A Weinberg on the measurement problem

vanhees71

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The mathematical formalism of quantum theory has nothing to say regarding the actual outcome of a single measurement event; such questions are not answerd by the minimal statistical interpretation as long as one doesn't confuse the minimal statistical interpretation with the ensemble interpretation: There is no mechanism which can be proposed for the occurrence of an actual outcome of a single measurement event, no algorithm for it can be given and no causal description is possible. Thus, in order to relate the mathematical formalism of quantum theory to our perceived reality – actual outcomes of single measurement events – the wave-packet reduction postulate has to be put in “by hand” as part and parcel of quantum physics. Period!
It has all to say about the outcome of a single measurement event that can be said about it: If the system is not prepared in a state, for which the measured observable takes a determined value, then the outcome of the single measurement is indetermined (which is a tautology!). Than all QT says and up to the knoweldge we have can be said are probabilities for the possible outcomes of such measurements given the state the system is prepared in. This prediction can be tested (imho only) by preparing a sufficiently large ensemble of equally prepared systems and statistical analysis of the outcomes of measurements on each member of the ensemble. Whether or not you find this satisfactory from some metaphysical or philosophical point of view, physics doesn't care about.
 

Demystifier

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Whether or not you find this satisfactory from some metaphysical or philosophical point of view, physics doesn't care about.
By "physics", do you mean Nature or community of physicists? If you mean the latter, then a significant part of it actually cares. If you mean the former, then physics also doesn't care about our incomplete effective theories (such as standard QFT).
 

vanhees71

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I mean physics. Of course, there are many physicists who care about things outside of physics (myself included). It would be a pretty narrow view on the world if you'd only care for the natural sciences.

I'm not so clear about, what you mean by "incomplete". Standard QFT is indeed incomplete in the sense that it doesn't describe gravitational interactions. From a more purist mathematician's point of view you could even say it's intrinsically not complete since many issues seem to be simply ill-defined. As a physicist I'm modest enough to think that we have a well-working effective theory, namely (sometimes to be resummed/unitarized) perturbative QFT.
 

Buzz Bloom

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Yes, that's the state reduction postulate.
Hi DarMM:

I tried to find an authoritative explanation of the state reduction postulate online, but the best I could find is
Is this postulate an alternative name for "wave function collapse"?

Of the five QM interpretations in
which ones include this postulate? My guess is that it is just the following one:
Statistical ensemble interpretation:​
Individual measurement outcomes exist, but QM has nothing to say about them. Therefore QM is complete.​

Regards,
Buzz
 

Demystifier

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I'm not so clear about, what you mean by "incomplete".
By incomplete, I mean an effective theory which describes only what we, the human beings with limited abilities, can observe in practice with current technology.
 

Mentz114

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What are these initial conditions if not a wavefunction? The preparation set up?
Obviously - but I feel I'm being led into a trap. Soon you will argue that not all the dof in the preparation can have values - which I will deny and we'll get nowhere.

The problem arises if one accepts ( even as a premise) that the WF exists and can influence a physical process.
 

DarMM

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Obviously - but I feel I'm being led into a trap.
I'm not sure why you think I'm trapping you rather than just discussing things.

Soon you will argue that not all the dof in the preparation can have values - which I will deny and we'll get nowhere.
This is inevitable in a theory that only gives probabilities. It is of no importance because every instance in a repeated experiment is governed by the dynamics of the system and the initial conditions, not the wave function.
The problem is that in QM the initial preparation, ##\rho## and the dynamics ##U(t)## do not give the outcomes in experiments. Thus it is not only the initial conditions and the dynamics that seem to govern experiments. Doesn't the Kochen-Specker theorem block all the dofs having values?
 

DarMM

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I tried to find an authoritative explanation of the state reduction postulate online, but the best I could find is
Is this postulate an alternative name for "wave function collapse"?
It's commonly used in textbooks as an alternative name for wave function collapse as you said. It's a common element of the practical application of the theory, so all interpretations have it. They just don't agree on its status (i.e. is it fundamental) and nature (i.e. is it a physical process or a calculational aid)
 

Stephen Tashi

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What should the "consciousness of the observer" have to do with quantum measurements, which you can just let dead apparati do fully automatically without interference of any living being.
The dead apparati do not interpret what they are measuring. Investigating probabilities experimentally involves repeated measurements of similar events. It's human's who judge that a series of actions repeats "the same" experiment. Two repetitions of literally "the same" experiment wouldn't be two repetitions of something, it would be just that single self-same experiment. So interpreting the statistical significance of measurements involves a decision to classify different things as being alike.

A question (not particularly for @vanhees71 ) is how and whether interpretations of QM that invoke the conscious observer actually need an observer who experiences the subjective feeling we call consciousness. Can their approach be explained by an "observer" who is merely a machine or process that classifies things?

Suppose an observer (conscious or not) judges that preparations A define "the same" experiment. While he is executing these similar experiments, he encounters some cases where event B happens and some where it does not. He has the option of consider the cases where B happens as a subset of the data for theories about what happens after preparation A. He also has the option of considering those cases alone and taking data relevant to "What happens after preparation A is made and event B occurs?". Variations in passive classification don't affect the outcome of experiments, but they do affect probabilities in the sense that they affect the very definition of what probabilities are being estimated.

Is it necessary to call the choices in classification subjective, or a belief, or a function of the knowledge of the observer? Those things are are associated with conscious human observers. But do interpretations of QM that invoke a conscious observer actually need consciousness? Or do they merely need a process that makes decisions about classification?


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Mentz114

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I'm not sure why you think I'm trapping you rather than just discussing things.



The problem is that in QM the initial preparation, ##\rho## and the dynamics ##U(t)## do not give the outcomes in experiments. Thus it is not only the initial conditions and the dynamics that seem to govern experiments. Doesn't the Kochen-Specker theorem block all the dofs having values?
Told you so. I knew you would bring that up.

QM is a theory that predicts the probabilities of outcomes. It has nothing to say about the underlying dynamics. Theorems that claim otherwise are mathematically true but prove nothing except that such statements have no physical import.
 

DarMM

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Told you so. I knew you would bring that up.
I referenced DOFs because you mentioned them in a way that seem to run counter to the Kochen-Specker theorem. I didn't originally intend to comment on them. I only did so in response to what you said in #33. It's odd to introduce a topic and then claim I brought it up. Of course it will now come up since you introduced it.

Are you saying that all DOFs have well-defined values prior to measurement?

Again my original intent was not even related to this, but you mentioned it.

QM is a theory that predicts the probabilities of outcomes. It has nothing to say about the underlying dynamics. Theorems that claim otherwise are mathematically true but prove nothing except that such statements have no physical import.
What theorems do you have in mind here?
 
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By incomplete, I mean an effective theory which describes only what we, The human beings with limited abilities, can observe in practice with current technology.
It seems that many scientists have still not become aware that what we call "nature" appears to us first of all through our consciousness. A consequence is for example :

Timothy H. Goldsmith said:
http://www.ler.esalq.usp.br/aulas/lce1302/visao_aves.pdf

It is true, as many youngsters learn in school, that objects absorb some wavelengths of light and reflect the rest and that the colors we perceive “in” objects relate to the wavelengths of the reflected light. But color is not actually a property of light or of objects that reflect light. It is a sensation that arises within the brain.
The correlation between wavelength and perceived color is imperfect. Similar perceptions of color can be associated with various mixtures of light of different wavelengths and intensities.

It is the same for all our senses.

For us human being, consciousness/Lived experience is the starting point of any inquiry, is where we start from and where all must link back to.

/Patrick
 

Mentz114

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I referenced DOFs because you mentioned them in a way that seem to run counter to the Kochen-Specker theorem. I didn't originally intend to comment on them. I only did so in response to what you said in #33. It's odd to introduce a topic and then claim I brought it up. Of course it will now come up since you introduced it.
I mentioned dof's in the hope you might realize the futility of quoting theorems to persuade me of your point.
You never address my main point that the wave function cannot influence a dynamic process and is only a formula to calculate probabilities etc which I've tried to restate in different ways above.

All your arguments contradict this and therefore have no weight for me.
 

DarMM

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I mentioned dof's in the hope you might realize the futility of quoting theorems to persuade me of your point.

All your arguments contradict this and therefore have no weight for me.
I wasn't aware I had a point I was arguing in favor of. I certainly was not advocating the wave function as real. I don't know a single place where I invoked this.

The Kochen Specker theorem doesn't even rely on nor is concerned with the wave function being real. What's your issue with it or why do you think you can ignore its implications considering they seem to run counter to what you have said? You seem to be saying all the values prexisted the measurement, but this seems impossible in light of the theorem and the theorem isn't about wave function reality. In fact it's a theorem about the observable algebra not the state.
 
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Mentz114

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I wasn't aware I had a point I was arguing in favor of. I certainly was not advocating the wave function as real. I don't know a single place where I invoked this.
Sorry about that. But you accept it as a premise, which is nearly as bad :confused:

The Kochen Specker theorem doesn't even rely on nor is concerned with the wave function being real. What's your issue with it or why do you think you can ignore its implications considering they seem to run counter to what you have said? You seem to be saying all the values prexisted the measurement, but this seems impossible in light of the theorem and the theorem isn't about wave function reality. In fact it's a theorem about the observable algebra not the state.
I admit that I have not tried to understand the theorem.

You make my point with the words I've emphasised. For the theorem to have physical import the 'operator algebra' must be physical. But it is a mathematical object. The theorem makes a statement about a methodology not about values of dynamical variables.
 

DarMM

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Sorry about that. But you accept it as a premise, which is nearly as bad
Where did I accept it as a premise?

You make my point with the words I've emphasised. For the theorem to have physical import the 'operator algebra' must be physical. But it is a mathematical object. The theorem makes a statement about a methodology not about values of dynamical variables.
That was the classic Kochen Specker theorem. The modern one in the ontological models framework can be proven directly as a contradiction between pre-existing values and observations, just as Bell's theorem does not rely on the mathematical structure of QM.
 

vanhees71

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By incomplete, I mean an effective theory which describes only what we, the human beings with limited abilities, can observe in practice with current technology.
That's of course a hard to answer question. We can always only get information about nature by observing her. It may well be that we cannot observe some aspects of nature. Also any theory is always "complete" as long as no observations indicate that something is missing. For me to say "a theory is complete" always includes an "as far as we know now", and in this sense many previous theories turned out to be incomplete in the one or the other way.

In that sense, as far as we know, QT is complete. It precisely describe what we observe. The key issue we always come back to in our debates over interpretation is the probabilistic meaning of the state. According to QT the implied randomness of nature is fundamental, i.e., it is not due to lack of knowledge about the value of an observable but even if we have determined the state of a system completely, i.e., determined the values of a complete set of compatible observables, some other observables are indetermined. According to QT this indeterminism is not due to lack of knowledge of the state but it's a necessary conclusion of the theory.

So far, despite some effort, nobody has found a way to save the determinism of classical physics in a way that's compatible with the observations. E.g., the time at which a given unstable nucleus decays is indetermined. It's not due to a lack of knowledge about its state but it simply is indetermined.

Everything we can say about nature is however only preliminary in the sense that we can always only use or most up-to-date knowledge (condensed to theories) to make statements like these discussed above. Maybe one day somebody finds a deterministic theory, but then it must explain at least the same phenomenology as QT does, and I'm not sure whether those who feel uneasy with QT, particularly it's state on ontolgy, will feel more comfortable with a non-local deterministic more comprehensive theory. If there's "quantum weirdness" (which I don't think there is, because I accept the posibility of genuine randomness without any quibbles), then I predict there'll be even weirder ideas necessary to formulate such a non-local determinstic theory.
 

vanhees71

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Told you so. I knew you would bring that up.

QM is a theory that predicts the probabilities of outcomes. It has nothing to say about the underlying dynamics. Theorems that claim otherwise are mathematically true but prove nothing except that such statements have no physical import.
What do you mean by "it has nothing to say about the underlying dynamics"? To the contrary QT has everything to say about dynamics. Given the initial state and the Hamiltonian of the system you can calculate the state at any later time. That's dynamics, isn't it? It's not a theorem but makes up part of the fundamental postulates of the theory.
 

Demystifier

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For me to say "a theory is complete" always includes an "as far as we know now"
So when you say that physics doesn't care about philosophical problems one might have with physics, you really mean that the best theories we currently have are just instrumental tools that work in practice, and from the point of view of their work in practice the philosophical questions are simply irrelevant. Asking philosophical questions about quantum mechanics is no more meaningful than asking philosophical questions about a hammer.
 

Mentz114

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What do you mean by "it has nothing to say about the underlying dynamics"? To the contrary QT has everything to say about dynamics. Given the initial state and the Hamiltonian of the system you can calculate the state at any later time. That's dynamics, isn't it? It's not a theorem but makes up part of the fundamental postulates of the theory.
I think you are referring to the 'dynamics' of the probabilities ##\psi(t) = e^{i\hat{H}t}\psi##. I mean something else.
 

Mentz114

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Where did I accept it as a premise?


That was the classic Kochen Specker theorem. The modern one in the ontological models framework can be proven directly as a contradiction between pre-existing values and observations, just as Bell's theorem does not rely on the mathematical structure of QM.
OK, I'll read up on the KS theorem when I get the chance. But it sounds as if it assumes that ##\psi## must be real.
 

DarMM

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OK, I'll read up on the KS theorem when I get the chance. But it sounds as if it assumes that ##\psi## must be real.
It doesn't. I don't know why you think it sounds like it does because it literally does not assume it.
 
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We can always only get information about nature by observing her. It may well be that we cannot observe some aspects of nature.
Are we observing from "nature " something other than a function of space and time F(r,t) or a function of sound and time F(s, t)?

For example, concerning the spin, what we observe is a position which is a function of space and time, and then we need a theoretical model to interpret it.

Another example: Cloud chamber.

/Patrick
 
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