Re: Is State Vector Reduction a 'Process'?

Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx> writes:

>rof@xxxxxxxxxxxx wrote:

>> Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx> writes:
>>
>> Your treatment of the Copenhagen
>> interpretation in the article claims that the "unresolved
>> quantum-classical interface issue (including the missing definition
>> of which situations constitute a measurement) is a serious defect
>> of the Copenhagen interpretation when viewed as a fundamental
>> interpretation of quantum mechanics."
>>
>> This is slightly unfair to the Copenhagen interpretation, in
>> which the wavefunction is understood to represent knowledge
>> about the system, rather than the system itself.

>No. As far as I can tell, the first mention of the claim that
>''the wavefunction is understood to represent knowledge'' is by
>Jaynes in the 1950ies, long after the establishment of the
>Copenhagen interpretation.

I may have confused the official Copenhagen interpretation with
what Bohr, Heisenberg, von Neumann and so on believed. As Scerir
pointed out in this thread, Heisenberg said "The discontinuous change
in the probability function, however, takes place with the act
of registration, because it is the discontinuous change
of our knowledge in the instant of registration that has its
image in the discontinuous change of the probability function.",
Hiesenberg, "Physics and Philosophy", 1958

It may be that Heisenberg changed his interpretation of quantum
mechanics before he wrote that. It's even possible that Jaynes
influenced him for all I know. From what you have said about
your own interpretation, I take it that you claim that
Heisenberg was completely wrong when he wrote the
sentence quoted above.

With due respect, and I sincerely mean no offense, I believe
that you have been infected with the mental disease that I
ranted about in an earlier post:
http://groups-beta.google.com/group/sci.physics.research/msg/69ca190957f25c12?dmode=source
My understanding is that this is why you react so negatively to the
suggestion that the wavefunction describes knowledge. There is
nothing inherently absurd about that idea, but physicists and
mathematicians who believe that their subject is "noble", and that
investigation of the mind is "dirty" will reject it immediately and
without very good arguments, although they will do a great deal of
sneering and insulting to make up for the lack of good counter-arguments
(this is not to suggest that you have done so, or that you should,
but it is the way people in general react when their mental diseases
are attacked).

This idea of nobility is, quite frankly, medieval savagery, but
people in general are quite willing to adopt such an idea if it
helps their self-esteem. Everybody wants to be noble. Of course,
that doesn't mean that people are fully aware of what is happening.
The thought "I'm superior to that other group of people over there?
I like that idea," probably doesn't explicitly pass through their
mind, but some low-level mental processing registers exactly that.

>> A definition
>> of measurement isn't missing because measurement is the
>> acquisition of new knowledge.

>This is not a good definition since it is never specified what
>constitutes acquisition of knowledge.

Acquisition of knowledge is what happens when you look at the
measuring device and see where the pointer is pointing. That's
perfectly precise for a normal person, but it seems insufficient
to somebody who wants to know about "the real objective world".

>The theory of knowledge
>acquisition is a branch of psychology, not of physics.

The theory of knowledge acquisition is actually part of
philosophy, and is called epistemology. It is what metaphysics
should be, but unfortunately, in their rush to find out
what "really exists", most people who think about metaphysics
end up doing ontology instead. Ontology is a false hope -
you can never know "what really really exists"; we learn this
if we study epistemology, which is the theory of knowledge
acquistion, and which is qualified to address questions
about what we can know. Those who rush into ontology,
however, never learn this. They take it for granted that
they can know the truth about what's real, and rush off
in search of it. "I'm not interested in knowledge," they
say, "I want to know what's real." When approached by
an epistemologist who wants to help them understand
the situation, they react with scorn, declaring that
the theory of knowledge acquisition is a branch of
psychology, implying that it is therefore unworthy
of study, less noble than the quest for what's "real".

Of course, if this is pointed out to them, they
deny it, saying "Why not at all - I am the most
reasonable of fellows. I have carefully deliberated
and decided that what I am doing is the most sensible
thing to do. Let me refute your arguments," and then
they produce arguments which are unconvincing even to
themselves.

>> State vector reduction happens
>> because the observer acquires new knowledge and then updates
>> the mathematical representation of his knowledge to reflect
>> the new knowledge that he has.

>I doubt whether any observer updates his or her knowledge according
>to Bayesian reasoning. Field studies probably show large deviations
>from this supposedly universal behavior.

I have seen this kind of argument many times, and have never
understood why anybody would think it was valid. The general
form of the argument goes like this:

A: X is the proper way to do task Y.
B: That's wrong because X is not the way the average man on the street
attempts to do task Y.

Now, it seems to me abundantly clear that what the man on the
street does is of little relevance to the question of whether
X is the proper way to do task Y. The assertion that Bayesian
reasoning is the correct way to proceed when one has incomplete
information is not an assertion about how people behave, and
cannot be disproved by field studies.

>Furthermore, knowledge depends on subjective decisions to trust
>a measurement. If we discard one as an artifact, there is no
>collapse. How can the collapse depend on such subjective issues?

In the "wavefunction represents knowledge" interpretation, the
wavefunction is not an objective thing, but different observers
will use different wavefunctions, depending on what knowledge they
have about the system. The "collapse" is what happens when the
observer receives new knowledge, and updates his mathematical
representation of his knowledge to reflect the new knowledge that
he has. This is a subjective thing, because a different observer,
who has not received any new knowledge, will continue to use his
original wavefunction, and so the collapse is not objective. So
the answer to "How can the collapse depend on such subjective
issues?" is that the collapse itself is subjective. This is evident
from what Heisenberg said above about the "discontinuous change in
our knowledge."

Recall that subjective doesn't mean simply bad. It means that
the thing in question is particular to a single observer,
and it not common to all observers.

>At the time of Bohr, von neumann and Wigner, the collapse meant
>something objective, though it might have been related to the mind
>in some unspecified way.

I have to disagree with that, although I do not mean it in an
adversarial way. The relation to the mind was perfectly clear and
very specific for these people, at least by the '50s. Also, since
they understood that the wavefunction represented knowledge, the
collapse wasn't an objective thing for them.

>>>Von Neumann takes the collapse as an axiom, hence also testifies to its
>>>reality.
>>
>> He uses it as an axiom, but that doesn't mean that he claimed that
>> the wavefunction didn't represent knowledge.

>But he certainly didn't claim that the wavefunction does represent
>knowledge.

As I quoted before,

"Let us assume that we do not know the state of a system, S, but
that we have made certain measurements about the state of S and
know their results. In reality, it always happens this way, because
we can learn something about the state of S only from the results
of measurements. More precisely, the states are only a theoretical
construction, only the results of measurements are actually available,
and the problem of physics is to furnish relationships between the
results of past and future measurements." p. 337

This is exactly a claim that the wavefunction represents
knowledge. "The states are a theoretical construction,
only the results of measurements are actually available" refers
to the fact that the results of measurements are the knowledge
available, and that the states are a theoretical construction
which encode that knowledge.

>> in his 1938 paper with Birkhoff, "The Logic of
>> Quantum Mechanics", for example, he expresses the view
>> that the formalism of quantum mechanics is the way it
>> is because the algebra of Hilbert-space subspaces is
>> that of a non-distributive orthomodular lattice, which
>> matches the structure of the collection of experimentally
>> verifiable propositions about a system. This seems to
>> me to be an indication that he considered rays of Hilbert
>> space to be associated with propositions (knowledge), rather
>> than with the actual configuration of the system.

>No. A proposition is a statement that is true or false,
>or undecidable. It has nothing to do with whether or not
>anyone knows (or claims to know) its truth or falsehood.

Logic, which includes the propositional calculus, is the formal
science of inference, and inference can only be done by the mind.
An inference is what allows one to derive new knowledge from
knowledge that one already has. Knowledge is always of the
form "I know that proposition X is true", so propositions
certainly have a lot to do with knowledge.

What you have done is to suggest that I said that what
a proposition is depends on whether somebody knows or
claims to know its truth or falsehood. I never said
that, and I don't claim it now.

The desire to assert that logic has nothing to do with the mind is,
I believe, rooted in the primitive notion of nobility, since logic
is clearly part of the foundation of mathematics and therefore
worthy of respect, while the mind is the province of philosophers
and psychologists, who are not worthy of a physicist's respect. The
assertion that logic has nothing to do with the mind, however, is
evidently incorrect. My dictionary defines logic as "the science
of reasoning, proof, thinking, or inference", which means that it
is the science of certain mental acts.

I have to anticipate how somebody could reject something as
simple as this. The only thing I can think of is that somebody
might claim that, since computers can be programmed to do
symbolic manipulation, logic has nothing to do with thinking.

The problem with this argument is that the fact that computers
can do the symbolic manipulation associated with formal logic
indicates only that logic can be represented by symbolic
manipulations, but establishes nothing about what those
symbolic manipulations describe. Logic was established
in its present form because those symbolic manipulations
describe certain rules of correct thinking.

>> "Let us assume that we do not know the state of a
>> system, S,

>This assumption already shows that the state of the system
>must exist independent of our knowledge.

Now, as far as you were aware when you read that, nobody
had claimed that the state of the system didn't exist.

I was not asserting that the state of the system, considered as a
separate thing from our knowledge of it, doesn't exist. I was
asserting that von Neumann was aware that we only know the results
of measurements, and so these are what the mathematical symbols
that we write down represent. He goes on to say:

"More precisely, the states are only a theoretical construction,
only the results of measurements are actually available, and the
problem of physics is to furnish relationships between the results
of past and future measurements. To be sure, this is always
accomplished through the introduction of the auxilliary concept
"state", but the physical theory must then tell us on the one hand
how to make from past measurements inferences about the present
state, and on the other hand, how to go from the present state to
the results of future measurements." p. 337

What he is saying is that, in quantum mechanics, what we call
a "state" is actually a theoretical construction which incorporates
information about the results of past measurements on the system.
That is why the wavefunction represents knowledge. We are free,
of course, to say that the actual system is in a state which
is distinct from our knowledge of it, and that the measurements
tell us information about the "real" state, but the "state"
in quantum mechanics incorporates only whatever information
is available from the results of past measurements, and the
concept of the "real" state is an auxilliary concept. To say
that it is an auxilliary concept does not denigrate it in
any way, or insult its nobility, or deny the existence
of an actual state of the system, but it means that the concept
carries with it no information which is relevant for predicting
future measurement results based on past ones.

>> The principle of psycho-physical
>> parallelism tells us that, whatever we claim to know
>> about the physical world, what we actually know about
>> is what's going on inside our body,

>I don't buy this. What we know is some platonic extract
>extrapolated from sense data. And much of it is mistaken
>in detail, but still we think we know and act accordingly.
>It has nothing to do with physics as understood pragmatically.

Basically, you are saying that knowledge is a dirty thing,
not worth investigating for a noble physicist. You are
right that it has nothing to do with physics as understood
pragmatically, which means that it is not relevant for
the practical purposes of turning on the measuring device
and pressing the buttons on it. On the other hand, it
is relevant for a proper understanding of physics.

Let me try to address your concern that knowledge is
human and therefore fallible. It might be said that
inference is human and therefore fallible. That is
why we develop logic as a formal science - to
relieve us of the labour of making inferences ourselves.
The fallibility of humans doesn't mean that logic
is somehow flawed; it means that people make mistakes in
their application of it.

With knowledge, there is also a way to think and process
knowledge without making mistakes, although people
might not always succeed in using it properly. That
is why we look for a symbolic formalism; if we develop
one, mistakes will be easier to spot, as they are in
logic.

Also, when you say "I don't buy this," are you saying that
you don't believe that von Neumann held this opinion,
namely that the principle of psycho-physical parallelism
tells us that we can consider what we are observing
to be within our own bodies? Because he did:

"We wish to measure a temperature. ... [we can] say: this
temperature is measured by the thermometer. ... we can
calculate the resultant length of the mercury column,
and then say: this length is seen by the observer. Going
still further, and taking the light source into consideration ...
we would say: this image is registered by the retina of the
observer. And were our physiological knowledge more precise
than it is today, we could go still further, tracing the
chemical reactions which produce the impression of this image on
the retina, in the optic nerve tract and in the brain, and then in
the end say: these chemical changes of his brain cells are
perceived by the observer." p.419

"That this boundary can be pushed arbitrarily into the interior
of the body of the observer is the content of the principle
of the psycho-physical parallelism." p.420

>> You might also want to read the paper by Lon Becker:
>> "That von Neumann Did Not Believe in a Physical Collapse",
>> http://bjps.oupjournals.org/cgi/content/abstract/55/1/121

>I'll read it and comment later, if I have more to say than
>what I said already.

Lon seems to be trying to present the view that von Neumann
believed in a relative-state interpretation, which is
presumably his own favourite interpretation, and I further
presume that he believed that he could garner support
for his interpretation by claiming that von Neumann
believed it.

Similarly, you are trying to claim that von Neumann shared your
"collapse is a physical process" interpretation, and I assert that
he believed the wavefunction represented knowledge.

He also didn't have the "subjective means bad" attitude of modern
physicists, and was aware that what we deal with in physics is
not "the real world", but rather with subjective observations:
"Indeed experience only makes statements of this type: an observer
has made a certain (subjective) observation; and never any like
this: a physical quantity has a certain value." p.420

For him, the distinction between the observer and the observed
was of fundamental importance in quantum mechanics; this is
the so-called quantum/classical boundary:
"That is, we must always divide the world into two parts,
the one being the observed system, the other the observer. ...
The boundary between the two is arbitrary to a large extent. ...
but this does not change the fact that in each method of description
the boundary must be placed somewhere, if the method is not to
proceed vacuously, i.e., if a comparison with experiment is to be
possible." p.420

So, from von Neumann's point of view, to use a "wavefunction of the
universe" would be to proceed vacuously.

R.

.