My understanding of Andrei's position is that there are *both*
subjective and objective probabilities. This position justifies the
quest for specific notion of quantum information theory. On the other
hand, some maintain that all probabilities are subjective. If this was
so, ordinary information theory would be sufficient, and quantum
probability theory would not be needed. A notable proponent of this view
was Edwin T. Jaynes (http://bayes.wustl.edu/) - his unfinished book
is very nice http://omega.albany.edu:8008/JaynesBookPdf.html ( an edited
version of it was later published by one of his collaborators
http://www.amazon.com/gp/sitbv3/reader/ref=sib_dp_pt/102-8431303-8078528?%5Fencoding=UTF8&asin=0521592712
)
* Infinite number of experiments required for Von Mises' probability
It is easy to view subjectivity as problematic: it's a loaded word after
all. Ultimately, as Koichiro says, we have objective observations. And
objective probabilities can be estimated, after a large number of
experiments. But in real world, we will not perform infinitely many
experiments as to get to those precise probabilities. There is no point
even trying this, as the experimental conditions will never be perfectly
identical.
* The subjective factor and models of models
For an extremely well-defined experiment with many experiments, there
will be overwhelming evidence for just one choice of probabilities.
Thus, the factor of subjectivity is minimized. On the other hand, when
there are few experiments, the subjective factor about what could those
measurements mean becomes more important. The whole point of subjective
probabilities is not to sweep this subjective factor under the rug, but
to instead embrace it, make it explicit, make it a topic of discussion.
We can learn a lot by building models of the assumptions, models of
models, and not just the models of phenomena. I think such intellectual
honesty and humility is a quality, not a deficiency.
* The inability to distinguish true randomness from ignorance
If we observe a non-deterministic dispersion of photons in the
experiment, it is clear that the experiment is not truly repeatable. The
*average* of the experiment is more or less repeatable, though. So what
is the reason for the experiment not to be repeatable? Perhaps it is
inherent stochasticity of nature - the true probabilities. But how do we
know that the probabilities are true? Perhaps we cannot control the
conditions of the experiment perfectly? Perhaps we don't know how to
measure without interfering with the experiment? Perhaps we only measure
a part of all that is there. The Copenhagen interpretation is about
getting rid of the "perhaps" (because we don't know anyway) and just
building a model of the objective results. When one doesn't have enough
information to decide on one interpretation, then just toss the
interpretation and calculate. As far as I am concerned, one should pick
the interpretation that one is most comfortable with. Perhaps, however,
one of the interpretations will be proven with some yet unknown technology.
* Context and subjectivity
I guess Andrei's contextual probabilities do capture a large part of
what subjective probability is technically about. If the observer's
assumptions (expressed as variables) are a part of this context, I'd
call the resulting probabilities subjective.
Best regards,
Aleks Jakulin
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