experiment. This is clearly independent of any
model for the probability associated with each outcome. In the
literature, people speak about "weights of branches". But what
does this mean? -- that there are more of some types of branch?,
or that some branches are more 'important' that others? It does
not seem clear to me that one can assign any operational meaning
to such a concept of "branch weights".
That's why I said that to make it work one needs to postulate that
there are many more branches than possible results, so that
results can be "weighted" by having more representation in the
ensemble of branches. Then probabilities are then proportional to
branch count. That gives a definite physical meaning to
probabilities in MWI. It's a physical model that provides
"weights". BUT it's a cheat as far as saying MWI implies or
derives the Born rule. The rule has been slipped in by hand.
It certainly is a cheat. And it is a different model. It is not just
an interpretation of QM -- it is a different model, incompatible with
Everett. Everett is quite clear: he postulates one branch -- one
'relative state' -- for each component of a quantum superposition.
This is incompatible with multiple branches for each such component.
In this situation, the set of n^N sequences of results for this
series of trials is independent of any a priori assignment of
probabilities to individual outcomes
I don't understand what you mean by that. Are you limiting this
to a binomial experiment, with H's and T's? And are you assuming
that at every trial each outcome occurs exactly once in the
multiverse?
Did you not see that I speak of 'n' possible outcomes for every
experiment? It is by no means limited to binary outcomes. And yes, I
am following Everett and assuming that each trial outcomes occurs
exactly once in the multiverse. If you go beyond this, then you are
talking about a different, non-Everettian model. I think that most of
your comments are based on your assumption that an uncountable
infinity of branches is associated with each possible outcome (to
accommodate all real weights). That is why we seem to be constantly
talking at cross purposes -- you have not made you assumptions clear.
I was trying to address both at once. But, yes I think Bruno's idea of
a MWI, as well as other people's, requires a very large number of
branches; but not a realized infinity, because that makes it impossible
to assign a measure.
: whatever the probabilities or weights, the set of sequences of
results is the same. In other words, for the experimentalist, the
data he has to work with is the same for any presumed underlying
probabilistic model.
Are you saying the data he obtains has no probabilistic relation
to the ensemble of possible outcomes? You seem to be putting the
Bayesian inference backwards. The data he has is in some sense
independent of any model. But he's evaluating his model given the
data. That fact that this doesn't change the data is the same in
any interpretation.
The point is that the data are independent of any probabilistic model
-- given a strict Everettian interpretation of the relative states and
branching. Thus the data cannot be used to evaluate any such model.
What are you calling "the data"? All the branch results, one per
result? All the branch results with weighting by multiple branches for
the same result? The observations of some particular observer? It seems
your conclusion only applies to the first.
Consequently, experimental data cannot be used to infer any
probabalistic model. In particular, experimental data cannot be
used to test any prior theory one might have about the
probabilities of particular outcomes from individual experiments.
Sure it can. The data can imply a low posterior probability for a
given model. The experimenter has gotten one particular result.
It is irrelevant that other results occurred to other copies of
the experimenter.
That is only if probabilities and branch weights have an objective
meaning. My contention is that they do not in a strictly Everettian model.
The conclusion would be that such a model is unable to account
for standard scientific practice, in which we definitely use
experimental data to test our theories, and as the basis for
developing new and improved theories. This is impossible on the
above understanding of MWI.
So this understanding of MWI is presumably flawed. But how? I do
not see any other realistic way to implement the idea that all
possible results occur in any trial. Talking about branch weights
and probabilities seems to be entirely irrelevant because these
things have no operational significance in such a model.
They are parameters to the hypothetical model to be evaluated by
calculating their posterior probability given the observed
results. All possible results don't occur in any branch. They
occur in other branched to other observers and that influences the
result no more than supposing the results are drawn from some
ensemble.
Again, you seem to be implicitly relying on the assumption that branch
weights actually exist and have objective meaning. In other words,
your comments presume your idea of implementing probabilities as
branch counts. This is a different model. It is not implicit in the
Schrodinger equation, and it is certainly not what Everett envisaged.
But it is implicit, or even explicit in Bruno's model. It's also
consistent with Barbour's model. My criticism of it is that by
requiring this multiple branching, so you need two branches if Pup=1/2,
Pdwn=1/2 but you need a thousand branches if Pup=501/1000,
Pdwn=499/1000, you have now resorted to something outside Schroedinger's
equation and you have to put in Born's rule by hand. But in Bruno's
theory he begins by assuming a potential infinity of computational
threads, which then branch from identical bundles. Whether he can get QM
and Born rule remains to be seen.
Brent
Bruce
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