Against "interpretation" - Comments

[Demystifier]

Greg Bernhardt submitted a new blog post

Against "interpretation"

Continue reading the Original Blog Post.

 

[PeterDonis]

Interesting viewpoint! I tend to dislike talk about "interpretations" as well, but I'm not sure if it's for the same reason, so let me briefly explain my reason.

In the article you give the example of two theories, T1 and T2, that both make the same experimental predictions. That means that it is not possible to decide by experiment which of the two theories is correct (or "more correct", or "better", or whatever comparative term you want to use). So any preference that someone has for one theory over the other can only be based on subjective judgments of one sort or another. And disagreements about such preferences can never be resolved (which is why PF threads on such topics tend to go on and on until one of the Mentors gets fed up enough to close the thread).

To me, the word "interpretation" (particularly when talking about QM) is a signal that the above situation exists, i.e., that whatever disagreement is being discussed can't be resolved, because the two theories (or "interpretations") being discussed both make the same experimental predictions. And since such a disagreement can't be resolved, I see very limited value, at best, in discussing it.

In the particular case of QM, at least, there is another aspect as well. Interpretations of QM not only all make the same experimental predictions, they do so via provably mathematically equivalent machinery. So the rationale for calling them different theories, as opposed to different interpretations of the same theory, is weaker than it would be if the different interpretations used mathematically distinct machinery, that just happened to result in the same predictions for experiments.

 

[fresh_42]

I follow your argumentation and appreciate its clarity. But don't you just merge the two terms and therewith shift all problems the term interpretation is charged with into the now new definition of theory? My impression is, that you merely shifted the problem of inconsistency into the unregarded territory of theory and model. The term theory is to me a very unfortunate one, not the least as it is regularly in conflict with what commonly is meant by it, namely a hypothesis. I admit that the term model may partly be in conflict with the specific meaning it has in logic, but that shouldn't be a problem here.

Thus my suggestion to solve the discrepancies wouldn't be the merger of theory and interpretation, but the merger of theory and model. I think this is what physicists usually mean: a theory - or model - is a mathematical framework to describe the experimental results, including possible predictions. On the other hand, an interpretation is merely an informal description of named theory / model to describe the mathematical framework in common language and by the frequent use of aphorisms and metaphors. In this sense, T1 and T2 are different models, which either coincide, i.e. are different but equivalent sets of mathematical language, or they make distinguishable predictions. Interpretations of T1 and T2, however, may differ a lot, as they were only descriptions a lecturer uses to explain the models behind them.

So my understanding is, that T1 (Heisenberg) and T2 (Schrödinger) are two different models of the same physics, and as such equivalent theories or models, whereas Kopenhagen and MWI are actually interpretations, namely metaphors to visualize the equations. This is in my opinion closer to the actual use of the terminology and doesn't need the merger theory with interpretation, the more as theory and model has already been merged. Furthermore, it doesn't create the next problem to explain why interpretation and model will be the same, nor does it leave a vacancy, namely: what are verbal descriptions of mathematical frameworks be called?

 

[A. Neumaier]

So you think that Copenhagen and MWI are two different theories that happen to share 99.9% of the theoretical part and disagree only about 0.1% of interpretation? Then quantum mechanics would be a collection of 20 or so theories that differ only marginally?

 

[Klystron]

Borrowing from military jargon, the professionals -- scientists, engineers, mathematicians, and their students -- work to understand and utilize theory and models. Civilians; depending on their training, ability, and access to correct reliable information; are often satisfied with various interpretations.

As an example consider the science writer James Gleick and his still popular interpretation of chaos theory Chaos: Making a New Science. I first read his book back in the 1970's in order to discuss it with my father, a trained chemist and electrical engineer but also a fan of popular science. Gleick's writing led to productive conversations. We even drove to Half-Moon Bay to observe the "fractal coastline" (and a neat sunset). Despite using aspects of chaos theory in my work, I never referenced Gleick's books, instead using math and science textbooks for actual applications.

[Edit: Change "electrical" to electronics engineer at ESL Sylvania as a project manager for the USAF.]

Accurate factual interpretations perhaps with the math explained rather than read as-is, may be a fair method for civilians to understand science. Students and teachers should be held to the more rigorous standard of understanding theory, the underlying models, and the limits of corroborating data.

 

[bhobba]

I think one the issues regarding interpretations is to consider them complete in some sense. Copenhagen fell into that trap eg the state is a complete description of the quantum system. I have posted it before, but I consider the following debate between Dirac and Heisenberg instructive:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf

Personally I am with Dirac on this one. I do not think QM is complete - it will slowly and gradually be superseded and in that vein you can look on interpretations as attempts to understand what direction the next step may take us.

Already we have no-go theorems putting constraints on acceptable interpretations that help us see in what direction research may lead us.

Thanks
Bill

 

[hagopbul]

T1 &T2 are approximations just like classical mechanics to special relativity

 

[ade]

Demystifier,

The admirable deed is that you walked all the way to the border!
When you manage to cross it, you will see wonderful things that reasoning cannot even imagine!

Keep it on!

 

[Peter Morgan]

Insofar as a given theory is some specific mathematical construction from some set of axioms and all its mathematical consequences, and all equivalent constructions from different axioms, different interpretations of that one theory (1) put different emphasis on one axiomatic construction or another, all isomorphic to each other, and/or (2) give a different relationship between elements of the theory and whatever experimental raw data there may be. I like Lakatos's term for (2), bridge principles, which, being between things mathematical and things in the world are neither of mathematics nor of the world. I think it's the bridge principal concept that your polemic misses. Mathematics is unworldly and not everything is mathematics: we have to learn and teach and experience and come to an intuition of the connection between mathematics and the world.
I suppose I'm saying that theory/interpretation/world is just a variant of the map/how to grok the map/territory problem, over which much ink has been spilt, so battle lines will have to be drawn.

 

[atyy]

Should Wilson's interpretation of renormalization be considered theory or interpretation?

 

[bhobba]

Should Wilson's interpretation of renormalization be considered theory or interpretation?

I would call it an approach. My understanding is its equivalent to say dimensional regularization - but others that know more about it than me may correct me on that.

Thanks
Bill

 

[martinbn]

What is an example of T1 and T2?

 

[Demystifier]

So my understanding is, that T1 (Heisenberg) and T2 (Schrödinger) are two different models of the same physics, and as such equivalent theories or models, whereas Kopenhagen and MWI are actually interpretations, namely metaphors to visualize the equations.

Then what about Bohmian mechanics? Is it a T3, or is it just a metaphor?

 

[Demystifier]

What is an example of T1 and T2?

There are many examples, but my favored one is this: T1 = standard textbook QM, T2 = Bohmian mechanics.

 

[atyy]

Traditionally, an interpretation is a solution of the measurement problem:

However, another meaning of interpretation is simply the meaning physical or operational meaning assigned to mathematical operations.

A third meaning of interpretation is the one that is disfavoured in the Insight of the OP.

Thus the Copenhagen Interpretation is the only valid interpretation (since BM is not an interpretation, but a different theory) of QM. However, the Copenhagen Interpretation is not a valid interpretation in the sense of being a possible solution of the measurement problem (it is basically the poster boy for having a measurement problem). Bohmian Mechanics is not an interpretation, but a different theory. However, since it is the only currently known possible solution of the measurement problem for a sufficiently broad domain of QM, BM is the only valid interpretation of QM even though it is a different theory.

 

[martinbn]

There are many examples, but my favored one is this: T1 = standard textbook QM, T2 = Bohmian mechanics.

I thought that BM gives different predictions in some cases?

 

[Demystifier]

I thought that BM gives different predictions in some cases?

Some versions of BM do, but the standard "minimal" version doesn't.

 

[Demystifier]

Should Wilson's interpretation of renormalization be considered theory or interpretation?

If only more Bohmians understood the depth and importance of this question ...

 

[anorlunda]

And disagreements about such preferences can never be resolved (which is why PF threads on such topics tend to go on and on until one of the Mentors gets fed up enough to close the thread).

That raises the question of why we allow public debate of interpretations on PF. Or why respected textbooks include chapters on interpretations.

If it was just a case of competing equivalent models, as @fresh_42 pointed out, then there is nothing to debate. The wise analyst keeps all possible models in his toolkit ready to use when advantageous. The value of a model is its utility.

Personally I am with Dirac on this one. I do not think QM is complete - it will slowly and gradually be superseded and in that vein you can look on interpretations as attempts to understand what direction the next step may take us.

That may be the answer to why allow it and why we support continued research. An interpretation might be described as a theory extension wannabe. Researchers hope to find a case where T₁ and T₂ predict different outcomes, so that experiment may prove one of them useful and the other not useful. But such hope should not be eternal. At some point, the rational thing to do is to declare the search futile, and deploy our resources elsewhere.

 

[Dr. Courtney]

Well articulated Insight. Thanks!

 

[martinbn]

Some versions of BM do, but the standard "minimal" version doesn't.

Can you give another example?

 

[Demystifier]

Can you give another example?

T1 = "Copenhagen" with collapse induced by measurement, T2 = many worlds

 

[martinbn]

T1 = "Copenhagen" with collapse induced by measurement, T2 = many worlds

I expected a non quantum example. So, you have in mind only QM interpretations, and you think they should be called theories. My opinion is that they are correctly called interpretations. The all start with QM or at least the core of QM, then add a bit more, yet don't get new predictions. To me that is not a different theory. To be a different theory it should build on something else, it should be possible to get to that theory even if you have never seen QM. And that is not the case of the interpretations.

 

[Auto-Didact]

There is another complication not yet explicitly mentioned, namely the role of the underlying mathematics from the viewpoint of mathematical physics: as an object in the theory or as a tool used to calculate objects in the theory. Key mathematical distinctions, unconventional among physicists, may then be trivialized prematurely. Here is a common example in physical theory.

A theory of some phenomenon most naturally formulated explicitly in terms of complex analysis may have very non-trivial conceptual differences (e.g. geometrically, topologically, algebraically, etc) from a less complete theory of the same phenomenon which was tentatively first formulated purely in terms of the way more familiar tools of real analysis.

For example, most theories start off describing the phenomenon in question in some kind of simplified and often linearized setting for simplicity; however when unsimplified to more general, complicated settings and/or fully formulated in terms of some general curved manifold, the theory then actually turns out to be mathematically very distinct from the simplified real analytic theory in some extremely non-trivial way.

This non-trivial difference may however not be directly visible from the surface, i.e. neither theoretically by textbook presentations and analytic calculations (especially when ad hoc linearization tools have become available widespread and conventional), nor experimentally from direct verification of the most straightforward extremely trivial laboratory setting in comparison with the natural settings of the phenomenon.

The problem of simplification and convention then multiplies enormously once the theoreticians - having become accustomed to the simplistic formulation of the theory together with their arbitrary ad hoc toolkit for handling difficulties - then end up not taking the underlying complex analytic structure seriously, which directly predicts the complications of the phenomenon.

Hereby a theory can become stuck in being viewed by both theoretician and experimentalists in a highly simplified fashion, with the conventional ad hoc simplification tools - both theoretically and experimentally - actually carefully masking the very departure of the simplified theory to the more general setting.

 

[atyy]

How about
T1 Weierstrassian analysis
T2 Non-standard analysis
?

 

[fresh_42]

How about
T1 Weierstrassian analysis
T2 Non-standard analysis
?

Two (mostly equivalent) theories models, no interpretation anywhere.

 

[Auto-Didact]

How about
T1 Frequentist statistics
T2 Bayesian statistics
?

To be a different theory it should build on something else, it should be possible to get to that theory even if you have never seen QM. And that is not the case of the interpretations.

To be fair, mathematically there actually are several ways to derive BM without ever having seen or even taken QM (of course, it helps to be able to recognize the correct derivation if one has ever seen e.g. the SE).

 

[atyy]

Two (mostly equivalent) theories models, no interpretation anywhere.

Are you using "model" in the sense of "standard and non standard models of arithmetic"?

 

[fresh_42]

Are you using "model" in the sense of "standard and non standard models of arithmetic"?

I use model as synonym for a mathematical calculus, in the sense of framework. I do not like theory, as it has far too many connotations and in the end it's only the calculations we're interested in, hence the term calculus. Standard and non standard are no mathematical categories, they already include an evaluation. Either a calculus is without contradictions, or at least those can be resolved as we are forced to do since we know that Hilbert's second is undecidable, or a calculus is none because it's useless.

 

[atyy]

I use model as synonym for a mathematical calculus, in the sense of framework. I do not like theory, as it has far too many connotations and in the end it's only the calculations we're interested in, hence the term calculus. Standard and non standard are no mathematical categories, they already include an evaluation. Either a calculus is without contradictions, or at least those can be resolved as we are forced to do since we know that Hilbert's second is undecidable, or a calculus is none because it's useless.

I guess the normal terminology in English is that the theory is Peano Arithmetic and the models are either standard or nonstandard.