Against "interpretation" - Comments

[Dale]

They are not quite equivalent since the Legendre transform that relates the two is not always defined.

$F/a=m$ is also not always defined. Shall we make that a new interpretation?

The word "interpretation" is just a word so we can define it to mean anything we like. It has a standard definition, and for historical consistency it is best to stick with standard definitions unless there is a compelling reason to change. Frankly, the standard definition of "interpretation" is already trivial enough for my taste, so I don't find further trivializing it to be a compelling reason to change.

 

[Demystifier]

The word "interpretation" ... It has a standard definition ...

What is the standard definition of the word "interpretation"? I think it has different meanings in different fields such as (i) mathematical logic, (ii) applied experimental physics and (iii) quantum foundations. Only in (iii) it has some negative "non-scientific" connotations.

 

[Demystifier]

$F/a=m$ is also not always defined. Shall we make that a new interpretation?

It is not so innocent as it may look. Some physicists interpret the 2nd Newton law not as a law but as a definition of force, defined as $F\equiv ma$.

 

[Demystifier]

They are two equivalent mathematical frameworks which can be derived from one another through mathematical operations. Why should we use a definition of “interpretation” where a straight mathematical operation generates a new interpretation? Every line of every theorem or homework problem would then be using a unique interpretation. Is that what you want the word to mean?

No I don't. As you can see from the first post, I would like to ban the word "interpretation" completely from quantum foundations, because the meaning of it, in my opinion, is not well defined. It makes much more sense to talk about "observationally equivalent theories". Hamiltonian and Lagrangian mechanics are one example, Copenhagen QM and Bohmian mechanics are another.

 

[Dale]

I think it has different meanings in different fields

Of course. That is typical. Even the word field has different meanings in different fields

 

[Demystifier]

Of course. That is typical. Even the word field has different meanings in different fields

So in the field of quantum foundations, what is the standard definition of "interpretation"? In the first post I have argued that neither of the possible definitions makes much sense.

 

[A. Neumaier]

$F/a=m$ is also not always defined. Shall we make that a new interpretation?

The word "interpretation" is just a word so we can define it to mean anything we like. It has a standard definition, and for historical consistency it is best to stick with standard definitions unless there is a compelling reason to change. Frankly, the standard definition of "interpretation" is already trivial enough for my taste, so I don't find further trivializing it to be a compelling reason to change.

Sure. I didn't imply with my comment that I would want to redefine the standard notion of interpretation.

For me, the formalism of classical mechanics to be interpreted in terms of reality consists of both the Lagrangian and the Hamiltonian view, their theoretical relations, and their generalizations. Interpretation only begins when one gives the potential, momentum, etc. meaning in terms of experiments.

 

[Demystifier]

Interpretation only begins when one gives ... meaning in terms of experiments.

Isn't interpretation in quantum foundations supposed to be the exact opposite, beginning only when giving meaning in terms of something not subject to experiments?

 

[A. Neumaier]

Interpretation only begins when one gives the potential, momentum, etc. meaning in terms of experiments.

Isn't interpretation in quantum foundations supposed to be the exact opposite, beginning only when giving meaning in terms of something not subject to experiments?

This would be interpretation of experiments, not interpretation of quantum mechanics.

Interpreting A in terms of B always means showing how aspects of A can be understood using concepts known from B. Thus to interpret quantum mechanics one need to explain the meaning of its concepts using concepts from outside quantum mechanics - i.e., from experimental practice in the widest sense.

On the other hand, to interpret experiments one needs theory; and both kinds of interpretation must mesh consistently to be acceptable.

 

[Dale]

So in the field of quantum foundations, what is the standard definition of "interpretation"?

To my knowledge in QM the standard definition of "interpretation" is as described in Wikipedia:

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

 

[vanhees71]

Isn't interpretation in quantum foundations supposed to be the exact opposite, beginning only when giving meaning in terms of something not subject to experiments?

I think that's the great misunderstanding between physicists and mathematicians. For a physicist there are quantifiable and thus measurable phenomena, to begin with. Experience shows that we find certain patterns, which we call natural laws, and from this we can try to make mathematical models or theories. The quantities/observables and states are defined empirically from the phenomena and mathematical descriptions use empirically useful primitive notions. The mathematician of course tries to make these primitive notions a system of axioms to seek for sharp definitions of the mathematical model and, if successful, then constructs even a theory. Then the mathematician forgets about the empirical foundation of the theory and thinks one has to rederive the empirical foundation from the theory.

In QT it's even worse, because there not only physicists and mathematicians are involved but also philosophers, making the quite complicated subject even more complicated by using a completely different language than the two languages already introduced by the physicists and mathematicians.

In other words: For a physicist QT is a probabilistic description for phenomena which are probabilistic to begin with, and the phenomena (observables and states) are defined empirically. There's nothing to be derived from the formalism, because the formalism is based on the empirically defined basic notions of observables (a measurement procedure) and states (a preparation procedure/observation of an initial condition).

For a mathematician there's an abstract formalism, from which the phenomena have to be derived, i.e., if it comes to the measurement problem the problem consists in the question, how there can be definite outcomes in a measurement given the "QT universe" only, where only probabilities exist. Usually one can settle the issue by using statistical arguments (though that seems not to be always the case).

For philosophers the problems become even more problematic, because there's some vague idea about "reality". The notion of "reality" differs from philosopher to philosopher, and you cannot make heads and tail of it. Then you discuss over thousands of pages problems that are not even well defined in either a physicist's nor a mathematician's way. You need a genius like Bell who can make out of philosophical unsharp problems a sound and solid scientific question, approachable by the scientific method of objective and quantitative observation by first finding a clear definition of "reality" or "realism" and finding a way to disprove either "local realistic hidden-variable theories" or "quantum theory". The result is known, and it's "quantum theory" that survived all these tests, and it's quantum theory in the clear and simple "minimal interpretation" just taking the standard textbook definitions of state and observables as the physical theory and accept that from a physicist's point of view nature is on a fundamental level behaving randomly and not deterministically.

 

[ftr]

Experience shows that we find certain patterns, which we call natural laws, and from this we can try to make mathematical models or theories. The quantities/observables and states are defined empirically from the phenomena and mathematical descriptions use empirically useful primitive notions.

I think this was more true in the past but for more than 100 years with mathematical sophistication physicists tend to deduce models based on specific and general understanding of concepts like what could work and try many until some prediction is obtained or matched by known observation (experiment play a kind secondary but important part). Schrodinger equation is a perfect example, not to mention QG, string, Unified ...etc.

 

[Elias1960]

For a physicist there are quantifiable and thus measurable phenomena, to begin with. Experience shows that we find certain patterns, which we call natural laws, and from this we can try to make mathematical models or theories. The quantities/observables and states are defined empirically from the phenomena and mathematical descriptions use empirically useful primitive notions. The mathematician of course tries to make these primitive notions a system of axioms to seek for sharp definitions of the mathematical model and, if successful, then constructs even a theory.

No. It is the theory that defines what is observable. And theories are free inventions of the human mind. They are empirical theories if one can make empirical predictions based on them. And in this case one can test if these predictions are correct. If not, the theory is falsified.

What you describe sounds like a naive version of empiricism. Empiricism is dead, as dead as possible for a philosophical theory, since Popper's Logic of Scientific Discovery.

In other words: For a physicist QT is a probabilistic description for phenomena which are probabilistic to begin with, and the phenomena (observables and states) are defined empirically.

Don't forget that "the theory that defines what is observable" is what Einstein told Heisenberg, and this had some influence on Heisenberg, helping him to create quantum theory.

 

[A. Neumaier]

theories are free inventions of the human mind.

But good theories aren't. They are heavily constrained discoveries of the human mind, and cannot be falsified in their domain of validity.

 

[Elias1960]

But good theories aren't. They are heavily constrained discoveries of the human mind, and cannot be falsified in their domain of validity.

There is, of course, the obvious restriction that the resulting predictions have to fit reality. But this does not tell you much about that theory. From the point of view of philosophy, it was important to reject the empiricist notion that the theories are somehow derived from observation. There is no such possibility of derivation. Usually no domain of validity is known a priori, at the moment of the invention of some theory. And if it can be falsified or not is nothing the scientist is able to know at that moment too.

 

[A. Neumaier]

There is, of course, the obvious restriction that the resulting predictions have to fit reality. But this does not tell you much about that theory. From the point of view of philosophy, it was important to reject the empiricist notion that the theories are somehow derived from observation. There is no such possibility of derivation. Usually no domain of validity is known a priori, at the moment of the invention of some theory. And if it can be falsified or not is nothing the scientist is able to know at that moment too.

This does not affect the validity of my statement.It simply takes some time before a theory can be known to be good.

 

[bhobba]

It is not so innocent as it may look. Some physicists interpret the 2nd Newton law not as a law but as a definition of force, defined as $F\equiv ma$.

True. How its resolved I could not figure out until John Baez explained it to me. I have mentioned it in passing on ocassion, but really it needs a thread of its own which I will create. I will give the final answer now however. The true basis of Newtonian mechanics is QM.

Thanks
Bill

 

[Demystifier]

To my knowledge in QM the standard definition of "interpretation" is as described in Wikipedia:

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

It's fine, but my objection is that there is no sharp borderline between "interpretational" and "non-interpretational" aspects of a theory. For instance, if we accept the wiki definition that interpretations are about reality, then even a shut-up-and-calculate approach to measurable quantities can be considered an "interpretation", because it is about measurable quantities which are real.

 

[Demystifier]

True. How its resolved I could not figure out until John Baez explained it to me. I have mentioned it in passing on ocassion, but really it needs a thread of its own which I will create.

If you will create it in the classical physics forum, please make a note/link here!

 

[A. Neumaier]

even a shut-up-and-calculate approach to measurable quantities can be considered an "interpretation", because it is about measurable quantities which are real.

No, it is about calculations only. The interpretation that (and how) the results of the calculations refer to experiments is already outside strict shut-up-and-calculate (unless one includes in the latter Born's rule in one of its interpretations).

 

[Demystifier]

No, it is about calculations only.

No it isn't, there is no paper (published in a peer-reviewed journal) that is only about calculations. If you think there is, show me an example and I will explain you why this paper is not only about calculations. If someone tried to publish a paper which is only about calculations, the reviewer would object that the paper misses motivation and meaning of those calculations.

 

[zonde]

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.

You are missing one point. Chronology is important. Predictions have to be made before factual observations. That's because people are very good at cheating themselves. All the reasoning done after the facts are known are very error prone and you have to be much more careful about checking the soundness of such reasoning. So it stands to reason to give such after the fact reasoning a different name.

 

[A. Neumaier]

No it isn't, there is no paper (published in a peer-reviewed journal) that is only about calculations. If you think there is, show me an example and I will explain you why this paper is not only about calculations. If someone tried to publish a paper which is only about calculations, the reviewer would object that the paper misses motivation and meaning of those calculations.

The papers always combine shut-up-and-calculate with non-shut-up heuristics involving their personal interpretation appropriate to the particular application. The resulting freedom is the main reason why shut-up-and-calculate is so successful in practice. It is also the reason why the Copenhagen interpretation (which was so vague in its meaning that it could be adapted freely) was sufficient for 30 years (and for many is still sufficient now).

 

[vanhees71]

No. It is the theory that defines what is observable. And theories are free inventions of the human mind. They are empirical theories if one can make empirical predictions based on them. And in this case one can test if these predictions are correct. If not, the theory is falsified.

What you describe sounds like a naive version of empiricism. Empiricism is dead, as dead as possible for a philosophical theory, since Popper's Logic of Scientific Discovery.

Don't forget that "the theory that defines what is observable" is what Einstein told Heisenberg, and this had some influence on Heisenberg, helping him to create quantum theory.

I know this quote of Einstein's by Heisenberg. Nevertheless, history shows that with such a scholastic approach almost never good physics comes out. You need the, admittedly vague, notions of observations and experiments first to create physically successful theories. A really aesthetic argument for a theoretical physicist is not if there's a free invention (e.g., Bohr's model of the atom) but if there's almost no freedom given the empirical foundations (e.g., Einstein's GR, which is almost inevitable given the strong equivalence principle and relativistic spacetime structure).

 

[Demystifier]

The papers always combine shut-up-and-calculate with non-shut-up heuristics involving their personal interpretation appropriate to the particular application. The resulting freedom is the main reason why shut-up-and-calculate is so successful in practice. It is also the reason why the Copenhagen interpretation (which was so vague in its meaning that it could be adapted freely) was sufficient for 30 years (and for many is still sufficient now).

Yes, exactly. That's why I insist that it is impossible to sharply distinguish "interpretational" research from "non-interpretational" one.

 

[A. Neumaier]

Yes, exactly. That's why I insist that it is impossible to sharply distinguish "interpretational" research from "non-interpretational" one.

In papers, on can easily distinguish this by looking at what is calculated and what is reasoned informally. Research is of course an umbrella for both.

 

[Demystifier]

In papers, on can easily distinguish this by looking at what is calculated and what is reasoned informally. Research is of course an umbrella for both.

I am talking about a paper as a whole, one cannot say this paper is interpretational and that paper isn't. Each paper contains elements of both.

 

[Dr. Courtney]

They are two equivalent mathematical frameworks which can be derived from one another through mathematical operations. Why should we use a definition of “interpretation” where a straight mathematical operation generates a new interpretation? Every line of every theorem or homework problem would then be using a unique interpretation. Is that what you want the word to mean?

I don't think the interpretation is in the mathematical operations, but rather in assertions regarding which quantities are more fundamental, especially which quantities that are not directly measured.

It is not so innocent as it may look. Some physicists interpret the 2nd Newton law not as a law but as a definition of force, defined as $F\equiv ma$.

The challenge with F = ma is that it can be viewed either as the definition of force or the definition of inertial mass. Of course, it cannot be the definition of both at the same time. Thus there is interpretation. Viewing F = ma as the definition of force requires some other definition of inertial mass - or a tacit understanding of some other fact such as inertial mass being the same as gravitational mass.

But good theories aren't. They are heavily constrained discoveries of the human mind, and cannot be falsified in their domain of validity.

I see this as somewhat circular, as history shows that that there is often not a clear distinction between falsification and narrowing of the domain of a theory's validity.

It's fine, but my objection is that there is no sharp borderline between "interpretational" and "non-interpretational" aspects of a theory. For instance, if we accept the wiki definition that interpretations are about reality, then even a shut-up-and-calculate approach to measurable quantities can be considered an "interpretation", because it is about measurable quantities which are real.

And which measurable quantities are fundamental. The thought often seems to be that quantities that are more directly measured (position, time) are somehow calculated from more direct measurements (energy, velocity). Of course, other viewpoints see energy as more fundamental than force.

 

[Elias1960]

This does not affect the validity of my statement.It simply takes some time before a theory can be known to be good.

But once we cannot know initially what is good, it fails to be an objection against the "free invention of the human mind". (Of course, the scientist himself will compare his invention with known empirical data, before he writes an article proposing it. But even this is a process, and even here the invention comes first, the check and rejection of the many false "good ideas" comes later.)

 

[Elias1960]

You need the, admittedly vague, notions of observations and experiments first to create physically successful theories. A really aesthetic argument for a theoretical physicist is not if there's a free invention (e.g., Bohr's model of the atom) but if there's almost no freedom given the empirical foundations (e.g., Einstein's GR, which is almost inevitable given the strong equivalence principle and relativistic spacetime structure).

Except that the equivalence principle itself was a free invention of Einstein's mind, one he was very happy that he has had it. And the relativistic spacetime structure is a metaphysical idea that has no relation to experiment at all, given that viable interpretations with absolute time and without any spacetime as a structure exist.

Which free inventions are valuable and which deserve to be forgotten is another question, and the great scientists are those who successfully throw away their bad inventions and develop their good inventions.

 

[Dale]

It's fine, but my objection is that there is no sharp borderline between "interpretational" and "non-interpretational" aspects of a theory. For instance, if we accept the wiki definition that interpretations are about reality, then even a shut-up-and-calculate approach to measurable quantities can be considered an "interpretation", because it is about measurable quantities which are real.

I am not sure what you think is un-sharp here. Shut-up-and-calculate is also (more correctly but less amusingly) known as the minimal interpretation, which as the name suggests is an interpretation.

A theory consists of one or more equivalent mathematical frameworks together with a minimal interpretation. That is what is necessary for using the scientific method, the mathematical framework is used to relate the various quantities within the theory and the minimal interpretation is used to link those quantities to experimental outcomes and predictions. Any interpretation going beyond the minimal interpretation can be removed or exchanged without changing the theory because any additional interpretation is not subject to investigation by the scientific method, but changing the minimal interpretation would change the theory since it would change the link between experiment and the mathematical quantities.

I suppose that there may be some people who argue that the minimal interpretation should not be considered an interpretation. Perhaps that is the concern you have and the reason you feel the distinction is not sharp. It seems pretty sharp to me.

 

[zonde]

(e.g., Einstein's GR, which is almost inevitable given the strong equivalence principle and relativistic spacetime structure)

I found this link interesting: A Peek into Einstein's Zurich Notebook
It does not seem from this that Einstein's path to GR was quite straightforward, but as most of mathematical details are lost on me I might be missing some possible insights.

 

[A. Neumaier]

There is, of course, the obvious restriction that the resulting predictions have to fit reality. But this does not tell you much about that theory.

It tells you whether it is a good theory. A good theory is one that has a known domain in which it is valid.
For example, we have lots of theories about quantum gravity but no good one.

Theories in general may be free inventions of the human mind, but good theories are not inventions; they are discoveries.

 

[bhobba]

If you will create it in the classical physics forum, please make a note/link here!

Good idea. About to do it now. It will be a little different to my other posts in that I will try a bit of a socratic approach. I will start with the questions posed in a quite old book on mechanics, I read long long ago, it never answered, then see what people say and hopefully be led to what John Baez explained to me.

Here is the link:
https://www.physicsforums.com/threads/what-do-Newtons-laws-say-when-carefully-analysed.979739/
Thanks
Bill

 

[Demystifier]

I am not sure what you think is un-sharp here. Shut-up-and-calculate is also (more correctly but less amusingly) known as the minimal interpretation, which as the name suggests is an interpretation.

So if even the minimal shut-up-calculate approach is an interpretation, it shows that it is impossible to do quantum physics without dealing with some interpretation. In other words, any work on quantum physics is an interpretation to a certain extent. So it doesn't make sense to accuse someone for dealing with interpretations instead of dealing with pure (quantum) physics.