Against "interpretation" - Comments

[PeterDonis]

Thread reopened.

 

[A. Neumaier]

Indeed. QED is even thought to be trivial, but I do not think anyone has proven it rigorously. If so that is strong evidence it could only be an effective theory - and of course we now know it is since its part of the electro-weak theory at high enough energies.

It's a genuinely uncertain issue. There are known cases where adding an $SU(2)$ gauge field to otherwise trivial theories renders them non-trivial and there are numerical simulations and simplified or limiting theories suggesting this might be what occurs in the Electroweak theory. So we currently don't actually know if the standard model is trivial.

Actual triviality just means that the continuum limit of the lattice theory is trivial. It says nothing about nonexistence of the continuum theory. See the discussions here and here.

Further on, 't Hooft also points out that some of our current theories may not have a continuum limit. At the physics level of rigour, QCD is thought to have a continuum limit, but QED is thought to have a Landau pole.
p50: "If a theory is not asymptotically free, but has only small coupling parameters, the perturbation expansion formally diverges, and the continuum limit formally does not exist."
p58: "Landau concluded that quantum field theories such as QED have no true continuum limit because of this pole. Gell-Mann and Low suspected, however, ... it is not even known whether Quantum Field Theory can be reformulated accurately enough to decide"

Note that the Landau pole of QED is at physically irrelevant energies, while QCD has (due to infrared issues) a Landau pole at experimentally accessible energies! Thus a Landau pole says nothing about existence or nonexistence, only about troubles in certain renormalization schemes.

 

[DarMM]

Actual triviality just means that the continuum limit of the lattice theory is trivial. It says nothing about nonexistence of the continuum theory. See the discussions here and here.

That's certainly true, were we saying otherwise?

Do you mean there might be a non-trivial continuum theory that is not the limit of lattice approximations?

The kind of thing suggested in Gallavottiv and Rivasseau's review paper from 1984 for example.

 

[A. Neumaier]

That's certainly true, were we saying otherwise?

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/

Do you mean there might be a non-trivial continuum theory that is not the limit of lattice approximations?.

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?

 

[Dale]

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.

 

[A. Neumaier]

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

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, 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.

 

[ftr]

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.

 

[Orodruin]

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.

 

[A. Neumaier]

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.

 

[DarMM]

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.

 

[atyy]

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

 

[DarMM]

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.

 

[Dale]

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”)

 

[Orodruin]

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.

 

[A. Neumaier]

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.

 

[Dale]

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?

 

[Orodruin]

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.

 

[A. Neumaier]

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.

 

[A. Neumaier]

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. In 1926, when 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 highly contentuous. Indeed, the meaning of the relation to observation changed during the first few years.

 

[Dale]

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.

 

[Orodruin]

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.

 

[Dale]

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 the 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.

 

[A. Neumaier]

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.

Since you quote wikipedia, let me also quote it:

An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics "corresponds" to reality. [...] An interpretation (i.e. a semantic explanation of the formal mathematics of quantum mechanics) [...]

This says exactly what I claimed. The same meaning is also echoed in another wikipedia page not related to quantum mechanics:

The mathematics of probability can be developed on an entirely axiomatic basis that is independent of any interpretation: see the articles on probability theory and probability axioms for a detailed treatment.

From another well-known common source on quantum mechanics:

Mathematically, the theory is well understood [...] The problems with giving an interpretation [...] are dealt with in other sections of this encyclopedia. Here, we are concerned only with the mathematical heart of the theory, the theory in its capacity as a mathematical machine, and — whatever is true of the rest of it — this part of the theory makes exquisitely good sense.

... and by implication, everything else is interpretation, about which ''there is very little agreement''. Very little is said in the cited article about how an observable or a state is related to reality, no operational definition is given how to measure a state or an observable. Loose connections are given in Section 3.4 (Born's rule) and statement (4.2) (special case of eigenstates). The second connection is too special to be representative of the meaning of QM; the first connection is already interpretation dependent (the formulation assumes collapse, a controversial feature) and nevertheless fraught with problems, as is said explicitly on the same page:

• The distinction between contexts of type 1 and 2 remains to be made out in quantum mechanical terms; nobody has managed to say in a completely satisfactory way, in the terms provided by the theory, which contexts are measurement contexts, and
• Even if the distinction is made out, it is an open interpretive question whether there are contexts of type 2; i.e., it is an open interpretive question whether there are any contexts in which systems are governed by a dynamical rule other than Schrödinger's equation.

But without contexts of type 2, nothing at all follows about the relation between the formalism and measurable cross sections or detection events. Thus the uninterpreted theory must be silent about the latter.

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.

So please spell out the operative definitions that relate the mathematical concepts of quantum theory to measurable quantities. You'll find that this is impossible to do independent of any of the interpretations of quantum mechanics that can be found in the literature. (Shut-up-and-calculate works only because it leaves the interpretation to the community without spelling out precisely what it consists of.)

Thus interpretation is a prerequisite for making quantum theory useful.

 

[Ian J Miller]

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.

 

[A. Neumaier]

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.

 

[akvadrako]

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.

 

[A. Neumaier]

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.

 

[Dale]

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.

Edit: I just noticed this discrepancy

Theory is the formal, purely mathematical part, and interpretation tells how this formal part relates to reality / observation.

You say that the interpretation provides the relationship to “reality/observation”. The standard definitions of theory include the relationship to observation and your quoted Wikipedia definition of interpretation includes only the relationship to “reality”.

So I think your mistake is including the link to observation in the interpretation whereas both the definitions of theory and interpretation disagree and place the link to observation in theory and not interpretation.

 

[bhobba]

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 by 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

 

[Lord Jestocost]

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……”

 

[A. Neumaier]

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.

 

[A. Neumaier]

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.

1. A mathematical framework defines the concepts of a theory and develops their logical implications.
2. An objective interpretation relates the concepts of the theory unambiguously to experiment.
3. A subjective interpretation gives a metaphysical description underlying the objective interpretation.
4. A theory consists of its mathematical framework and its objective interpretation.
5. An interpretation consists of the objective interpretation of the theory and its subjective interpretation.
6. Thus the objective interpretation is the intersection of interpretation and theory.

Can we agree on that? Then I'll accept this terminology for the sake of our discussion.

 

[ftr]

But to his dying day thought it incomplete

It 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.

 

[bhobba]

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

 

[Dale]

Fo you, reality seems to be something metaphysical

Yes, 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.