From: Amara Graps (amara@amara.com)
Date: Fri Sep 13 2002 - 01:11:55 MDT
Serafino:
>Bohr wrote (in 'The Unity of Science') " [Complementarity
>should] be seen as a logical expression of our situation
>concerning objective description in this area of experience. The
>realization that the interaction between measuring devices and
>the physical systems forms an integrating part of quantum
>phenomena, has not only revealed an unexpected limitation of the
>mechanistic view of nature which attributes well defined
>properties to the objects themselves, but it has forced us to
>give special attention to the problem of observation when
>ordering the experiences. "
>Bohr also wrote (in Atomic Physics and Human Knowledge, Wiley,
>1959) " ... a subsequent measurement to a certain degree
>deprives the information given by a previous measurement of its
>significance for predicting the future course of phenomena.
>Obviously, these facts not only set a limit to the extent of the
>information obtainable by measurement, but they also set a limit
>to the meaning which we may attribute to such information. We
>meet here in a new light the old truth that in our description
>of nature the purpose is not to disclose the real essence of the
>phenomena but only to track down, so far as it possible,
>relations between the manifold aspects of our experience."
>Note he uses the terms 'information' and 'limit'. They are the very
>essence of the Copenhagen Interpretation.
Yes, in that Bohr's 'Copenhagen Theory' says that even when the QM state
vector gives only probabilities, it is a complete description of
reality in the sense that nothing more can ever be known; not because
of technological limitations, but because of fundamental principles.
But Jaynes seems pretty convinced ('Clearing Up Mysteries,the Original
Goal') about Bohr's way of perceiving physics problems. He says that
persistent in Bohr's writings (which Jaynes calls vague, puzzling,
foglike) is a common logical structure which indicates that Bohr was
never on the ontological level traditional in physics. Always he
discussing _not_ Nature, but our _information_ about Nature, but that
physics at that time did not have the vocabulary for expressing ideas
on that level, so then his words appeared muddy.
About Dirac: I learned (from Jaynes' writings) Dirac was working with
Harald Jeffreys (a Bayesian ...) side by side for a little while at
St. John's College, and he seems to have not realized what Jeffrey's
probability theory could offer, that is, a vehicle for expressing
epistemological notions quantitatively. Jaynes said that if either
Bohr or Dirac understood the work of Jeffreys, the recent history of
theoretical physics might have been very different: they would have
the language and the technical apparatus with which Bohr's ideas could
be stated and worked out precisely without mysticism. Had they done
this, and explained clearly the distinction between the ontological
and epistemological levels, Einstein would have understood it and
accepted it.
It seems to me that the Q.M. Bayesian folks should collect their papers
plus the much older work going back to the first half of last century
and put it in a book for more accessibility. There is a lot of
Bayesian literature on this Q.M. topic going back 50 years but it is a
really scattered. If the handful of Q.M. Bayesians that I met at my first
(and only) MaxEnt conference four years ago is a representative number, then
there must be a couple dozen people in the world actively working on this
topic at present.
Anyway, "if, then, should, could.." I've already written (too) many
times about Bayesian stuff in past years on this list and I have bigger
things on my plate, as you know.
I'll simply summarize with some things that a former Bayesian acquaintance
told me four years ago while I was writing a popular science article
about this Bayesian stuff.
Amara
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A summary: "Who are The Bayesians?"
by A. Gottvald, September 1998.
The Bayesians assert that:
Our inference is always conditional to some prior information,
involving also our data. There is nothing like "unconditional
probability". All human's knowledge is _conditional_.
Probability of an event is interpreted as a state of our knowledge
about the event.
Probability of an event (and consequently, an information about the
event) is not an absolute physical attribute of the event, but rather
a model representing our state of knowledge abou thte event. For a
Bayesian, the information is neither a physically existing nor an
absolute "fluid" flowing from a transmitter to a receiver; the
information is unseparable from a prior state of our mind.
An orthodox 'frequentist' interpretation of probability, in terms of
"random variable", is only a very special case of a Bayesian concept
of probability. Bayesians does not use the concept of a "random
variable" approaching a probability in a limit, as it is too
restrictive and fuzzy for many phenomena.
A probability of probability represents a difference between a
stability of our state of knowledge about many events. E.g. consider a
stable probability assigned to a dice, versus an unstable probability
assigned ot an existence of life on Mars.
Using all prior knowledge (contextual information) available is the
most objective way to analyze our data (hypotheses). In general, also
the data provide some prior knowledge how to analyze them, and the
prior knowledge reduces the uncertainty of our inference.
A logical relationship between the event (and their probabilities)
does not imply a causal (physical) relationship between the events.
Here is an origin of a Mind Projection Fallacy, which is behind a huge
number of misconceptions and 'paradoxes' in mathematics (set theory,
information theory, Fourier transform,...) physics (quantum and
relativistic physics, potential, ...) philosophy (Bohr, Einstein,
Bohm, Popper, Penrose, ...) which puzzled a big part of science in the
[last] century. In contrast, the Bayesian know that when a new fossil
changes our picture about a dinosaur, it does not mean that we
physically changed something in Jurassic park.)
Bayes Theorem is only a multiplication rule of probability theory,
which shows a relationship between a posterior probability, a
likelihood of data to model, and prior probability. The Bayes Theorem
is only an important segment of the probability theory understood as
an extended logic of rational inference.
The prior probability and posterior probability are not necessarily
related in time. These concepts show just a different relationship to
the data to be analyzed.
The Bayesian methodologies approach the scientific inference from "first
principles", grasping an n-parametric event directly with an
n-dimensional posterior probability distribution. This general model
shows a systematic straightforward way to integrate out some nuisance
parameters, to compute maximum unbiased estimations of parameters, to
evaluate probabilities of hypotheses, etc.
As a practical rule, the Bayesian methodology (of inference) assign
practically identical probabilities to the events (parameter
estimations) only in an abstract limit, when no prior knowledge about
the event is available. When some prior information is available, the
Bayesian methodology is superior in detecting some existing and
refusing some non-existing phenomena.
In summary, the Bayesians deal with the uncertainty of our inference,
and its fundamental relationship to prior information. They clarify
some puzzling relationships between our data, our models, and our
prior and posterior knowledge. The Bayesians apply their systematic
methodology to see neither too much nor too little in our data. They
actually apply an extended log of scientific inference, which
translates our human's knowledge to some rational statements about our
external perceptions.
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-- *********************************************************************** Amara Graps, PhD email: amara@amara.com Computational Physics vita: ftp://ftp.amara.com/pub/resume.txt Multiplex Answers URL: http://www.amara.com/ *********************************************************************** "There's only one thing more beautiful than a beautiful dream, and that's a beautiful reality." --Ashleigh Brilliant
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