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.
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.
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?
: 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.
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.
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.
Brent
Bruce
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