Against “interpretation”
I am against “interpretations” of Quantum Mechanics (QM) in a sense in which John Bell [1] was against measurement in QM and Travis Norsen [2] is against realism in QM. Bell was not against doing measurements, he was against using the concept of measurement as a central concept in quantum foundations. Norsen does not think that realism does not exist, he thinks that the existence of realism is so obvious and basic that one should not even talk about it. In a similar spirit, I do not think that physicists should not study interpretations, I think that it is misleading to talk about interpretations as something different from theories. The titles “Against measurement” [1] and “Against realism” [2] were chosen by Bell and Norsen to provoke, by imitating the provocative style of Paul Feyerabend – the famous philosopher of science who was “Against method” [3]. My intentions here are provocative too.
Physicists often say that in physics we need theories that make new measurable predictions and that we don’t need interpretations that make the same measurable predictions as old theories. I think it’s nonsense. It’s nonsense to say that theories are one thing and interpretations are another. The interpretations are theories. Making a distinction between them only raises confusion. So we should ban the word “interpretation” and talk only about the theories.
Let me explain. Suppose that someone develops a theory called T1 that makes measurable predictions. And suppose that those predictions were not made by any previous theory. Then all physicists would agree that T1 is a legitimate theory. (Whether the predictions agree with experiments is not important here.)
Now suppose that someone else develops another theory T2 that makes the same measurable predictions as T1. So if T1 was a legitimate theory, then, by the same criteria, T2 is also a legitimate theory. Yet, for some reason, physicists like to say that T2 is not a theory, but only an interpretation. But how can it be that T1 is a theory and T2 is only an interpretation? It simply doesn’t make sense.
To resolve that issue, one might say that both T1 and T2 are interpretations. Fine, but then what is the theory? T1 was a legitimate theory before someone developed T2, but now T1 ceased to be a theory just because someone developed T2? It doesn’t make sense either.
Or perhaps the theory is just the set of final measurable predictions of T1 and T2, while all the other “auxiliary” elements of T1 and T2 are the “interpretation”? It doesn’t make sense either, because no theory in physics deals only with measurable predictions. All physics theories have some “auxiliary” elements that are an integral part of the theory.
Or perhaps an interpretation is a theory that emphasizes philosophical aspects? I think this is what most physicists mean by interpretation, even if they don’t want to say it explicitly. The problem with this definition is that it cannot be put into a precise form. All theories have some philosophical aspects, some theories more, some less. So exactly how much of philosophy does a theory have to have to call it an interpretation? It’s simply impossible to tell. And where exactly is the borderline between philosophy and non-philosophy? There is no such borderline.
To conclude, we can talk about a theory, we can distinguish the measurable predictions of the theory from other elements of the theory that cannot be directly measured, but it doesn’t make sense to distinguish an interpretation from a theory. There are no interpretations of QM, there are only theories.
References:
[1] J. Bell, Against measurement, https://m.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf
[2] T. Norsen, Against “realism”, http://de.arxiv.org/abs/quant-ph/0607057
[3] P. Feyerabend, Against method, https://en.wikipedia.org/wiki/Against_Method
Read my next article on Anyons
Theoretical physicist from Croatia
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?
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..
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.
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.
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?
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.
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.
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
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
BillIs there a good guide to open problems anywhere? I just finished Griffith's book "Consistent Histories" today and I'm eager to know more.
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
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.
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 – defined objectively? Truly objective is only the mathematical framework!
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.
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 meDidn'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.
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
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.
– – – – -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.
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
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.
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.
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.
I am skeptical that they are as beneficial as you sayWhy? What do you base that on?
in my opinion if you ignore the interpretations and the issues they seek to tackle one has a weaker understanding of QMAnd 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.
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.
– – – – –
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.
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.
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 argue[SUP]1[/SUP] 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, inaccuraciesSet 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.
– – – – –
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.
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.
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.
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.
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?
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.
Then they are different theories, per the standard definition, and calling them merely different interpretations is somewhat of a misnomer.My insight is precisely to point out that such standard definition is inadequate. It can be applied to other sciences too, but since this standard definition is rarely used in other sciences, this insight is in fact most relevant to QM.
I hope this doesn't need to be forked into another thread. I found the above to be alarming.As did I, bhobba is one of those dangerous frequentists who use Kolmogorov's axioms for their own nefarious ends.:oldbiggrin:
Kolmogorov was sympathetic to the frequentist interpretation advocated by Richard von Mises and in fact believed his axioms were Taylor Kolmogorov made for a frequentist concept of probability.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 argue[SUP]1[/SUP] that the complexity view is a form of Frequentism, if you take that view replace "Frequentist vs Kolmogorov" with "von Mises vs Kolmogorov".
From what I can tell, the books referenced in the quote and in post 112 are about philosophy and general audience books/ writeups. They aren't math books. (I do happen to like Gigerenzer though.) People complain about general public books on QM all the time. I don't see why we shouldn't have similar sentiment here.A similar sentiment regarding what though? 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 or often taking a specific view on things and providing that view as the explanation. @A. Neumaier 's books don't seem to be doing that. In fact I don't understand the connection at all. What sentiment should we have, ignore books discussing interpretational issues?
[SUP]1[/SUP] Just like in QM there are debates about how to classify interpretations!
Funnily enough I always thought QM was very similar to probability theory in this regard. Although most people just apply it, there is a pretty active community of debate on Foundations, e.g. Frequentist vs Kolmogorov vs Di Finetti vs Jaynes. Famously summed up in I.J. Good's title "46656 Varieties of Bayesians" for the Third Chapter of his 1983 book "Good Thinking: The Foundations of Probability and Its Applications".
My view on foundations would likely be described as rigorously Kolmogorovian but intuitively frequentest.I hope this doesn't need to be forked into another thread. I found the above to be alarming.
Kolmogorov was sympathetic to the frequentist interpretation advocated by Richard von Mises and in fact believed his axioms were Taylor Kolmogorov made for a frequentist concept of probability. Reference: pages 43-45 of Probability and Finance by Shafer and Vovk, which includes a translated letter from Kolmogorov regarding exactly this point. Also of interest, page x of the book's Preface
Vovk's work on the topics of the book evolved out of his work, first as an undergraduate and then as a doctoral student, with Andrei Kolmogorov, on Kolmogorov's finitary version of von Mises's approach to probability.
– – – – –
From what I can tell, the books referenced in the quote and in post 112 are about philosophy and general audience books/ writeups. They aren't math books. (I do happen to like Gigerenzer though.) People complain about general public books on QM all the time. I don't see why we shouldn't have similar sentiment here.
People don't realize that a properly worked out version of their favorite interpretation has more "obviously daft" features than they think.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.
The general impression I get is that they think the wave function is a real thing that undergoes collapse upon measurement, without really thinking how odd measurement as a fundamental is or what even is collapse. The almost pop science "It's in two places at once until observed"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.
Thanks
Bill
What! You degenerate!You bet your sweet Bippy. I only study it to become an actuary so I can get the big bucks :-p:-p:-p:-p:-p:-p:-p
On the other hand I think people who don't engage with the interpretations aren't "pragmatists unconcerned with philosophical mumbo jumbo", there is something deeply strange about entanglement and measurement in quantum theory and when I've spoken to these people and shown them things like the Kochen-Specker theorem, Bell's theorem, PBR theorem, they then do become interested in interpretations, i.e. most physicists think there is nothing to this because they carry around a vague interpretation that they don't think about much and really doesn't make much sense when analysed. Not because there isn't a problem and only a pedantic philosopher would think so.Regardless of ones attitude to interpretation there is something quite deep going on with entanglement:
https://arxiv.org/abs/0911.0695
And indeed the program of describing a classical world purely with QM has made great strides but is still not quite there yet – maybe it never will be in which case Einstein may have the last laugh over his good friend Bohr. Interestingly, even though they were good friends, and admired each other greatly, as reported by Ohanian – 'When Bohr visited the institute in 1948, Einstein refused to meet with him. In a comical incident during this visit, Einstein sneaked into an office in which Bohr was having a discussion with Pais, and found himself suddenly face to face with Bohr – but he merely wanted to borrow some tobacco for his pipe from a tin sitting on a shelf.'. Maybe Einstein, who evidently was only a shadow of his former self in his later years, became sick and tired of debating with Bohr.
Thanks
Bill
My view on foundations would likely be described as rigorously Kolmogorovian but intuitively frequentest.What! You degenerate!
Seriously though, yes I think the interpretation debate is much louder here (and on the net in general) than it is in day to day practice in physics. Now I think two things about this.
On the one hand I think that is because many in the interpretation "wars" don't realize that beyond a certain point there are currently no more no-go theorems and even though interpretation X might make more personal sense to you, that's as far as it goes. At a certain point you just have people saying position X is "obviously daft" not recognizing that every interpretation by necessity has something that classically is "obviously daft". Also often advocates of interpretations don't know the fully modern version of their interpretation and what they should be accepting with it. Just compare "Beginner's MWI" with it's basic idea of splitting universes, with the modern version that comes out from Wallace et al's work of uncountably infinite worlds, approximate splittings, human perspective being what possibly defines worlds, etc. People don't realize that a properly worked out version of their favorite interpretation has more "obviously daft" features than they think.
On the other hand I think people who don't engage with the interpretations aren't "pragmatists unconcerned with philosophical mumbo jumbo", there is something deeply strange about entanglement and measurement in quantum theory and when I've spoken to these people and shown them things like the Kochen-Specker theorem, Bell's theorem, PBR theorem, they then do become interested in interpretations, i.e. most physicists think there is nothing to this because they carry around a vague interpretation[SUP]1[/SUP] that they don't think about much and really doesn't make much sense when analysed. Not because there isn't a problem and only a pedantic philosopher would think so.
[SUP]1[/SUP]The general impression I get is that they think the wave function is a real thing that undergoes collapse upon measurement, without really thinking how odd measurement as a fundamental is or what even is collapse. The almost pop science "It's in two places at once until observed"
Although most people just apply it, there is a pretty active community of debate on Foundations, e.g. Frequentist vs Kolmogorov vs Di Finetti vs Jaynes. Famously summed up in I.J. Good's title "46656 Varieties of Bayesians" for the Third Chapter of his 1983 book "Good Thinking: The Foundations of Probability and Its Applications".You are probably correct (drats I used that word – probably). It's likely we get a rather different sample on this forum to what people using QM generally do. Certainly when I did my studies in probability and stats nobody worried about it, although as you advance you pick up that there is a debate about its foundations, just like there is debate about the foundations of math itself. I wasn't that attracted personally to the area, liking analysis better, but always enjoyed the lectures of the professor taking it – he was a funny guy so took more subjects in it than I had to. My view on foundations would likely be described as rigorously Kolmogorovian but intuitively frequentest.
Thanks
Bill
For the case of quantum mechanics, that's the real question. I believe not, if taken literally.
the interpretations ultimately gave different predictions.Then they are different theories, per the standard definition, and calling them different interpretations is a misnomer.
Funnily enough I always thought QM was very similar to probability theory in this regard. Although most people just apply it, there is a pretty active community of debate on Foundations, e.g. Frequentist vs Kolmogorov vs Di Finetti vs Jaynes. Famously summed up in I.J. Good's title "46656 Varieties of Bayesians" for the Third Chapter of his 1983 book "Good Thinking: The Foundations of Probability and Its Applications".J. von Plato, Creating modern probability, Cambridge Univ. Press, Cambridge 1994.
discusses the history of the concept and interpretation of probability.
L. Krüger, G. Gigerenzer and M.S. Morgan (eds.), The Probabilistic Revolution: Ideas in the Sciences, Vol. 2, MIT Press, Cambridge, MA, 1987.
discuss the history of probability in the various fields of application.
L. Sklar, Physics and Chance, Cambridge Univ. Press, Cambridge 1993.
discusses the philosophical problems of the probability concept, with an emphasis on statistical mechanics.
This insights article is not specifically about QM and frankly, I think that the current discussion about specific interpretations of QM in this thread is off-topic and I have suggested its removal.Isn't this very strange? In view of the fact that the article begins with the very first sentence
I am against “interpretations” of Quantum Mechanics (QM)and ends with the very last sentence
There are no interpretations of QM, there are only theoriesthe topic is clearly the non-interpretation of quantum mechanics, though the title is different, and the argument is made more abstractly.
The various interpretations of any given theory, when presented with a given experimental setup, would all predict the same quantitatively measurable outcomes, no?For the case of quantum mechanics, that's the real question. I believe not, if taken literally. This is why even Nobel prize winners such as Weinberg and t'Hooft spend significant effort on the interpretation issue. Though they did it only after their retirement: While paid they researched more important issues and kept the issues on the back burner.
The various interpretations of quantum mechanics would predict it only by being quite liberal with the interpretation details, and assuming a lot about the culture of doing physical experiment (which is far more complex than what interpretations usually consider).
I answered the above though you want to keep the discussion off quantum mechanics. But then it becomes nearly empty. In most fields of science there is agreement on the interpretation, hence no way to discuss your question meaningfully. The only exceptions are quantum mechanics, statistical mechanics, and applied probability theory, which share some of the foundational problems.
But historically, the question whether light was wave or matter was another such topic, and the interpretations ultimately gave different predictions. These were checkable, which decided in favor of the wave nature, long before it was known what waved….
An interesting observation is that in math we generally do not worry about interpretations of probability – we either apply it as most books like Feller's classic do or we simply look at the consequences of the Kolmogorov axioms as books on rigorous probability theory do. People generally do not get caught up much in the interpretation issue – but in Quantum Theory we have all sorts of, how to put it, 'vigorous' discussions about it. That always has struck me as, well interesting.Funnily enough I always thought QM was very similar to probability theory in this regard. Although most people just apply it, there is a pretty active community of debate on Foundations, e.g. Frequentist vs Kolmogorov vs Di Finetti vs Jaynes. Famously summed up in I.J. Good's title "46656 Varieties of Bayesians" for the Third Chapter of his 1983 book "Good Thinking: The Foundations of Probability and Its Applications".
So please spell out the operative definitions that relate the mathematical concepts of quantum theory to measurable quantities.I don't know enough about quantum mechanics to do that. QM is not the only scientific theory and not the only place where interpretations arise.
However, even if I did know enough QM to do that I would not. Frankly, the obsession with interpretations is the reason why I stay out of the QM forum. I would like to know more about QM, but I have no interest whatsoever in becoming embroiled in the 10000 th pointless argument on the topic here. The constant deluge of such threads is a real turn-off for me, which is a pity because in my case it has diluted the educational mission of PF as a whole.
This insights article is not specifically about QM and frankly, I think that the current discussion about specific interpretations of QM in this thread is off-topic and I have suggested its removal. The QM forum's obsession with interpretations is not something that I want spreading to other parts of the forum.
I refuse to pick up any QM-related gauntlet. Let's keep the discussion general, about theories, interpretations, and the scientific method.
So according to our compromise terminology, and in agreement with the claim by @Demystifier in the insight article under discussion, we would have as many different quantum theories as there are interpretations of quantum mechanicsI think you are misusing the compromise terminology. The various interpretations of any given theory, when presented with a given experimental setup, would all predict the same quantitatively measurable outcomes, no?
There are many reasons it's incomplete.Quantum mechanics might seem to be incomplete if one prefers to come back to the idea of an objective real world, i.e. the reality concept of classical physics.
Fo you, reality seems to be something metaphysicalYes, by definition “reality” is a concept which is defined by and studied in the philosophical discipline of ontology which is one of the major branches of metaphysics. It is not that I doubt that experiments are real, it is just that the whole concept of reality is a philosophical one that cannot be addressed by the scientific method.
OK, so let me try to make your terminology precise, as I understand you.This is not my terminology. This is an effort to construct a compromise terminology for clarity here.
My terminology would not make use of subjective and objective. 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. I believe that is the standard usage of the word “theory” and although it less clear I also believe that is the standard usage of the word “interpretation”.
However, I think your previous post is good compromise terminology for the purposes of this discussion. It clarifies the concepts and allows the discussion to proceed. Let’s use it for now.
It is incomplete in the sense that all couplings and mass are put in by hand and are not emergent from the theory.There are many reasons it's incomplete. Only time will tell us if they are resolvable or not.
Thanks
Bill
But to his dying day thought it incompleteIt is incomplete in the sense that all couplings and mass are put in by hand and are not emergent from the theory
Mathematical formalisms such as the one presented in basic form in the previous chapter are in themselves rather abstract; they say nothing about concrete reality.Although mass and couplings are part of concrete reality but see above.
Now, as to whether this section on interpretation is consistent with your view of interpretation depends a little on what is meant by “corresponds with reality”.Yes. For me, experiment is an obvious part of everyday reality. If we deny it this status, nothing objective is left. Fo you, reality seems to be something metaphysical, unrelated to experience (of which experimental evidence is a part).
I would only agree that the objective interpretation is what makes a theory useful, and that is already part of the theory itself.OK, so let me try to make your terminology precise, as I understand you.
Can we agree on that? Then I'll accept this terminology for the sake of our discussion.
an instrumentalist minimal interpretation. In such an interpretation, Hermitian operators represent macroscopic measurement apparatus, and their eigenvalues indicate the measurement outcomes (pointer positions) which can be observed, while inner products give the probabilities of obtaining particular measured values. With such a formulation, quantum mechanics remains stuck in the macroscopic world… but still has the problem to say what probabilities mean. Observed are only frequencies, not probabilities.
The first stage of interpretation of the mathematical formalism establishes the connection to the empirical world as far as needed for everyday physics in the laboratory or at the particle collider.This is presumably what @Dale calls objective interpretation.
ost physicists would also prefer to have some idea of what is behind those measurements and observational data, i.e. just how the microscopic world which produces such effects is really structured.and this would be what he calls subjective interpretation.
I may be off on this topic a bit but in a binary system wouldn't repulsion of the objects cause instability unless the density of the system was such that it acted as a glue force. i was pondering 0, 1, 2 and 3 and I keep coming to the conclusion that you can't have 0, 1 would be a singularity, 2 would be unstable (unless, see above) and 3 would be a triangle in matter.
forgive me if it sounds stupid but i had to use the most basic method i could think of.
Maybe, the following quotes might help to clarify some issues (from “The Philosophy of Quantum Physics” by Cord Friebe, Meinard Kuhlmann, Holger Lyre, Paul M. Näger, Oliver Passon and Manfred Stöckler, 2018):
“Not only in philosophy, but even in physics itself, one depends on interpretations. Mathematical formalisms such as the one presented in basic form in the previous chapter are in themselves rather abstract; they say nothing about concrete reality. They require an interpretation, initially in the sense that the mathematical symbols and operations must be associated with elements of physical reality……
If one tries to proceed systematically, then it is expedient to begin with an interpretation upon which everyone can agree, that is with an instrumentalist minimal interpretation. In such an interpretation, Hermitian operators represent macroscopic measurement apparatus, and their eigenvalues indicate the measurement outcomes (pointer positions) which can be observed, while inner products give the probabilities of obtaining particular measured values. With such a formulation, quantum mechanics remains stuck in the macroscopic world and avoids any sort of ontological statement about the (microscopic) quantum-physical system itself….
The first stage of interpretation of the mathematical formalism establishes the connection to the empirical world as far as needed for everyday physics in the laboratory or at the particle collider. Born’s rule allows a precise prediction of the probabilities of observing particular outcomes in real, macroscopic measurements. The fact that this minimal interpretation makes statements only about macroscopic, empirically directly accessible entities such as measurement setups, particle tracks in detectors or pulses from a microchannel plate may be quite adequate for those who see the goal of the theory within an experimental science such as physics as being simply the ability to provide empirically testable predictions. For the metaphysics of science, this is not sufficient, and most physicists would also prefer to have some idea of what is behind those measurements and observational data, i.e. just how the microscopic world which produces such effects is really structured. In contrast to the instrumentalist minimal interpretation, however, every additional assumption which might lead to a further-reaching interpretation remains controversial……”
I believe you intend to include both the mapping to experiment and also metaphysical claims about reality.Good point I hadn't thought of before.
John Baez's writings has often influenced me in my views on interpretations:
http://math.ucr.edu/home/baez/bayes.html
In particular:
'It turns out that a lot of arguments about the interpretation of quantum theory are at least partially arguments about the meaning of the probability!'
You have to have an interpretation of probability to do the mapping. Interpretations like the ensemble do only that. I would call them minimal.
An interesting observation is that in math we generally do not worry about interpretations of probability – we either apply it as most books like Feller's classic do or we simply look at the consequences of the Kolmogorov axioms as books on rigorous probability theory do. People generally do not get caught up much in the interpretation issue – but in Quantum Theory we have all sorts of, how to put it, 'vigorous' discussions about it. That always has struck me as, well interesting.
But others go further – even Copenhagen goes further (at least in some versions – there seems no standard version). But it generally seems to be something like (from a blog discussion on it):
1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)
The above contains quite few debatable points:
1. Is a quantum system completely described by the wave function?
2. Wave particle duality – its really neither wave or particle – it's quantum stuff.
3. There are in a sense no classical systems – its all really quantum stuff. If you do not view it as all quantum stuff you face a problem – exactly where is the dividing line?
Every one of those really requires a thread of their own, so I will not discuss them here except to say modern interpretations like decoherent histories realize they are issues and try to correct them – which was the view of the blog I got it from. But we should not be too harsh, Copenhagen was formulated in the early days of QM – things have moved on a lot since then.
On thing that always brings a bit of a smile to my face is Einstein was the original champion of the Ensemble interpretation. It seems to have come through mostly unchanged to modern times. But Copenhagen, championed his old sparring partner, and good friend, Bohr, didn't. Could it be Einstein, after his debates with Bohr saw to the heart of it better? Einstein was wrong to object to QM so strongly at it's birth, but eventually he came to accept it as correct. To be fair though his objections did strengthen the theory. But to his dying day thought it incomplete – which due to various unresolved issues like quantum gravity is of course true – but may change in the future – or actually be shown as incomplete.
Thanks
Bill
This says exactly what I claimed.I am not convinced that this is exactly the same as what you were claiming. First, this is the definition of interpretation, not the definition of theory. The definition of theory is not consistent with your definition of theory. The theory itself includes the mathematical framework as well as the mapping to experiment. It specifically rejects your definition of theory as being only the math.
Now, as to whether this section on interpretation is consistent with your view of interpretation depends a little on what is meant by “corresponds with reality”.
I believe you intend to include both the mapping to experiment and also metaphysical claims about reality. In that case there is some overlap between the definition of theory and interpretation since they both include the mapping to experiment. This usage would be consistent with the term “minimal interpretation” to describe that mapping.
However, the phrase “corresponds to reality” could be taken to refer exclusively to the metaphysical statements only. After all, it is possible to assert a relation to measurement while not asserting whether or not the results of measurements are “real”.
I don’t think that definition is as strong a support for your position as you think. At best it gives a kind of messy overlap between theory and interpretation where the useful part (link to measurement) is part of both.
In either case, the theory consists of the portion that is experimentally testable, the mathematical framework and the mapping to experiment. If you like the overlapping concept then you could talk about the objective interpretation and the subjective interpretation to distinguish between the scientific and philosophical portions of the interpretation.
I would only agree that the objective interpretation is what makes a theory useful, and that is already part of the theory itself.
This is just arguing over definitions, right?Yes, because the Insight article defining this thread tries to change definitions:
It doesn’t make sense to distinguish an interpretation from a theory. There are no interpretations of QM, there are only theories.Without good reasons, I think; see my post #4.
This is just arguing over definitions, right? Maybe the only thing that can be said is there is enough disagreement that when these words are important, they should be defined in each discussion. Even if one definition is 90% popular, that's still pretty ambiguous. If PF had a mentor-editable glossary that might cut down on the convergence times.
Theory is the formal, purely mathematical part, and interpretation tells how this formal part relates to reality / observation. In simple cases, the interpretation is simply done by choosing the right words for the formal concepts, but in relativity, more is needed since it is no longer intuitive, and in quantum mechanics, much more is needed since the meaning is – a mess.Another independent wikipedia source also follows my notion of interpretation:
Attempts to formalize the principles of the empirical sciences use an interpretation to model reality, in the same way logicians axiomatize the principles of logic. The aim of these attempts is to construct a formal system that will not produce theoretical consequences that are contrary to what is found in reality. Predictions or other statements drawn from such a formal system mirror or map the real world only insofar as these scientific models are true.
In my opinion, there is a problem with interpretations in that when you have a different one, you cannot know in advance that there are no circumstances where you will not get to either different outputs, or easier ways of going about something. I know here you are not supposed to mention your own work, but with QM there is a small group of interpretations where it is assumed there is a physical wave (De Broglie, Bohm). Now, if you assume the wave is the cause of diffraction in the two slit experiment, then you might consider the wave has to travel with the particle. This gives a physical relationship not present in standard QM, and when coupled with Euler's complex number theory (from which the antinode is not complex) you get a much simpler means of calculating properties of the chemical bond. (You also get a relationship that has not been noted in standard theory.) Now, whether simplified means of calculating is worth bothering about is a matter of opinion, but for me it is.
But to give precise references – if you still want them – I need to do some research.So I found a few references that clearly disagree with your definition of "theory" at least. Wikipedia says "A scientific theory is an explanation of an aspect of the natural world that can be repeatedly tested and verified in accordance with the scientific method" https://en.wikipedia.org/wiki/Scientific_theory where clearly a theory must be testable. The purely mathematical concept of theory that you propose is not testable, so it does not fit the Wikipedia definition.
I also found a paper entitled "What is a scientific theory?" by Patrick Suppes from 1967 (Philosophy of Science Today) who says "The standard sketch of scientific theories-and I emphasize e word “sketch”-runs something like the following. A scientific theory consists of two parts. One part is an abstract logical calculus … The second part of the theory is a set of rules that assign an empirical content to the logical calculus. It is always emphasized that the first part alone is not sufficient to define a scientific theory".
As he describes this as the "standard sketch" and as this also agrees with the Wikipedia reference and my previous understanding, then I take it that your definition of theory is not that which is commonly used. I have not found a similar clear definition of "interpretation", but clearly the term theory includes the mapping to experimental outcome that is necessary to make it useful on its own for designing and analyzing experiments. Thus, by the standard usage it is also not the interpretation which makes a theory useful, the theory is already useful without an interpretation.
It is the interpretation that makes a theory useful.No, it is the operative definitions of how to relate mathematical concepts of the theory to measurable quantities that make a theory useful. This is not interpretation in the common nomenclature typically used here, regardless of what Born and Schrödinger thought about the issue.
It is the interpretation that makes a theory useful.Even using your definitions I would disagree with this claim. With your definition it is only the so-called “minimal interpretation” that makes the theory useful. All other interpretations are subjective per your terms.
I disagree. The theory must include the relation to observation. Otherwise it is useless.It is the interpretation that makes a theory useful.
Sorry, but in my mind this is severely twisting the meaning of the word "interpretation" in this discussion.I just observe that Schrödinger and Born thought differently about the issue. At the time where the interpretation problems in quantum mechanics became relevant, there was good theory, and there was disagreement about the relation to observation in general – just pieces that were undisputable but others that were hoghly contentuous. Indeed, the meaning of the relation to observation changed during the first few years.
To me what is scientifically important is the distinction between the portions of a model which can be experimentally tested using the scientific method and the portions that cannot. I don’t care too much about the terminology, but that distinction is important so it should have some corresponding terminology. In my usage that would be “theory” vs “interpretation”.
What words would you personally use to make that distinction?objective = testable and subjective = untestable.
If theory = testable and interpretation = untestable there would have not been nearly 100 years of dispute about the interpretation issues.
As I said, in simple cases, the interpretation is simply calling the concepts by certain names. In the case of classical Hamiltonian mechanics, ##p## is called momentum, ##q## is called position, ##t## is called time, and everyone is supposed to know what this means, i.e., to have an associated interpretation in terms of reality.Sorry, but in my mind this is severely twisting the meaning of the word "interpretation" in this discussion.
But to give precise references – if you still want them – I need to do some research.I would appreciate that and I will look for similar explicit definitions as well. My “implicit” definitions are quite opposed to yours.
To me what is scientifically important is the distinction between the portions of a model which can be experimentally tested using the scientific method and the portions that cannot. I don’t care too much about the terminology, but that distinction is important so it should have some corresponding terminology. In my usage that would be “theory” vs “interpretation”.
What words would you personally use to make that distinction?
But this is not standard terminology. Theory is the formal, purely mathematical part, and interpretation tells how this formal part relates to reality / observation. In simple cases, the interpretation is simply done by choosing the right words for the formal concepts
That is not how I have seen the distinction. Do you have an authoritative reference for this usage? (What you are calling “theory” I have seen called “mathematical framework”)It is surely implicit in the discussions of 1926-1928 about the interpretation of quantum mechanics by their originators. Schrödinger's and Heisenberg's theories were proved to be equivalent (i.e., the mathematical frameworks were interconvertible), but views about the interpretation differed widely. Moreover, different interpretations even made different predictions, and the analysis turned out to give a harmonizing Copenhagen interpretation, both relaxing the incomatible hardliner positions that Born and Schrödinger originally had.
But to give precise references – if you still want them – I need to do some research.
It is the interpretation that makes a theory useful.
Classical Hamiltonian mechanics is surely a theory. But it needs interpretation to be used: How to interpret energy in terms of reality/observation is clearly not part of the theory.
I disagree again. It is the prediction of measurable quantities that makes a theory useful.
[Classical Hamiltonian mechanics] certainly does not need interpretation to be used and tested. You do not need to give a "deeper meaning" to the Hamiltonian to test Hamiltonian mechanics or to give a meaning to why the Poisson brackets with the Hamiltonian give the time evolution of a system. You need a description of phase space, an expression for the Hamiltonian, and the measurable predictions resulting from it.As I said, in simple cases, the interpretation is simply calling the concepts by certain names. In the case of classical Hamiltonian mechanics, ##p## is called momentum, ##q## is called position, ##t## is called time, and everyone is supposed to know what this means, i.e., to have an associated interpretation in terms of reality.
Of course, to be useful, a theory must not only have an interpretation but also give valid predictions of measurable results.
It is the interpretation that makes a theory useful.I disagree again. It is the prediction of measurable quantities that makes a theory useful.
Classical Hamiltonian mechanics is surely a theory. But it needs interpretation to be used: How to interpret energy in terms of reality/observation is clearly not part of the theory.It certainly does not need interpretation to be used and tested. You do not need to give a "deeper meaning" to the Hamiltonian to test Hamiltonian mechanics or to give a meaning to why the Poisson brackets with the Hamiltonian give the time evolution of a system. You need a description of phase space, an expression for the Hamiltonian, and the measurable predictions resulting from it.
But this is not standard terminology. Theory is the formal, purely mathematical part, and interpretation tells how this formal part relates to reality / observation.That is not how I have seen the distinction. Do you have an authoritative reference for this usage? (What you are calling “theory” I have seen called “mathematical framework”)
Sure I agree. That has never been the question. The question is whether a lattice model (at finite spacing) could provide a non-perturbative definition for the currently successful experimental predictions of QED, QCD and the standard model. If that is a reasonable research programme (at least as reasonable as looking for a continuum 4D QED theory), then one can say that the standard model may be consistent with non-relativistic QM. It is not an "either-or" question. One could believe that both research programmes are reasonable.I agree, when I said numerical results in my initial post I was referring to Lattice theories and you'll find plenty of discussions about Lattice versions of the Standard Model suggesting non-triviality in Callaway's paper that I referenced. I also consider both programs reasonable.
Then just to be clear I was stating something else, that for theories involving ##SU(2)## gauge fields there are strong arguments that they are not trivial, so I was rather referencing some evidence against triviality for the Standard Model.
However I share your doubts about typical arguments against ##phi^{4}_{4}## and ##QED_4## as I don't think the Landau pole is a particularly strong argument. It's just a perturbative suggestion that a particular approach to the continuum limit is blocked. Alan Sokal's PHD thesis "An Alternate Constructive Approach to the ##phi^{4}_{3}## Quantum Field Theory, and a Possible Destructive Approach to ##phi^{4}_{4}##" has some interesting material on this. He uses the sum of bubble graphs to argue for triviality of the continuum.
For anybody reading there is the possibility that there are non-trivial continuum ##QED_4## and ##phi^{4}_{4}## theories. It's simply that they aren't the ##a rightarrow 0## limit of a lattice theory and so the triviality of the lattice theories when taking the continuum limit isn't a definitive proof of triviality.
My personal gut intuition is that is that ##phi^{4}_{4}## is trivial on its own, but not when embedded in the electroweak theory. I suspect ##QED_4## is not trivial as you do.
In general I strongly suspect that properly controlled non-perturbative quantum field theory will show that plenty of folk wisdom about QFT is just wrong. For example it might emerge that having a simple Higgs is the only way of having massive gauge bosons that has a nonperturbative definition and alternates like technicolor aren't defined. Similarly many parameters that look like they can take any value perturbatively and non-rigorously might be restricted to certain ranges non-perturbatively. Also the Standard Model might be much more natural and less adhoc seeming, perhaps only theories of its form exist non-perturbatively in 4D.
Basically we're currently operating under the assumption that the space of QFTs in 4D is identical to to the space of field theories that are perturbatively renormalizable. However this is incorrect as ##Gross-Neveu_3## is pertrubatively non-renormalizable and yet non-perturbatively exists.Sure I agree. That has never been the question. The question is whether a lattice model (at finite spacing) could provide a non-perturbative definition for the currently successful experimental predictions of QED, QCD and the standard model. If that is a reasonable research programme (at least as reasonable as looking for a continuum 4D QED theory), then one can say that the standard model may be consistent with non-relativistic QM. It is not an "either-or" question. One could believe that both research programmes are reasonable.
Example of papers within a research programme for a lattice standard model are:
https://arxiv.org/abs/0912.2560
https://arxiv.org/abs/1809.11171
atyy's statement sounded like it. He thinks that Landau poles are the death blow to a continuum theory and wants to substitute finite lattices for the true, covariant theories. But in fact the Landau pole of QED just says that the lattice approximation of QED is always poor, so it is actually the death blow to his lattice philosophy. We had discussed this in several threads:
https://www.physicsforums.com/threads/lattice-qed.943462/
https://www.physicsforums.com/threads/does-qft-have-problems.912943/
Yes. I am convinced that ##phi_4^4## and ##QED_4## exist, though I don't know how to prove it. But I have been collecting ideas and techniques for a long time, and one day I might be prepared to try….
Klauder has some nonrigorous ideas how to do perturbation theory from a different starting theory: https://arxiv.org/abs/1811.05328 and many earlier papers propagating the same idea. Nobody seems to take up Klauder's challenge and tries; hence I don't know whether it has merit. Do you see any obvious faults in his proposal?Then just to be clear I was stating something else, that for theories involving ##SU(2)## gauge fields there are strong arguments that they are not trivial, so I was rather referencing some evidence against triviality for the Standard Model.
However I share your doubts about typical arguments against ##phi^{4}_{4}## and ##QED_4## as I don't think the Landau pole is a particularly strong argument. It's just a perturbative suggestion that a particular approach to the continuum limit is blocked. Alan Sokal's PHD thesis "An Alternate Constructive Approach to the ##phi^{4}_{3}## Quantum Field Theory, and a Possible Destructive Approach to ##phi^{4}_{4}##" has some interesting material on this. He uses the sum of bubble graphs to argue for triviality of the continuum.
For anybody reading there is the possibility that there are non-trivial continuum ##QED_4## and ##phi^{4}_{4}## theories. It's simply that they aren't the ##a rightarrow 0## limit of a lattice theory and so the triviality of the lattice theories when taking the continuum limit isn't a definitive proof of triviality.
My personal gut intuition is that is that ##phi^{4}_{4}## is trivial on its own, but not when embedded in the electroweak theory. I suspect ##QED_4## is not trivial as you do.
In general I strongly suspect that properly controlled non-perturbative quantum field theory will show that plenty of folk wisdom about QFT is just wrong. For example it might emerge that having a simple Higgs is the only way of having massive gauge bosons that has a nonperturbative definition and alternates like technicolor aren't defined. Similarly many parameters that look like they can take any value perturbatively and non-rigorously might be restricted to certain ranges non-perturbatively. Also the Standard Model might be much more natural and less adhoc seeming, perhaps only theories of its form exist non-perturbatively in 4D.
Basically we're currently operating under the assumption that the space of QFTs in 4D is identical to to the space of field theories that are perturbatively renormalizable. However this is incorrect as ##Gross-Neveu_3## is pertrubatively non-renormalizable and yet non-perturbatively exists.
I disagree. The theory must include the relation to observation. Otherwise it is useless.It is the interpretation that makes a theory useful.
Classical Hamiltonian mechanics is surely a theory. But it needs interpretation to be used: How to interpret energy in terms of reality/observation is clearly not part of the theory.
Theory is the formal, purely mathematical part, and interpretation tells how this formal part relates to reality / observation.I disagree. The theory must include the relation to observation. Otherwise it is useless. The problem comes with interpretations imposing some sort of unneseccary ”reality” on top of this, which unless you can provide observational differences will always remain purely philosophical.
I think the whole ordeal started from QM being a theory based on experiments and model fitting more or less. The interpretation is needed because the theory does not show the origin of mass or charge …etc. They must be emergent from a more fundamental concept.
If we don’t use the word “theory” for the parts which can be scientifically tested and “interpretation” for the parts which cannot be testedBut this is not standard terminology. Theory is the formal, purely mathematical part, and interpretation tells how this formal part relates to reality / observation. In simple cases, the interpretation is simply done by choosing the right words for the formal concepts, but in relativity, more is needed since it is no longer intuitive, and in quantum mechanics, much more is needed since the meaning is – a mess.
Or perhaps the theory is just the set of final measurable predictions of T1 and T2, while all the other “auxiliary” elements of T1 and T2 are the “interpretation”? It doesn’t make sense either, because there is no theory in physics that deals only with measurable predictions. All physics theories have some “auxiliary” elements that are an integral part of the theory.I disagree with the T1 and T2 analogy entirely, but particularly with this paragraph here.
Regardless of the existence of an interpretation-free theory, it is useful to distinguish the parts of a model which can be tested with the scientific method from the parts that cannot. If we don’t use the word “theory” for the parts which can be scientifically tested and “interpretation” for the parts which cannot be tested with the scientific method, then what terms should we use to distinguish them? We would need to coin some new terms for the same concepts.
No, the standard terminology is fine. It is pointless to change the names since the distinction between testable and untestable is scientifically important and captured in the current terminology.