Against "interpretation" - Comments

[Dale]

My insight is precisely to point out that such standard definition is inadequate.

Yes, but I disagree with your reasoning. The definitions of theory and interpretation are not dependent on the status of other theories or interpretations.

The parts of T1 that are the mathematical framework and the mapping to experiment are theory, regardless of the presence or absence of T2. The remainder of T1 is part of the interpretation, again regardless of the presence or absence of T2. Nothing about the theory/interpretation status of T1 changes with the advent of T2 because the definitions of theory and interpretation do not reference the presence or absence of any other theory or interpretation in any way.

I see nothing inadequate in the standard definition of theory, it was simply misapplied in your example scenarios. You are complaining that the standard definitions “don’t make sense” but you never even write down those definitions and then you carelessly apply them in your scenarios.

It is a straw man argument in my opinion. Yes, you have shown that something doesn’t make sense, but it isn’t the standard definition of theory.

 

[Demystifier]

The parts of T1 that are the mathematical framework and the mapping to experiment are theory, regardless of the presence or absence of T2. The remainder of T1 is part of the interpretation, again regardless of the presence or absence of T2.

Fine, then let us apply this to Bohmian mechanics. It has the guiding equation that other versions of QM don't have. If this equation is part of the theory, then what is the interpretational part of Bohmian mechanics?

 

[Dale]

Fine, then let us apply this to Bohmian mechanics. It has the guiding equation that other versions of QM don't have. If this equation is part of the theory, then what is the interpretational part of Bohmian mechanics?

I can’t help you there. As I made pretty clear above I have little knowledge of and substantially less interest in QM interpretations.

It may be that the standard definitions are difficult to apply to one theory or interpretation. That could be a problem with the definitions, but it would be a different one from what you highlighted in your article. Alternatively, (more likely) it could be a problem with the theory/interpretation in question. Perhaps the authors of the theory/interpretation should clarify their work rather than rewrite definitions that work well elsewhere.

 

[Demystifier]

As I made pretty clear above I have little knowledge and substantially less interest in QM interpretations.

That's perfectly OK. I just hope that the destiny of the insight about the interpretations will be decided by someone who does have a knowledge and interest on this stuff.

 

[Dale]

That's perfectly OK. I just hope that the destiny of the insight about the interpretations will be decided by someone who does have a knowledge and interest on this stuff.

No need to worry about that. It will stay, I am just voicing my opinion about it as a participant, not as a moderator.

I don’t think that the standard definitions are in need of a major overhaul. If the specific case of BM causes problems then I think the “repair” belongs there.

 

[StoneTemplePython]

Kolmogorov did have a different view to von Mises though, the whole "propensities" view and is often listed separately to frequentism in books on interpretations of probability theory. Later in life he had the complexity interpretation, again different from von Mises's view. It's these views I listed above informally as "Kolmogorov". Some still argue¹ that the complexity view is a form of Frequentism, if you take that view replace "Frequentist vs Kolmogorov" with "von Mises vs Kolmogorov"...There is a debate about foundations and interpretation in probability with various schools that disagree with each other. Jaynes for example is fairly scathing of Frequentism in his book "Probability Theory: The logic of Science". @A. Neumaier 's references simply discuss this issue. The complaints about general books on QM is more related to their sensationalist content, inaccuracies

Set aside Jaynes for a moment, it's a very peculiar book: a polemic mixed with some deep math insights. (I've only read part of the book but he seems to use e.g. Feller as some kind of straw-man punching bag. It's unfortunate.) It also technically isn't one of the books I was referring to in my post.
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I don't think there is debate about foundations in probability. Finite additivity isn't really used much (i.e. de Finetti lost). There is a standard set of axioms used and these come from Kolmogorov. There are debates on interpretations.

What I'm saying is that the further you get from Kolmogorov and actual math books, they tend to get sensationalist and inaccurate. Vovk and Shafer directly address on page 45 that a lot of mathematicians thought it was von Mises vs Kolmogorov for forms of frequentism. Kolmogorov didn't think that way, nor did others in USSR who worked closely with him. If you want to call them mildly different flavors of frequentism, that's ok by me. But it isn't sensationalist enough to sell wide audience books. And it certainly is not 'Kolmogorov vs Frequentism'.

n.b.
when you say Kolmogorov view of probability I assumed you meant the standard austere, axiomatic approach to mathematical probability, laid down by Kolmogorov. I've never heard someone use it to mean subsequent complexity work, especially in a line of discussion that talks "about Foundations". The former (axiomatic approach) quite literally is foundational. The latter is not. (As mentioned in italics in my prior post -- Kolmogorov also had a finitary version of von Mises' probability... the reality is Kolmogorov did a lot of different stuff in probability.)

I also will flag that I've read and like 2 or 3 books by Gigerenzer though they are tied in with psychology, misuse of probability, and public messaging not math per se.

 

[DarMM]

OMG - that's pretty close to my view when I started posting here about 10 years ago now. My views have changed a LOT, and even now are changing as I learn more - but not at the rate they did during my first few years of posting - I wince thinking about some of my early posts.

I would have been no different about ten years ago as well. Certainly in the last two years I've learned a lot on this topic, so you're not the only one here who thought stuff like that. The shameful thing is that I had quite a good knowledge of QFT from a mathematical perspective.

Copenhagen is agreed by many proponents to be obviously daft. Have you read Landau and Lifshitz's QM textbook? They say this in a polite way, perhaps too polite as not everyone gets their message.

I have, but quite a while ago. Would you have the page reference where they imply this? I'd love to have a look.

I can’t help you there. As I made pretty clear above I have little knowledge of and substantially less interest in QM interpretations.

Just to say, in my opinion if you ignore the interpretations and the issues they seek to tackle one has a weaker understanding of QM. I say this based on myself as per my reply to @bhobba above, as well as conversations with others. Bell's theorem, the PBR theorem, Hardy's theorem, all result from restricting interpretations and contain major insights into QM.

 

[DarMM]

Set aside Jaynes for a moment, it's a very peculiar book: a polemic mixed with some deep math insights. (I've only read part of the book but he seems to use e.g. Feller as some kind of straw-man punching bag. It's unfortunate.) It also technically isn't one of the books I was referring to in my post.
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I don't think there is debate about foundations in probability. Finite additivity isn't really used much (i.e. de Finetti lost). There is a standard set of axioms used and these come from Kolmogorov. There are debates on interpretations.

This is just a difference in the use of the word "Foundations", which is sometimes used to include interpretations.

Also see the parts in bold.

"There is no debate in Foundations of probability if we ignore the guys who say otherwise and one of them lost anyway, in my view"

Seems very like the kind of thing I see in QM Foundations discussions.

"Ignore Wallace's work on the Many Worlds Interpretation it's a mix of mathematics and philosophical polemic" (I've heard this)
"Copenhagen has been shown to be completely wrong, i.e. Bohr lost" (also heard this)

I think if I asked a bunch of subjective Bayesians I'd get a very different view of who "won" and "lost".

Jaynes is regarded as a classic by many people I've spoken to, I'm not really sure why I should ignore him.

What I'm saying is that the further you get from Kolmogorov and actual math books, they tend to get sensationalist and inaccurate. Vovk and Shafer directly address on page 45 that a lot of mathematicians thought it was von Mises vs Kolmogorov for forms of frequentism. Kolmogorov didn't think that way, nor did others in USSR who worked closely with him. If you want to call them mildly different flavors of frequentism, that's ok by me. But it isn't sensationalist enough to sell wide audience books. And it certainly is not 'Kolmogorov vs Frequentism'.

I don't know why we're talking about best seller general audience books. (Although if somebody can turn an account on Kolmogorov's axioms into a international bestseller they deserve every cent they get!)

It also doesn't really matter if Kolmogorov himself viewed it as some major "battle", the point is that they are different views on probability theory and held by different groups today.

when you say Kolmogorov view of probability I assumed you meant the standard austere, axiomatic approach to mathematical probability, laid down by Kolmogorov. I've never heard someone use it to mean subsequent complexity work, especially in a line of discussion that talks "about Foundations".

"Foundations" here includes interpretations, so "Kolmogorov vs Jaynes" for example was meant in terms of their different views on probability. There are others like Popper, Carnap. Even if you don't like the word "Foundational" being applied it doesn't really change the basic point.

Also note that in some cases there is disagreement over which axioms should be the Foundations. Jaynes takes a very different view from Kolmogorov here, eschewing a measure theoretic foundation.

 

[Dale]

in my opinion if you ignore the interpretations and the issues they seek to tackle one has a weaker understanding of QM

And as a direct result of the constant bickering about interpretations I have a less than weak understanding of QM and a substantially weaker desire to fix it. I am skeptical that they are as beneficial as you say, but the constant arguments are certainly detrimental to me personally.

 

[DarMM]

I am skeptical that they are as beneficial as you say

Why? What do you base that on?

 

[Dale]

Why? What do you base that on?

My experience with philosophy in general and interpretations in relativity. And a lack of any personal benefit from reading the interpretations threads here, and the moderation issues they frequently generate.

 

[DarMM]

My experience with philosophy in general and interpretations in relativity.

Okay but note that many major textbooks in Quantum Mechanics (Landau and Lifshitz, Weinberg, Ballentine, Griffiths, Auletta et al and many more) have discussions on interpretations, in some cases a lengthy chapter is devoted to them. It's an important issue.

I can appreciate why you feel that way from the two sources you mentioned, but note very few introductory textbooks in Relativity have chapters about interpretations and foundational issues. The case is simply different in QM.

 

[DarMM]

And a lack of any personal benefit from reading the interpretations threads here, and the moderation issues they frequently generate.

Sorry I missed this the first time around.

I can appreciate this, but I would say that:
(a) One is unlikely to derive much benefit from interpretational and foundational discussions on most topics without a strong basis in that subject. Although I am aware of how such threads have developed over the forums past and yes heat/light tends to zero as thread length increases so I do appreciate how you feel on this.
(b) I wouldn't use how annoying threads are on a topic here to gauge it's role in a subject. Not to say I'd do differently if I were in your position, I'd probably be pretty tired off it as well.

Basically if you want to learn QM, just jettison the irritation from threads here and go read Auletta et al, I think you'll find the chapter on the measurement problem interesting, full of insight on QM and included in the textbook for a reason.

 

[atyy]

I have, but quite a while ago. Would you have the page reference where they imply this? I'd love to have a look.

I'll just quote the bits here (all from p3 of LL QM). I don't agree entirely with what they say, but they state the classical/quantum cut clearly, and already I think one would think it absurd. The part I don't entirely agree with is they stress the independence of measurement from the observer. However, I think this is not strictly wrong, since the drawing of the cut itself is presumably subjective, and hence the objectivity that one obtains is still a subjective objectivity.

"In this connection the "classical object" is usually called apparatus, and its interaction with the electron is spoken of as measurement. However, it must be emphasized that we are here not discussing a process of measurement in which the physicist-observer takes part. By measurement, in quantum mechanics, we understand any process of interaction between classical and quantum objects occurring apart from and independently of any observer."

The part where they politely point out that measurement is weird is:

"Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation."

Personally, I got the message. However, Bell (who helped Sykes translate) did think they were way too polite: https://m.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf

 

[atyy]

Set aside Jaynes for a moment, it's a very peculiar book: a polemic mixed with some deep math insights. (I've only read part of the book but he seems to use e.g. Feller as some kind of straw-man punching bag. It's unfortunate.) It also technically isn't one of the books I was referring to in my post.
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Yes, am not a fan of Jaynes either for the polemic. At the very least, one can get non-uniqueness by considering the various Renyi entropies, instead of just using the Shannon one.

I don't think there is debate about foundations in probability. Finite additivity isn't really used much (i.e. de Finetti lost). There is a standard set of axioms used and these come from Kolmogorov. There are debates on interpretations.

I agree. Bayesians can use the Kolmogorov axioms, just interpreted differently. (And yes, interpretation is part of Foundations, but the Kolmogorov part is settled.)

I think interpretation is even settling, with de Finetti having won in principle, but in practice one uses whatever seems reasonable, or both as this cosmological constant paper did: https://arxiv.org/abs/astro-ph/9812133.

 

[bhobba]

And as a direct result of the constant bickering about interpretations I have a less than weak understanding of QM and a substantially weaker desire to fix it. I am skeptical that they are as beneficial as you say, but the constant arguments are certainly detrimental to me personally.

Outside this forum and on the internet in general I think that the issues of interpretation are very much a backwater. What I think hooks most people really into QM is its incredible beauty. For example chapter three of Ballentine was a revelation to me - Schrodinger's equation etc really comes from symmetry. Then you see how the path integral approach explains the Principle Of Least Action and you realize that everything is really quantum. The appreciation of symmetry's power in physics reaches it full flowering in QM and QFT. To me that has been the most startling revelation of modern physics and has nothing to do with issues of interpretation. I personally find QM even more beautiful than GR which is generally considered the beautiful theory of physics. But GR, even though I was once heavily into it, seems to have lost its sparkle when I returned to it after becoming a mentor and wanting to widen the scope of my involvement with PF beyond QM. I found with Lovelock's Theorem, which I knew before, but hadn't really thought about its power, has killed a lot of the magic of GR for me. The theorem itself is magical, but it doesn't leave much mystery for me. Now combining GR and QM - that's another matter - it intrigues me greatly. I want to understand better than I do the following paper:
https://arxiv.org/abs/1209.3511

I am now pretty hooked on the EFT approach to quantum gravity and others seem as well eg:
https://blogs.umass.edu/donoghue/research/quantum-gravity-and-effective-field-theory/

Trouble is I am now 63 and things that came easy in my youth now take longer - but it is still possible to learn - it just takes longer.

Thanks
Bill

 

[DarMM]

The appreciation of symmetry's power in physics reaches it full flowering in QM and QFT. To me that has been the most startling revelation of modern physics and has nothing to do with issues of interpretation. I personally find QM even more beautiful than GR which is generally considered the beautiful theory of physics. But GR, even though I was once heavily into it, seems to have lost its sparkle when I returned to it after becoming a mentor and wanting to widen the scope of my involvement with PF beyond QM. I found with Lovelock's Theorem, which I knew before, but hadn't really thought about its power, has killed a lot of the magic of GR for me

Didn't know Lovelock's theorem, very interesting!

Symmetries in QM are incredible, especially as the link between the conserved quantities and transformations is so much closer than it is in classical mechanics and as you said it doesn't have anything to do with interpretations.

For @Dale , as @bhobba said interpretations are much bigger here and on the net than they are "on the ground" in physics, so I wouldn't let the issue put one off. On a personal level I in fact I only recall two discussions about it over the last eleven years.

Note that many physicists don't know much about the Fiber Bundle view of Yang Mills. It's a bit like that, not crucial, certainly not common, but worth knowing in my opinion as it gives one a deeper appreciation of certain aspects of the theory.

 

[A. Neumaier]

Basically if you want to learn QM, just jettison the irritation from threads here and go read Auletta et al, I think you'll find the chapter on the measurement problem interesting, full of insight on QM and included in the textbook for a reason.

Apart from the textbook ''Quantum Mechanics'' by Auletta, Fortunato, and Parisi 2009, there is also a book ''Foundations and Interpretation of Quantum Mechanics'' by Auletta 2001 , with many historical details, explaining among others why interpretation is important in quantum mechanics, and why it is controversial.

 

[A. Neumaier]

All of the objective parts would be theory and all of the subjective parts would be interpretation in my terminology with no overlap between theory and interpretation.

How would you differentiate between objective and subjective? How is measurement, or an electron, or a particle position, or an ideal gas, or a laser, or a Geiger counter, etc. - defined objectively? Truly objective is only the mathematical framework!

 

[Dale]

How would you differentiate between objective and subjective?

We already discussed that, didn’t we? Anything necessary to predict the outcome of an experiment is objective.

Truly objective is only the mathematical framework!

No, you cannot predict the outcome of an experiment with only the mathematical framework.

 

[bhobba]

How would you differentiate between objective and subjective? How is measurement, or an electron, or a particle position, or an ideal gas, or - defined objectively?

That is an issue Gell-Mann and others are grappling with in trying to complete the decoherent histories program. Progress has been made, but problems remain.

Thanks
Bill

 

[DarMM]

That is an issue Gell-Mann and others are grappling with in trying to complete the decoherent histories program. Progress has been made, but problems remain.

Thanks
Bill

Is there a good guide to open problems anywhere? I just finished Griffith's book "Consistent Histories" today and I'm eager to know more.

 

[bhobba]

Is there a good guide to open problems anywhere? I just finished Griffith's book "Consistent Histories" today and I'm eager to know more.

I think you have to look at some of the papers eg:
https://arxiv.org/abs/1312.7454

Thanks
Bill

 

[A. Neumaier]

We already discussed that, didn’t we? Anything necessary to predict the outcome of an experiment is objective.

This begs the issue. What is is that is necessary to predict the outcome? How do you differentiate between the necessary and the unnecessary?

An experiment tells, for example that when you point an unknown very weak source of light to a photodetector, it will produce every now and then an outcome - a small photocurrent, measured in the traditional way. Nothing predicts when this will happen. Predicted is only the average number of events in dependence on the assumed properties of the incident light, in the limit of an infinite long time - assuming the source is stationary. Nowhere photons, though the experimenters talk about these in a vague, subjective way that guides them to a sensible correspondence between their assumptions and the theory. All this is murky waters from the point of view of the subjective/objective distinction.

 

[A. Neumaier]

No, you cannot predict the outcome of an experiment with only the mathematical framework.

Only in as far as the outcome involves subjective elements.

In his famous textbook [H.B. Callen. Thermodynamics and an introduction to thermostatistics, 2nd. ed., Wiley, New York, 1985.] (no quantum theory!), Callen writes on p.15:

Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory.

At first sight, this sounds like a circular definition (and indeed Callen classifies it as such). But a closer look shows there is no circularity since the formal meaning of ''consistently described by thermodynamic theory'' is already known. The operational definition simply moves this formal meaning from the domain of theory to the domain of reality by defining when a real system deserves the designation ''is in an equilibrium state''. In particular, this definition allows one to determine experimentally whether or not a system is in equilibrium.

Nothing else is needed to relate a mathematical framework objectively to experiment.

What is ''consistent'' in the eye of a theorist or experimenter is already subjective.

 

[Dale]

Nothing else is needed to relate a mathematical framework objectively to experiment.

Ok, I have a mathematical framework: $a=bc$. Using nothing more than that framework, what is the objective relationship to experiment?

 

[A. Neumaier]

Ok, I have a mathematical framework: $a=bc$. Using nothing more than that framework, what is the objective relationship to experiment?

This is not the framework of a physical theory. It is just a mathematical formula.

According to Callen, if it were the mathematical framework of a physical theory it would predict that whenever you have something behaving like a and b, the product behaves like c. That's fully objective, and as you can see, needs a subjective interpretation of what a,b,c are in terms of reality (i.e, experiment).

A mathematical framework of a successful physical theory has concepts named (the objective interpretation part) after analogous concepts from experimental physics, in such a way that a subjective interpretation of the resulting system allows the theory to be successfully applied.M. Jammer, Philosophy of Quantum Mechanics, Wiley, New York 1974.

gives on p.5 five axioms for quantum mechanics (essentially as today), and comments:

p.5: ''The primitive (undefined) notions are system, observable (or "physical quantity" in the terminology of von Neumann), and state.''

p.7: ''In addition to the notions of system, observable, and state, the notions of probability and measurement have been used without interpretations.''

That's the crux of the matter. Since the properties of probability and measurement are not sufficiently specified in the framework, they remain conceptually ill-defined. Therefore one cannot tell objectively whether something on the level of experiments is consistent with the framework. One needs subjective interpretation.

And indeed, Jammer says directly after the above statement:

Although von Neumann used the concept of probability, in this context, in the sense of the frequency interpretation, other interpretations of quantum mechanical probability have been proposed from time to time. In fact, all major schools in the philosophy of probability, the subjectivists, the a priori objectivists, the empiricists or frequency theorists, the proponents of the inductive logic interpretation and those of the propensity interpretation, laid their claim on this notion. The different interpretations of probability in quantum mechanics may even be taken as a kind of criterion for the classification of the various interpretations of quantum mechanics. Since the adoption of such a systematic criterion would make it most difficult to present the development of the interpretations in their historical setting it will not be used as a guideline for our text.

Similar considerations apply a fortiori to the notion of measurement in quantum mechanics. This notion, however it is interpreted, must somehow combine the primitive concepts of system, observable, and state and also, through Axiom III , the concept of probability. Thus measurement, the scientist's ultimate appeal to nature, becomes in quantum mechanics the most problematic and controversial notion because of its key position.

 

[Dale]

This is not the framework of a physical theory.

It is a perfectly valid mathematical framework, one of the most commonly used ones in science.

It is your claim (as I understand it) that objective science can be done with only a mathematical framework. I think that is obviously false, as shown here.

 

[A. Neumaier]

It is a perfectly valid mathematical framework, one of the most commonly used ones in science.

It is your claim (as I understand it) that objective science can be done with only a mathematical framework. I think that is obviously false, as shown here.

You didn't show anything. I gave the experimental meaning of your framework $ab=c$, in precisely the same way as any physical framework gets its physical meaning:

whenever you have something behaving like a and b, the product behaves like c..

 

[Dale]

I gave the experimental meaning of your framework ab=cab=cab=c, in precisely the same way as any physical framework gets its physical meaning:

Nonsense, you cannot do an experiment with only that “experimental meaning”. It is insufficient for applying the scientific method.

Suppose I do an experiment and measure 6 values: 1, 2, 3, 4, 5, 6. Using only the above framework and your supposed “experimental meaning” do the measurements verify or falsify the theory?