Statistical ensemble interpretation done right

[PeterDonis]

Just tell me, how I should call, real-lab measurement results, which are evaluated by statistical means to compare them to the predicted probabilities.

I have already responded to this.

 

[PeterDonis]

Yes I do!

No, you don't. You have repeated a question that has already been answered, as I posted just now.

Just tell me, how you want me to phrase things, so that we can avoid this nonsensical debates about semantics!

Again, this has already been answered. But apparently you are not reading the answers, although you seem to believe that you are.

 

[vanhees71]

I have overlooked the answer then. Sorry for that. Can you just tell me, which word(s) to use, so that we can come back to a constructive discussion?

 

[PeterDonis]

I have overlooked the answer then. Sorry for that.

Apologies for overlooking something mean nothing if you don't go back and do the thing you overlooked.

Can you just tell me, which word(s) to use, so that we can come back to a constructive discussion?

Can you just read the answer that has already been given in this thread, instead of making people repeat themselves?

 

[vanhees71]

Apologies for overlooking something mean nothing if you don't go back and do the thing you overlooked.Can you just read the answer that has already been given in this thread, instead of making people repeat themselves?

I have done so right now. You haven't answer my question explicitly. So once more: Which term do you want me to use when I refer to a real-lab table of measurement results on a (necessarily finite) set of "equally prepared" systems. In everyday used language among my colleagues that's often called an "ensemble". It's of course only an approximation to a mathematical abstract infinitely large ensemble. I admitted this right from the beginning.

 

[PeterDonis]

You haven't answer my question explicitly.

You're right: I, personally, didn't. I just pointed you to a post by another person, @A. Neumaier, who did. Please go and read what he posted and respond to it, instead of quibbling.

 

[vanhees71]

I've read it. He calls it "statistical sample". Fine! Can we FINALLY get on-topic again now?

 

[A. Neumaier]

I've read it. He calls it "statistical sample". Fine! Can we FINALLY get on-topic again now?

A statistical sample is the standard name for a finite, empirically observed approximation to the theoretical ensemble characterized classically by a probability measure and in quantum mechanics by a mixed (or in special cases pure) state.

From p.26 of Volume 5 of the treatise by Landau and Lifschitz:

we may consider simultaneously, in a formal manner, a very large (in the limit infinite) number of exactly identical subsystems, [footnote:] Such an imaginary set of identical systems is usually called a statistical ensemble.

Thus the statistical ensemble is a merely imagined idealization, a formal construct, whereas a statistical sample consists of the results of actual observations.

Loosely speaking (as often done by physicists), one can use both terms interchangeably, but when interpretation details matter, one should distinguish the two.

 

[vanhees71]

The point is that we got totally off topic although it's fully clear, how I meant the term "ensemble" here. Thanks for giving the simple answer. I try to call it "statisical sample" in this forum from now on, and we can get back to the really interesting discussions.

 

[PeterDonis]

we can get back to the really interesting discussions

What interesting points do you think we haven't covered yet?

 

[vanhees71]

E.g., why you don't accept the standard answer to the question, how "classical behavior" of macroscopic systems are understood by the pracitioners of the field (e.g, condensed-matter physicists). What's not satisfactory for you? Why do you think, we must still refer to the hand-waving arguments of 80 years ago like a "quantum-classical cut" or "collapse of the state", etc.?

 

[A. Neumaier]

The point is that we got totally off topic although it's fully clear, how I meant the term "ensemble" here. Thanks for giving the simple answer. I try to call it "statisical sample" in this forum from now on, and we can get back to the really interesting discussions.

I added to my answer an authoritative quote from Landau and Lifschitz.

 

[PeterDonis]

why you don't accept the standard answer to the question, how "classical behavior" of macroscopic systems are understood by the pracitioners of the field

It's not just me; there is a whole community of physicists who think that the "standard answer", while it is, as a I said, fine and workable in a practical sense, does not actually resolve the measurement problem at a foundational level.

Why do you think, we must still refer to the hand-waving arguments of 80 years ago like a "quantum-classical cut" or "collapse of the state", etc.?

The community of physicists I just referred to above are not using hand-waving arguments of 80 years ago. They are looking at the most up to date developments in, for example, decoherence theory. And, as I said, they do not think that all those developments have solved the measurement problem.

You can say you disagree with them, but you cannot say their viewpoint doesn't exist.

 

[vanhees71]

I don't say their viewpoint doesn't exist although I don't know that any of my colleagues would think that there's a measurement problem. I may be too naive, but indeed, I don't understand, where there is a problem, because QT from the very beginning was very successful to quantitatively describe the phenomena, starting from the black-body spectrum (Planck 1900), the spectra of atoms (Pauli 1925/Schrödinger 1926 for the hydrogen atom and quickly also of many-electron atoms), cross sections of scattering processes (Born 1926), etc. etc.

 

[PeterDonis]

I don't say their viewpoint doesn't exist although I don't know that any of my colleagues would think that there's a measurement problem.

So because you don't personally know anyone who thinks it's a problem, you don't see a problem.

I don't understand, where there is a problem

Yes, we know that. But other people think there is one, even if they can't explain why to your satisfaction. And you have given no argument at all about why there isn't one; you have simply asserted without argument that the practical methods you describe are, in your opinion, good enough. Yes, we know that's your opinion. But there's no way to have a productive discussion on that basis. So when other people want to discuss what they see as a measurement problem, it does not help at all for you to jump in for the umpteenth time and assert that you don't think there is one. That adds no value.

 

[vanhees71]

My argument is that QT precisely describes, what's observed, and that you can't expect more from the natural sciences than precisely describing what's observed. The discussions about this topic is so unproductive, because it's not clear, what's lacking. You also don't tell us, what precisely it is what you think QT is lacking!

 

[PeterDonis]

The discussions about this topic is so unproductive

Speak for yourself. If you seriously can't see any productive use for such discussions, why do you keep posting in them and hijacking them?

You also don't tell us, what precisely it is what you think QT is lacking!

That's because, as I posted in the other thread just now on Gleason's Theorem where we are having a similar exchange, I have concluded that doing so with you is a waste of my time.

 

[Fra]

you can't expect more from the natural sciences than precisely describing what's observed.

From the perspective of theory evolution, the problem I have with this pragmatic perspective ö is that you always end up with an effective theory, that is experimentally fine tuned. That gives you a description, but very little explanation meaning its hard to see the pointers forward.

For me the better explanation there is, the less finetuning you need. Explanation to me means how all things that seem tuned, really are related.

The things that are fine tuned in QM/QFT are for example the 4D spacetime continuum background. Here I am sure we disagree, but I personally associate this background structure to the "macroscopic classical environment" that to Bohr is the "observer". This is a connection between dynamics of spacetime background and the QM foundations (dynamics of observers). Here also the fact that there are no "infinite ensembles" in nature and that the ensemble is fiction, compares to that a fixed spacetime background is also a fiction.

But you denied this connection, as does many others. And maybe on reasonable grounds: that the experimental signs of this is out of reach. But could fine tuning problems be a symptom of this? One can of course think that naturalness is not a must.

/Fredrik

 

[vanhees71]

From the perspective of theory evolution, the problem I have with this pragmatic perspective ö is that you always end up with an effective theory, that is experimentally fine tuned. That gives you a description, but very little explanation meaning its hard to see the pointers forward.

Sure, we don't have a theory of everything, and all theories we have so far are as you describe: On a fundamental basis we have the Standard Model of elementary particle physics with 20+x free parameters, which have to be determined by experiment. This, to the dismay of most physicists looking for "physics beyond the Standard Model", describes all known matter in terms of quarks, leptons, gauge bosons, and the Higgs boson.

Then we have General Relativity, which provides the space-time model and describes the gravitational interaction on the level of a classical field theory. The space-time model (usually approximated as Minkowski space, one solution of the Einstein Equations for an "empty" universe) also to a large extent determines, how the dynamics of the Standard Model looks like. For that you only need one more parameter, the universal coupling between the "matter energy-momentum tensor" and the gravitational field.

This together is the effective theory of contemporary physics. It's pretty clear that it's preliminary as all physical theories we know always have been. With new empirical evidence maybe one day we'll get a more complete new theory "beyond standard physics". That's, how the natural sciences make progress in gaining knowledge about the objective properties of Nature. Philosophy is "incomprehensibly ineffective", as Weinberg once put it.

For me the better explanation there is, the less finetuning you need. Explanation to me means how all things that seem tuned, really are related.

That's indeed a very common opinion. The hope is that with new theories we find new relations of the kind you imply.

The things that are fine tuned in QM/QFT are for example the 4D spacetime continuum background. Here I am sure we disagree, but I personally associate this background structure to the "macroscopic classical environment" that to Bohr is the "observer". This is a connection between dynamics of spacetime background and the QM foundations (dynamics of observers). Here also the fact that there are no "infinite ensembles" in nature and that the ensemble is fiction, compares to that a fixed spacetime background is also a fiction.

Indeed, that's the really big fundamental question, and not fruitless philsophical quibbles about the result of 20th century physics that Nature is inherently random and to be described by QT rather than classical deterministic models.

But you denied this connection, as does many others. And maybe on reasonable grounds: that the experimental signs of this is out of reach. But could fine tuning problems be a symptom of this? One can of course think that naturalness is not a must.

I never denied these obvious facts. How do you come to that conclusion? What I deny is the assumption that one makes progress by philosophical speculations about how Nature should behave rather than finding solid empirical hints to find a new ansatz for a new, more comprehensive theory, e.g., discovering new particles to get an idea, how dark matter might be described or a hint, how to find a satisfactory QT description of the gravitational interaction, maybe implying that the classical space-time description is also an emergent phenomenon as the classical behavior of macroscopic objects is from the point of view of quantum many-body physics.

Particularly, I don't believe that we find a solution of these problems by thinking about a "measurement problem". For that QT is simply too successful in describing all empirical facts within the above described realm of applicability (everything except gravitation and spacetime).

/Fredrik

 

[Morbert]

The things that are fine tuned in QM/QFT are for example the 4D spacetime continuum background. Here I am sure we disagree, but I personally associate this background structure to the "macroscopic classical environment" that to Bohr is the "observer". This is a connection between dynamics of spacetime background and the QM foundations (dynamics of observers). Here also the fact that there are no "infinite ensembles" in nature and that the ensemble is fiction, compares to that a fixed spacetime background is also a fiction.

I don't understand this association. A quantum theory of gravity/spacetime would be as equally subject to various interpretations and discussions about observers, closed systems etc as quantum mechanics, as you would still presumably have a noncommutative algebra of observables.

 

[Fra]

I never denied these obvious facts. How do you come to that conclusion?

Becuase you often finish in this way :)

(everything except gravitation and spacetime).

It's because while you agree that we have not unified theory yet, but you seem to pragmatically categorize any attempt to analyse the structure of theories, and how different theories my be related in a bigger theoryspace (ie beyond what what they simply predict) as fruitless philosophy.

In particular in discussions about the "foundations of QM", you don't see any problems, because the subtle issues of conceptual and logical coherence in reasoning does not immediately manifest themselves as observable deviations today.

I admit that I like your pragmatic view, and the empirical stance, is that is a very important thing even in how I think of this, but I find that you are a bit too pragmatic to the point where you reject things that are admittedly a but fuzzy. But to me, the process of inquiry IS fuzzy.

I also agree that it often happens that things get too fruitless also for me. For example "interpretations" that has no aspiration to make a difference even in the future, or giving no insight into open problems, those discussions don't interest me. But I don't think that means one has to be either or. I think one can manage a balance.

What I deny is the assumption that one makes progress by philosophical speculations about how Nature should behave rather than finding solid empirical hints

Philosophy is "incomprehensibly ineffective", as Weinberg once put it.

I rather see it this way. The rate at which we do find new empiritcal hints, will increase if we know precisely where to look. And questions is then: What clues to be have from where we are? This is what this is all about for me. Is keep spending money to be increase accelerator energies the only way forward? I am not convinced, are you?

Your pragmatism seems to work like a noise reduction that rejects the some clues that we get from analysing the structure of the theory, and see on what ground it rests (premises, axioms, implicit prior information etc).

Particularly, I don't believe that we find a solution of these problems by thinking about a "measurement problem". For that QT is simply too successful in describing all empirical facts within the above described realm of applicability

Exactly, which is to me another way of saying, as long as we ignore the different between finite and infinite "observers" or "ensembles". Your arguments are clear to me, so you are consistent so I think I understand your perspective. I prefer to keep looking for clues, where you seem to "wait for more data". Isn't the fine tuning and lack of even a coherent GUT, enough food for thought? Do we need more data to realize that we have no clear understanding on how one effective theory merges into another one, over the energy ranges, this seems be a conclusion you can draw from looking at the theory? The problem isn't nature, the problem is our theories. We can see it already now I think.

/Fredrik

 

[Fra]

I don't wish to diverge the thread to elaborated my own associations, as that wasn't the point. My main point was that at least I do see a link between the foundations of QM and the foundations of the future theory. And I tried to divert from twisting words to the more interesting discussions.

I don't understand this association. A quantum theory of gravity/spacetime would be as equally subject to various interpretations and discussions about observers, closed systems etc as quantum mechanics, as you would still presumably have a noncommutative algebra of observables.

But very briefly:

Your comment here, to me, seems like you see QG as trying to understand what would happen if we can produce and observe black holes at accelerators; then yes, it would still be relative to the background spacetime where the lab is. But in a way that would also reproduce GR in the low energy limit. For example the thinking used in string theory.

But there is another logically possible perspective, which (relates more to fine tuning and how theories scale). You can ask; what OTHER theory than a QFT, describes the effective theories of inside observers, in a away that reproduces QFT in the limit of an infinitely massive observer; and yield gravity for observers with finite mass. This would then introduce "interactions" between two observers of finite mass (this the association to finite ensembles).

/Fredrik

 

[A. Neumaier]

you can't expect more from the natural sciences than precisely describing what's observed.

You don't expect more, but many others (including myself) expect more, namely to have a mathematically coherent explanation of the measurement process in terms of the fundamental dynamics realized in the universe.

I collected here (pp.5-7) a large number of quotes from very influential physicists of the past and the present, indicating that there is more to be expected.

 

[vanhees71]

Sure, it's always nice to understand the observations from as close to first-principle descriptions as possible, and I've no doubt, that there is a lot to be learnt about the interaction of "quantum systems" with "macroscopic measurement devices" in greater detail than we know today, but I don't think that there'll be much more possible to be learnt concerning at least the rough picture we have today, i.e., the description of the macroscopic measurement device and the pobability distributions of the measurement outcomes due to some effective "open-quantum system description"?

 

[A. Neumaier]

I don't think that there'll be much more possible to be learnt concerning at least the rough picture we have today,

But rough means refinable. Interpretation questions become relevant when one investigates the possibilities for refinement.

 

[vanhees71]

I think it's rather tough mathematical problem than any philosophical pondering about"interpretation".

 

[A. Neumaier]

I think it's rather tough mathematical problem than any philosophical pondering about"interpretation".

Finding the right framework in which to solve tough mathematical problems that have been unsolved for years in spite of many attempts usually involves much philosophical pondering about the "interpretation" of the problem!

The philosophical part goes away only after the problems have been solved.

 

[Morbert]

Finding the right framework in which to solve tough mathematical problems that have been unsolved for years in spite of many attempts usually involves much philosophical pondering about the "interpretation" of the problem!

The philosophical part goes away only after the problems have been solved.

In your quantum tomography paper you say "A suggestive notion for what constitutes a quantum detector and for the behavior of its responses leads to a logically impeccable definition of measurement.". Is it your position that the thermal interpretation is a solution to the mathematical problems of measurement? Or more specifically, that it offers "a mathematically coherent explanation of the measurement process in terms of the fundamental dynamics realized in the universe"?

 

[A. Neumaier]

In your quantum tomography paper you say "A suggestive notion for what constitutes a quantum detector and for the behavior of its responses leads to a logically impeccable definition of measurement.". Is it your position that the thermal interpretation is a solution to the mathematical problems of measurement? Or more specifically, that it offers "a mathematically coherent explanation of the measurement process in terms of the fundamental dynamics realized in the universe"?

Almost. The definition of measurement is already impeccable, and within the formal framework of quantum mechanics. Thus - unlike in Born's rule, where measurement is an undefined notion - one can prove mathematical facts about measurement processes. The theory in the quantum tomography paper together with the thermal interpretation already goes a long way towards a solution. There are some unsettled issues (discussed towards the end of my paper), but the remaining issues are of a purely mathematical nature, and hence seem tractable (or can be refuted if incorrect).

 

[Fra]

Almost. The definition of measurement is already impeccable, and within the formal framework of quantum mechanics. Thus - unlike in Born's rule, where measurement is an undefined notion - one can prove mathematical facts about measurement processes. The theory in the quantum tomography paper together with the thermal interpretation already goes a long way towards a solution. There are some unsettled issues (discussed towards the end of my paper), but the remaining issues are of a purely mathematical nature, and hence seem tractable (or can be refuted if incorrect).

Do you mean this as beeing of pure matematical nature?

"It was pointed out that to fully solve the quantum measurement problem, more research is needed on the characterization of quantum systems that are nonstationary on experimentally directly accessible time scales."
- page 91 in your paper https://arxiv.org/pdf/2110.05294.pdf

If so, don't you see potential conceptual complications with this, regarding to establish objectivity?

/Fredrik

 

[A. Neumaier]

Do you mean this as being of pure mathematical nature?

yes. Purely mathematical concepts (in the shut up and calculate style) informed by the philosophy of the thermal interpretation.

"It was pointed out that to fully solve the quantum measurement problem, more research is needed on the characterization of quantum systems that are nonstationary on experimentally directly accessible time scales."
- page 91 in your paper https://arxiv.org/pdf/2110.05294.pdf

... on the mathematical characterization of such quantum systems.

If so, don't you see potential conceptual complications with this, regarding to establish objectivity?

Objectivity is properly discussed in Section 10.4 (p.84f) of my paper. Of course, observation of unique events of fleeting duration are only as objective as the observer taking notes of the event is. But this is in the nature of objectivity, and not a conceptual weakness.

 

[Fra]

yes. Purely mathematical concepts (in the shut up and calculate style) informed by the philosophy of the thermal interpretation.

Do we presume your interpretation(which everyone may not), and then its purely mathematical given your framework. If so I may understand better.

Objectivity is properly discussed in Section 10.4 (p.84f) of my paper. Of course, observation of unique events of fleeting duration are only as objective as the observer taking notes of the event is. But this is in the nature of objectivity, and not a conceptual weakness.

Note sure I follow. In 10.4 you refer repeatedly in the arguments to stationarity.

"Through quantum tomography, the quantum state of a sufficiently stationary source, the quantum measure of a measurement device, and the transmission operator of a sufficiently linear and stationary filter can in principle be determined with observer-independent protocols. Thus they are objective properties of the source, the measurement device, or the filter, both before and after measurement."

/Fredrik

 

[A. Neumaier]

Do we presume your interpretation(which everyone may not), and then its purely mathematical given your framework. If so I may understand better.

Assumed are the definitions given in the paper, which are formal and mathematical, together with their interpretation, which are informal and philosophical, also given in the paper.

Note sure I follow. In 10.4 you refer repeatedly in the arguments to stationarity.

"Through quantum tomography, the quantum state of a sufficiently stationary source, the quantum measure of a measurement device, and the transmission operator of a sufficiently linear and stationary filter can in principle be determined with observer-independent protocols. Thus they are objective properties of the source, the measurement device, or the filter, both before and after measurement."

Yes, verifiable objectivity is tied (even in classical physics) to approximate repeatability. This either requires a sufficiently stationary source, or a nonstationary source that can be taken to be a stationary source of identically distributed short time nonstationary processes. Such a nonstationary source must exhibit some form of ergodicity (discussed on p.77f), to be proved or taken as empirically given.

 

[vanhees71]

Finding the right framework in which to solve tough mathematical problems that have been unsolved for years in spite of many attempts usually involves much philosophical pondering about the "interpretation" of the problem!

The philosophical part goes away only after the problems have been solved.

But there are many solutions (for particularly simple cases though), deriving (semi-)classical transport equations from quantum many-body theory or the entire field of "open quantum systems", using Markovian approximations in terms of quantum master equations (Lindblad). I think this vast work gives enough glimpses on more comprehensive descriptions to exorcize any philosophical speculations ;-)).

 

[A. Neumaier]

But there are many solutions (for particularly simple cases though), deriving (semi-)classical transport equations from quantum many-body theory or the entire field of "open quantum systems", using Markovian approximations in terms of quantum master equations (Lindblad). I think this vast work gives enough glimpses on more comprehensive descriptions to exorcize any philosophical speculations ;-)).

I know all this. But unless one adopts the thermal interpretation, it doesn't answer questions about observations on single systems. For example, Lindblad equations and all decoherence arguments always average over a whole ensemble of identically prepared systems.