Re: Is State Vector Reduction a 'Process'?
- From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
- Date: Wed, 1 Jun 2005 13:27:44 +0000 (UTC)
rof@xxxxxxxxxxxx wrote:
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
I commented that already. the 'acto of registration' happens on the photographic plate or in the eye, not in the mind, and is simply the irreversible magnification due to dissipation by interaction with a macroscopic detector. It is objective and has no connection to any 'knowledge'.
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.
No; only that your interpretation of what he said in terms of knowledge is a postmodern interpretation, and either the Copenhagen interpretation nor Heisenberg's intention.
With due respect, and I sincerely mean no offense, I believe
that you have been infected
Whatever I am infected with, I hope it is highly infectuous and incurable, so that it spreads and has a lasting effect.
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
This is a long post, I cannot recognize myself reflected in it. Neither do I recognize signs of a mental disease in my behavior.
My understanding is that this is why you react so negatively to the
suggestion that the wavefunction describes knowledge.
I followed the historical development of the interpretations of QM
quite closely, reading hundreds of papers, to be able to make up my
own mind of how _I_ should interpret QM (and other physics).
In the discussions on s.p.r., I share my insights for those who might
wish to learn from it. I simply think that phrasing objective
descriptions in a psychological language, making them dependent on
mental processes, is neither necessary to understanding nor does it serve any useful purpose. There is nothing inherently absurd about
this assessment.
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,
I considered lots of argumewnts of all sides of the discussion, and believe to have excellent arguments for my point of view, that can compete well with other arguments. They have nothing to do with nobility, but with realism, intelligibility, easy visualitization. I believe that certain things really exist and can be described objectively, and that even the subjective, observer-dependent aspects can be described objectively. This makes for clear foundations, which is my supreme objective in my quest about physics.
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".
It seems that it is sufficient for you. But it is insufficient for me.
I want a mathematical model of reality within which one can clearly
say what exists, what is an experiment, an observer, a measurement,
a record, etc., in such a way that one can predict in principle which
experiments give outcomes with which accuracy.
Such arguments are common in qunatum mechanical foundations (e.g. discussions of the Heisenberg microscope) but currently based on
informal notions of experiment, observer, measurement, record
only.
My goal is to put the foundations of physics on a basis similarly to the foundations of mathematics, where the whole logical process of coherent deduction can be modelled on a metalevel and gives clarity to the foundations of mathematics that is missing in physics.
And I think that such foundations are possible and will provide the same clarity for physics.
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.
Phiosophy can only discuss what should be, but not how knowledge acquisition actually happens. The latter is an experimental question, not a purely deductive one, and hence belongs to psychology, not to philosophy.
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".
No. First, I didn't react with scorn (again you put guessed emotions of your choice into my statements), but simply observed what to me is a fact. Second, I don't think that psychology is not worth studying, quite on the contrary, it is a very interesting science. I only assert that psychology is a poor foundation for physics.
Of course, if this is pointed out to them, they
deny it, saying "Why not at all - I am the most
reasonable of fellows.
Everyone who has a sensible point of view argues that way, including you. What I point out to you does not seem sensible to you, and conversely. This is the natural situation in topics of controversy, and does not prove that you are right.
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.
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.
If you assert that the wave function is about knowledge then knowledge resides somewhere - according to you in some mind. But the claimed behavior of these minds is something that can be studied by field studies.
Your argument sounds as if you are not claiming that the wave function collapse is about the change of real knowledge of real minds, but about how knowledge should change if someone observes something and acts completely rational. But then it becomes a moral statement completely outside science.
However, the collapse was formulated by the founders as a necessity to make sense of quantum mechanics, and not as a postulate about moral
standards for maintaining knowledge in minds.
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,
How then can a non-objective thing change in time in an objective way??? (Please don't be offended by the three ?s!)
but different observers
will use different wavefunctions, depending on what knowledge they
have about the system.
If I know nothing about an experiemnt, which wave function should I use?
Should I use instead of a pure state the microcanonical ensemble,
suggested by many statistical mechanics treatments as noninformative prior? Then I make observations and find that they are not in accordance
with the predictions of my ensemble since it is born of ignorance
rather than knowledge...
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 must be a ficticious observer invented to suit your interpretation.
A real observer with a real mind has no wave function in his mind -- that changes unitarily according to a differential equation whose solution requires a computing capacity much beyond the mind's power, and once it sees a measurement (any look out of the window, or only a careful look at the detector needle to be sure of the third decimal?) it computes the solution of the corresponding eigenvalue problem to find out how the wave functions must be collapsed to be consistent.
At least you won't find that when interrogating the most competent experimental physicists who know how they update their knowledge.
Recall that subjective doesn't mean simply bad.
I never assumed that. But subjective means outside the realm of science,
unless that subjectivity can be explained and predicted by models of how
it arises from something objective, such as the subjective observer-dependence in special and general relativity.
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.
Please support your claims by solid evidence!
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.
I cannot understand how you can possibly arrive at this statement.
If your claim were true, what von Neumann actually said (first sentence)
would mean: ''Let us assume that we do not know what we know (the state of S)'', and then he deduces correctly from this (obviously false)
premise everything he likes.
"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.
No; it refers to the fact that the state is something that exists (since we can learn something about it) but we _don't_ know, hence must infer by a theoretical construction, while we _do_ know the results of the measurements, and can infer from them partial information about the state.
This is a much more coherent interpretation of his statement, and conforms quite well with the form of knowledge experimenters actually have, and with the practice of state estimation in high quality quantum experiments.
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.
No. It is routinely (and more reliably) done by computers.
We accept (usually without doubt) the inferences that a system like Mathematica performs upon our requests. And if we doubt, we usually doubt first _our_ abilities to make the right requests (resulting in a process called 'debugging') rather than the inference abilities of the computer.
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.
Of course knowledge is about propositions, but propositions are not about knowledge.
People discuss the consequences of the proposition 'The Riemann hypothesis is true' in the absence of any knowledge about the truth of this statement. The same happens routinely in proofs by contradiction, where we assume some proposition although we know (and want to demonstrate to someone else) that it is _not_ true.
The desire to assert that logic has nothing to do with the mind is,
I believe, rooted in the primitive notion of nobility,
No. For example, it can be rooted in the fact that logic can be performed by microchips, which have little to do with mind as commonly understood.
I was
asserting that von Neumann was aware that we only know the results
of measurements,
I agree with this assertion. It is in flat contradiction with your claim
that the wave function represents our knowledge. For a wave function
needs infinitely many bits to specify, while the results of measurements
(according to what you just stated, the _only_ thing we know about the system) can be coded in the finite number of bits making up a protocol.
"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
but with the same objective status as mass, temperature, momentum, charge distribution, etc. of an object. These are also theoretical constructs used to organize our observations.
And with the same objective status as the galaxy as an assembly of myriads of hot and heavy stars, a theoretical construction used to organize the information we can gather about certain light dots in the sky.
All of physics is theoretical construction based on past measurements.
Even the measurement results ('the spin of this particle was up') themselves are theoretical constructions, indirectly derived from
the raw observations.
which incorporates information about the results of past measurements on the system.
just as we infer the temperature field in a room from information about the results of past measurements of a thermometer.
That is why the wavefunction represents knowledge.
In this sense, it is a tautology. But this is not what von Neumann could have had in mind.
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,
No. You read this into my statements. Knowledge has nothing to do with cleanliness. Dirty things can be washed; I wouldn't know how to wash knowledge.
Knowledge is what we (think we) know. This may be a number of experimental results to within some accuracy, an approximate description of a quantum mechanical state, the rough temperature distribution in a room, the behavior of a piece of equipment according to the manufacturer's manual (perhaps corrected by our own calibration experiments), the weight, length and age of the persons working in a room, etc. It is (in some idealization) something describable in a finite string of symbols.
On the other hand, fundamental physics is about the mathematical
model of Nature resulting from such information. This model
(von Neumann's ''theoretical construction'') is inferred from observations and contains more accurate parts, less accurate parts,
probably a few mistaken parts, and completely unknown parts -
it is like a 17th century world map, but instead for the
physical phenomenon under study. The objective state of the
system is one of the polethora of states compatible with the
asvailable information - which one, we don't know. But if we know
sufficiently much, all compatible states are approximately the same,
so working with any particular of them will give good predicitions.
Nothing here prevents one of taking the system to be the whole universe. The state of the universe must simply be compatible with all details we observed in the parts of the universe accessible to our experiments.
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
Von Neumann says that collapse happens in each particular physical
system (defined by its boundary), but that consistency requires that
if we regard a particular system as part of a bigger system then
the collapse of the larger system must give, for the smaller system,
results compatible with the collapse of the smaller system considered
by itself. This is nothing more than an obvious compatibility
condition. It has nothing to do with the nature of the two systems,
You might care to notice that von Neumann carefully avoids to invoke either the 'mind' or the observer's 'knowledge'.
Von Neumann simply argues that the collapse is consistent with the psycho-physical parallelism (to the extent that one can define the
latter by the assertion that the ''boundary can be pushed arbitrarily into the interior of the body of the observer''). But his general
argument does not require a body or a brain; it is true wherever
the boundary is placed, for example when the boundary is placed
between the exposed photographic plate and the process developing
the plate to see the picture.
Thus the psycho-physical parallelism is completely inessential for the interpretation of the collapse.
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.
I read it and found it wanting. It projects a particular prejudice into his statements.
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
Von Neumann is more careful in his use of language than you in your interpretation of his words.
There is a difference between 'experience' and 'experiment'. The former is a psychological concept; the latter is a concept of physics.
An experience produces subjective sensory perceptions; an experiment produces recorded values of physical quantities.
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. ...
... to such an extent that his observer can be an inanimate object like a camera or a thermometer.
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.
Only in this last statement I agree with your interpretation of his position.
At this point my view of quantum mechanics differs from his. And with good grounds.
Arnold Neumaier
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