# Insights Against "interpretation" - Comments

#### A. Neumaier

Exactly. You have to go beyond the mathematical framework and map the experimental results to the labels.
But this mapping is not part of the theory; it is done by the experimenter who wants to use the theory. Each time someone finds a new way of testing the theory, the mapping changes! In your case, there are many possibilities to do the mapping, hence a multitude of interpretations.

The part of the context that gives the mapping from the framework to experiment is part of the theory. This is precisely the point where your misuse of the term “theory” is causing problems.
Then please expand your theory fragment (or another one of your choice) to a complete theory that we can discuss.

even someone who is openly antagonistic to the standard definition admits that it is in fact the standard definition.
No. he does not even give it the status of a definition - he admits only that it is the standard sketch, and emphasizes this weak status!

But as far as I am aware the standard sketch remains the standard meaning of the terms and the scientific community has not adopted his “better informed” opinion.
You are indeed not aware of the state of the art! Not only Suppes, your only witness among the philosophers of science, but also Wikipedia, your only other authoritative source, testify against you:

Wikipedia said:
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, using accepted protocols of observation, measurement, and evaluation of results. [...] theory [...] describes an explanation that has been tested and widely accepted as valid.
It explicitly separates scientific theory (''an explanation of an aspect of the natural world"") and the relation to experiment (''the scientific method'').

Wikipedia cites other authorities to support its definition; none of them requires a map between theory and experiment as part of the theory:
Stephen Jay Gould said:
Theories are structures of ideas that explain and interpret facts
The United States National Academy of Sciences said:
The formal scientific definition of theory is quite different from the everyday meaning of the word. It refers to a comprehensive explanation of some aspect of nature that is supported by a vast body of evidence.
The American Association for the Advancement of Science said:
A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment.
Wikipedia said:
The logical positivists thought of scientific theories as statements in a formal language.
Wikipedia said:
The semantic view of theories, which identifies scientific theories with models rather than propositions, has replaced the received view as the dominant position in theory formulation in the philosophy of science. A model is a logical framework [...] One can use language to describe a model; however, the theory is the model (or a collection of similar models), and not the description of the model. A model of the solar system, for example, might consist of abstract objects that represent the sun and the planets. These objects have associated properties, e.g., positions, velocities, and masses.
This is exactly my view, except that they have ''logical framework'' where you had suggested the term ''mathematical framework''!
Wikipedia said:
Engineering practice makes a distinction between "mathematical models" and "physical models"
Wikipedia said:
In physics, the term theory is generally used for a mathematical framework
Maybe our dispute comes from the fact that you are an engineer and I am a mathematician and physicist!
But note that this discussion is in a physics forum, not an engineering forum.

#### PeterDonis

Mentor
Each time someone finds a new way of testing the theory, the mapping changes!
It might be helpful if you would give a concrete example. Perhaps this would qualify as one: the "theory" (for your meaning of that term) is the standard quantum theory of a qubit. Two different possible "mappings" are: interpreting the qubit theory as describing the spin of an electron in a Stern-Gerlach experiment; interpreting the qubit theory as describing the polarization of a photon passing through a beam splitter. Is that the sort of thing you have in mind?

If it is, then I think you are using the term "interpretation" differently from the way it is used when discussing the foundations of QM (which is the meaning of "interpretation" that this thread is supposed to be discussing). QM "interpretation" has nothing to do with which particular experiment you are analyzing. It has to do with what kind of story you tell about what is happening in the experiment. In the above example, say we pick the first "interpretation" in your sense: we interpret the quantum theory of the qubit as describing the spin of an electron. Then we still have different possible QM interpretations: a collapse interpretation says the spin of the electron collapses into an eigenstate when it passes through the Stern-Gerlach device; the many worlds interpretation says the electron's spin gets entangled with its momentum so it ends up in a superposition of two states, one with "up" spin coming out of the device in one direction, the other with "down" spin coming out of the device in a different direction. But there is no way to tell experimentally which of these "interpretations" is right, and these "interpretations" have nothing to do with how you match up the math of the standard quantum theory of a qubit with experimental observations.

#### A. Neumaier

It might be helpful if you would give a concrete example.
I already gave in #153 and #167 the example of the axioms for natural numbers (plus a little finite set theory for the Cartesian product), and in #151 and #173 that of projective planes. What they demonstrate is the key to a correct understanding. (Though it doesn't quite answer your query - please be patient!)

Let me give a complete example inspired by Onaep, a little known Russian contemporary of François Viète (who invented the notion of variables).

Onaep said:
I is a rebmun. If Z is a rebmun then ZI is a rebmun. If ZI=YI then Z=Y. Never ZI=I. Every rebmun is generated in this way.
In 1600, Dnikeded, an ambitious student of math, sits in Prof. Onaep's class, being told that he is a capacity in the field of applied algebra. He is reading the above (as part of one of Onaep's exercises) for the first time and has not the slightest idea what he is talking about. He never heard of anything called rebmun. Determined to figure out the meaning and being familiar with Viete's concept of variables, he plays with the statements given. Well, at least he knows that I is a rebmun. Setting Z=I he discovers that II is a rebmun. Setting Z=II he discovers that III is a rebmun. Setting Z=III he discovers that IIII is a rebmun. Setting Z=IIII he discovers that IIIII is a rebmun. This reminds him of counting. Each new rebmun is obtained by adding an I to the previous rebmun. The process goes on for ever.... Remembering what he had learnt already about algebra, Dnikeded noticed that the rebmuns could be interpreted in terms of stuff he was familiar with - numbers. If he identified I with 1 then he could equate II with 2, III with 3, IIII with 4, IIIII with 5, etc. ''Ah, this is a variant of the way we count the number of beers in the pub,'' he thought, ''except that each 5th bar would be drawn vertically, a minor issue that doesn't really change things.'' But well, there were more properties: If ZI=YI then Z=Y. ''True - if my friend and I both order a beer and then have the same number of beers, we must have had the same number of beers before. Thus Onaeps theory is predictive, and things come out correctly. Let me try the next item, never ZI=I; can I falsify my interpretation?'' He tries and finds no problem with it - I is too short to be of the form ZI. Dnikeded is left with the final statement to be figured out. He thinks about what he can generate so far: 1,2,3,4,5,6,7,8,9,10,11,... a never ending list of numbers. But neither 0 nor fractions like 2/3. Also no negative numbers. Suddenly everything makes sense. ''Ah, I finally understand. rebmuns are nothing else than the numbers I have been familiar with since childhood, before I got interested in more advanced number theory!''

The mapping from theory to reality/experiment that Dale was conjuring up as belonging to the theory appeared out of nowhere!

The map is not provided by the theory, but it exists for any theory that deserves to be called scientific. The map is created/discovered (and has to be recreated/rediscovered by each individual) in the process of understanding the meaning of a scientific theory! Initially the theory is just a formal system, but after we understand it it is related to our own experience. When we see that it matches experience and satisfies some empirical tests, we know that we really understood! As all students of physics know, this may be quite some time after we heard the details of the theory and checked the logical consistency of the formal stuff we try to understand. We can solve the exercises long before we have a good feeling for the theory, i.e., a good map between theory and experience.

This is the generic situation of a theory without an interpretation problem - the interpretation is essentially forced upon us by the structure of the theory, no matter how things are named. The naming only simplifies the process of understanding.

But wait...

When Dnikeded compared his solution of the exercise with that of his friend Rotnac, he noticed that the latter had another way of interpreting Onaep. He had also played with the statements in Onaep's riddle and associated it with marbles in his pocket.He linked changing Z to ZI to putting a new marble into the pocket. Starting with the empty pocket that contained no marble, he got the correspondence I=0, II=1,III=2,III=3, etc.. Both Dnikeded and Rotnac tried to figure out who made an error and whose interpretation was defective. But they couldn't find one. So they went to Onaep, asking for his advice. Onaep declared both interpretations to be valid.

Indeed, the modern concept of natural numbers (based on the Peano axioms) exists in two forms, and the two different traditions have two different interpretations, depending on whether they call 0 a natural numbers (e.g., friends of C++ and set theorists) or whether they don't (e.g., friends of Matlab and all before Cantor). I belong to the second category and believe that 0 is an unnatural number since I have never seen someone count 0,1,2,3..., and it took ages to discover 0 - and many more centuries to declare it natural.

The two interpretations are related by the fact that $x\to x+1$ is an isomorphism between the two. (As Peter Donis mentioned in his reply #179, one could similar start with any number $a$ and count from there, corresponding to an isomorphism $x\to x+a$.) This is analogous to the interpretation of classical mechanics, which unique only up to the choice of an orthonormal coordinate system. In the latter case, a rigid motion provides the necessary isomorphism.

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#### PeterDonis

Mentor
I already gave in #153 and #167 the example of the axioms for natural numbers (plus a little finite set theory for the Cartesian product), and in #151 and #173 that of projective planes.
I was talking about an example using QM, since interpretations of QM is the topic of this thread.

the interpretation is essentially forced upon us by the structure of the theory
Except that, as you say, there are two interpretations that are consistent with the theory (the one starting with 0, and the one starting with 1).

And even that doesn't exhaust the possibilities: you can pick any integer (positive, negative, or zero) you like, and adopt it as the starting "natural number", and you will satisfy all of the axioms. In other words, there are an infinite number of possible isomorphisms to some "canonical" set of natural numbers (say the ones starting with 1, since those are the ones you say you prefer), each of the form $x \rightarrow x + a$, with $a$ being any integer.

In other words, while it is certainly possible to discover a mapping between a mathematical model and experience in the process of understanding the mathematical model, there is no guarantee that the mapping you discover is the only mapping. So people both using the same mathematical model can still end up making different predictions, if they have not taken steps to ensure that they're both using the same mapping as well. For example, if you use 1-based counting and I use 0-based counting, we're likely to get confused trying to match up our counts if we don't realize the difference and make appropriate adjustments.

With all that said, I still come back to what I said in my previous post: none of this has anything to do with interpretations of QM, because different interpretations of QM all agree about which mapping between the mathematical model and experiment to use. (This mapping still depends on the specific experiment: in my previous post I gave the example of the same qubit mathematical model applying to both electron spins and photon polarizations.) The different QM interpretations only disagree about what story to tell about "what is going on behind the scenes", so to speak; but those stories have nothing to do with matching up the mathematical model to experiment. So I don't see how any of what's been said about matching up the mathematical model to experiment/experience has anything to do with QM interpretations, which is the topic of this thread.

#### A. Neumaier

And even that doesn't exhaust the possibilities: you can pick any integer (positive, negative, or zero) you like, and adopt it as the starting "natural number", and you will satisfy all of the axioms. In other words, there are an infinite number of possible isomorphisms to some "canonical" set of natural numbers (say the ones starting with 1, since those are the ones you say you prefer), each of the form $x \rightarrow x + a$, with $a$ being any integer.

In other words, while it is certainly possible to discover a mapping between a mathematical model and experience in the process of understanding the mathematical model, there is no guarantee that the mapping you discover is the only mapping. So people both using the same mathematical model can still end up making different predictions, if they have not taken steps to ensure that they're both using the same mapping as well. For example, if you use 1-based counting and I use 0-based counting, we're likely to get confused trying to match up our counts if we don't realize the difference and make appropriate adjustments.
Yes, and as I had said in my last post, exactly the same happens in classical mechanics, which can be mapped only up to a rigid motion.

With all that said, I still come back to what I said in my previous post: none of this has anything to do with interpretations of QM, because different interpretations of QM all agree about which mapping between the mathematical model and experiment to use.
No, they don't. Please give me a reference to an online article or well-known textbook that gives this unique ''mapping between the mathematical model and experiment''. And I'll show (like Suppes did) that it says almost nothing about real experiments. Theoretical sources only say something about relations to abstract buzzwords like ''observable'' and ''measure'' about whose precise meaning the interpretations (and the experimental practice) widely differ. There are many thousands of experiments to be covered, the term ''experiment'' in your comment is something very theoretical....

It might be helpful if you would give a concrete example. Perhaps this would qualify as one: the "theory" (for your meaning of that term) is the standard quantum theory of a qubit. Two different possible "mappings" are: interpreting the qubit theory as describing the spin of an electron in a Stern-Gerlach experiment; interpreting the qubit theory as describing the polarization of a photon passing through a beam splitter. Is that the sort of thing you have in mind?
Well this is a meta setting in which the real world is replaced by a theoretical world, in which the qubit has two different interpretations. No, this was not what I had meant.

In your context, consider the qubit first discussed by Weyl 1927 in the context of a Stern-Gerlach-like experiment. [H. Weyl, Quantenmechanik und Gruppentheorie, Z. Phys. 46 (1927), 1-46.] The title of the first part is ''The meaning of the repesentation of physical quantities through Hermitian operators'' (''Bedeutung der Repräsentation von physiksalischen Größen durch Hermitesche Formen''). It discusses among others the paradox that the angular momentum in the three coordinate axes can only take the values $\pm 1$ (in units of $\hbar/2$) but the angular momentum in other directions, too - which is inconsistent with the algebra. This shows the need for proper interpretation. He then introduces the ensemble interpretation (ensemble = ''Schwarm'') in pure and mixed states, and resolves the paradox in the well-known statistical way. (Thus - @bhobba, @atyy - the ensemble interpretation starts at least with Weyl 1927, and not only with Ballentine 1970!)

The map from theory to experiment is stated not as part of the theory but as ''the assumption by Goudsmit and Uhlenbeck, which has proven itself well'' [Goudsmit, S. and Uhlenbeck, G.E., 1926. Die Kopplungsmöglichkeiten der Quantenvektoren im Atom. Z. Physik A 35 (1926), 618-625.] - but for electrons, and it was formulated in purely spectroscopic terms. Weyl applies it to a Stern-Gerlach-like experiment (with electrons in place of the original silver atoms).

Why was he allowed to do that? One map from theory to experiment was given through spectroscopy, another map was given through Stern-Gerlach for silver atoms. Fron these, Weyl created by analogy (not by theory) a third map for electrons in the Stern-Gerlach-like experiment. Thus the map changed.

Moreover, there are many more experiments related to angular momentum, and no quantum theory book I know points out how these are connected to the theory.

Nobel prizes are given to new ways of devising useful measurements at unprecedented accuracy, but nobody ever has suggested that each time the theory needs to be amended by mapping its mathematics to these new experimental possibilities. This mapping is described instead in papers published in experimental physics journals!

This is very typical. A theory book gives informally (not as part of the theory, since different expositions of the same theory use different examples) some key experiments in a very simplified description and relates these in an exemplary manner to theory, in order to create suggestive relations between theory and experiment. These are of the same nature as the (according to @Dale ''highly suggestive'') hints to reality given in a purely mathematical theory to make it intelligible. And they have precisely the same limitations that Dale pointed out:
The mapping to experiment is separate from the mathematical framework itself, even when the names are highly suggestive.
By the same token, the mapping to experiment is separate from the physical theory itself. No theory book gives more than highly suggestive names and pointers to experiments. The connection to real experiments must be made by the experimenter who understands the difference between a real experiment and a symbolic toy demonstration.

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#### PeterDonis

Mentor
Please give me a reference to an online article or well-known textbook that gives this unique ''mapping between the mathematical model and experiment''.
As you note, a theory textbook won't do this except for a highly idealized experiment. Obviously, as you say, an experimenter doing a real experiment has to do significant additional work to connect what the theory says to what he actually does in his lab.

However, none of this changes what I was saying. Let me try to rephrase what I was saying to show this. Suppose we are running a Stern Gerlach experiment--a real one, like the original one Stern and Gerlach did, where you are using silver atoms, not individual electrons, and you have a beam of them, not individual ones passing through the apparatus one at a time, and you vary the magnetic field and watch the beam on the detector split, as shown on the postcard that they sent to Bohr (IIRC). Obviously, as you say, a lot of work has to be done to match up what they saw in this real experiment with the theoretical model of a qubit.

But the point I'm trying to make is that none of that work has anything to do with QM interpretations as that term is used in the article in the OP of this thread. Collapse vs. MWI, for example, does not enter into that process at all; a collapse proponent and an MWI proponent can both tell their preferred stories about what happens, unaffected by any of the work the experimenters had to do to match up the theory with the actual events in their lab.

At least, that's how I see it; but perhaps, since you discuss the ensemble interpretation, the argument you are making is that experiments like Stern-Gerlach, properly interpreted, actually do rule out, say, the MWI? Or a collapse interpretation that makes claims about individual electrons (or silver atoms) instead of ensembles? If so, that certainly does not seem to be a common view among physicists.

#### A. Neumaier

I was talking about an example using QM, since interpretations of QM is the topic of this thread.
It is difficult to satisfy everyone. @Dale wants to leave quantum physics out of the discussion, you want to concentrate exclusively on it.

a theory textbook won't do this except for a highly idealized experiment.
But according to Dale, a scientific theory must contain the map from theory to experiment, and surely a book on quantum theory should provide enough of the theory so that it is a scientific theory. According to you, it would not be a scientific theory in Dale's sense. Do you agree with Dale or with Suppes in this respect?

the point I'm trying to make is that none of that work has anything to do with QM interpretations as that term is used in the article in the OP of this thread. Collapse vs. MWI, for example, does not enter into that process at all; a collapse proponent and an MWI proponent can both tell their preferred stories about what happens, unaffected by any of the work the experimenters had to do to match up the theory with the actual events in their lab.
In MWI nothing ever is predicted, unless you tell MWI which world is realized in the experiment. Thus MWI robs quantum mechanics of its predictive value.
Of course, the MWI proponents hide this by fuzzy terminology, but when you follow up on their justification of the empirical recipes you find nothing of substance.

In Bohmian mechanics, additional unobservable position variables are introduced, but it seems that these positions have no empirical content and hence give a misleading sense of ''reality''.

In the Copenhagen interpretation, nothing is predicted if you consider the solar system as a quantum system, since none of our observations are done from the outside. Of course, the Copenhagen interpretation was not intended for large systems such as the solar system, but for tiny systems under study in the 1920's and 1930's. But it showed its limitations later, and ultimately was found questionable by many. In the microscopic realm it is fully adequate. But it refuses to give a map to experiment as Dale would require it; it leaves that to classical physics, which is outside the scope of Copenhagen quantum physics (except in a correspondence limit).

The same hold for the statistical interpretation, but for different reasons: We cannot create enough independent copies of the solar system to perform adequate statistics on it. Again, for tiny systems, there are no problems with this interpretation.

Similar things can be said for any of the interpretations of quantum mechanics listed in Wikipedia.

Thus for tiny systems, shut-up-and-calculate is adequate. The mathematical framework of quantum mechanics (with highly suggestive names for the concepts) has enough structure to enforce its interpretation in the microscopic realm. This is meant in the same sense as I had demonstrated it for numbers and for projective planes - for simplicity, both to avoid having to discuss all the stuff specific to quantum mechanics, and since Dale wanted the discussion to apply to general scientific theories.

For large systems, in particular for the solar system, no current interpretation of quantum mechanics is adequate. Although quantum theory is obviously complete on this level (when gravitation is modelled semiclassically in the post-Newton approximation), the physics community simply does not know how to set up a mapping from theory (with or without interpretation) to experiment that is both logically consistent and applies to the solar system and all its subsystems. But the principles of quantum theory have been unchanged since around 1975 (with the advent of POVMs and the standard model) and are unlikely to change in the future, except perhaps with the incorporation of gravity.

This is the reason why the number of interpretations has proliferated, each new proposal being made in the hope that its fate would be better than that of the earlier ones. It also shows that the mapping from theory (with or without interpretation) to experiment cannot be part of quantum theory

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#### PeterDonis

Mentor
It is difficult to satisfy everyone. @Dale wants to leave quantum physics out of the discussion, you want to concentrate exclusively on it.
@Dale has said that he himself has little interest in QM interpretations, yes. But for better or worse, that is what this thread is supposed to be about, since that's what the article in the OP is about. @Dale can always just not post further in this thread if the topic gets too tiresome for him. Or we can spin off a separate thread about the "what is a theory" question so it can be discussed independently of QM interpretations.

#### A. Neumaier

Or we can spin off a separate thread about the "what is a theory" question so it can be discussed independently of QM interpretations.
It is a mix of QM and QM-independent stuff that is difficult to disentangle, hence it is better to leave it here. @Dale could open a new thread, however, and I'd repeat the main features of my point of view.

#### bhobba

Mentor
(Thus - @bhobba, @atyy - the ensemble interpretation starts at least with Weyl 1927, and not only with Ballentine 1980!)
Of course. Einstein himself was a proponent of it. As I think I mentioned it is interesting the interpretation has come through to modern times pretty much unchanged, Copenhagen - not so well. Of course Copenhagen has the added issue of there being all sorts of different versions. When I speak of Copenhagen I mean the version advocated by Bohr even though he is a bit too philosophical for my taste - just me of course - its got nothing to do with its validity - just I find such hard to understand. It is of course understandable - I have no doubt Einstein understood what his good friend was saying even though he disagreed with him - but I am a philosophical philistine as my philosophy teacher was only too well aware (I took a graduate course in philosophy - actually two, but the second one I pulled out of because it really was philosophy in a historical context and history did not interest me that much).

Thanks
Bill

#### A. Neumaier

Einstein himself was a proponent of it.
But he never gave an explicit formal expression of it, I think. While Weyl is quite explicit about it - well before the Bohr-Einstein debate.

#### A. Neumaier

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 De 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".
The debate is actually older than the debate of the foundations of quantum mechanics. An interesting snapshot from 1957 is given by the proceedings

S. Körner (ed.), Observation and Interpretation, Butterworths, London 1957.

It shows similarities and interrelations between the interpretation problems in quantum mechanics and in probability theory.

The proceedings contain a paper by Rosenfeld (pp.41-45) discussing the relation of theory to physical experience, expressing also the same view as I did, not @Dale's:
Rosenfeld (his italics are here bolded) said:
The ordinary language, (spiced with technical jargon for the sake of conciseness) is thus inseparably united, in a good theory, with whatever mathematical apparatus is necessary to deal with the quantitative aspects. It is only too true that, isolated from their physical context, the mathematical equations are meaningless: but if the theory is any good, the physical meaning which can be attached to them is unique.
The proceedings also contain a paper by D. Bohm on his hidden variable theory, with discussion.

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#### Dale

Mentor
The proceedings contain a paper by Rosenfeld (pp.41-45) discussing the relation of theory to physical experience, expressing also the same view as I did, not @Dale's:
I read that and I totally disagree that this supports your view over mine, but I am not willing to argue the point further. Everyone has a built in psychological tendency towards what is called confirmation bias, where evidence is fit into a preconceived view. I believe that you are suffering from that quite strongly, and I assume that you feel I am also suffering from the same. To me, that same passage supports my view, not yours.

#### A. Neumaier

I read that and I totally disagree that this supports your view over mine, but I am not willing to argue the point further. Everyone has a built in psychological tendency towards what is called confirmation bias, where evidence is fit into a preconceived view. I believe that you are suffering from that quite strongly, and I assume that you feel I am also suffering from the same. To me, that same passage supports my view, not yours.
Schrödinger did not have my confirmation bias. He confirmed in his 1958 paper ''Might perhaps energy be a merely statistical concept?'' my reading of Rosenfeld although he strongly opposed its truth:
Erwin Schrödinger said:
I feel induced to contradict emphatically an opinion that Professor L. Rosenfeld has recently uttered in a meeting at Bristol, to the effect that a mathematically fully developed, good and self-consistent physical theory carries its interpretation in itself, there can be no question of changing the latter, of shuffling about the concepts and formulae.
The problem with quantum mechanics is of course its lack of self-consistency, because of the ambiguity of the dynamics, the applicability of which depends on a vague concept of measurement. Thus it doesn't fit into the collection of theories considered by Rosenfeld (though somehow both seemed to assume it did).

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#### AlexCaledin

Why, naturally, the QM is the only theory that tries to deal explicitly with the choice between the available variants of the universe, each variant obeying all the other theories.

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#### Fra

If you look at the abstractions here, I see strong analogies in the discussion here between the "theory vs interpretations" and other concepts such as the nature of gauge symmetry, and questions of philosophy of science such as objective vs subjective information.

This characterisation is tempting to make for me:

Theory ~ equivalence class of the versions of the theories we index by interpretation.

Here the new question induced is, how does one scientifically defined the equivalence class? How do we know that the set of versions of theories are exhausted? How much interactions and comparasion are required to concluded equivalence? Is this process even physically realisable in finite time with by bounded physical system?

Ie. we can consider the equivalence class the "theory" and the choice of interpretations as gauge choices, that in some contexts are also described as redundancies, of choosing an observer.

However, this raises more deep complicated questions, that puts the focus on how objectivity (as in gauge equivalences, or gauge symmetries) are actually established, given that the process of "science" (inference) take place INSIDE this system; not outside or external to.

One can also associate this into an evolutionary perspective, and here it seems that different interpretations, yield difference expectations on the future development by the natural extrapolation. Each interpretation defines a measure of naturality and extrapolations.

So i associate the interpretations in the context of evolution as part of the variability required. This is how i always talked about "interpretations"; they make no difference and are of no survival value at the present moment, but they represent the healthy variation that sets out the researhc direction for the future; and there they will be discriminated.

This is why my personal view is that "interprations of QM" become interesting only when they are taking to their full implications BEYOND the standard model.

/Fredrik

#### A. Neumaier

the choice between the available variants of the universe
In reality, we have no choice but to be content with the given one in which we live.

#### AlexCaledin

In reality, we have no choice but to be content with the given one in which we live.
But Professor Henry Stapp comforts me a bit, saying that my conscious choice of the thought pattern in my brain is a genuine quantum choice . . .

#### A. Neumaier

But Professor Henry Stapp comforts me a bit, saying that my conscious choice of the thought pattern in my brain is a genuine quantum choice . . .
Oh, really? Poor you! (How does he know you so well??)

My conscious choices are almost never random but usually based on more or less predictable preferences. (Of course predictable only by those who know me well enough.)

I also prefer my friends to be reliable rather than that they act randomly....

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#### Rive

Demystifier said:
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.
Latecomer's comment: let's take mechanics as an example. By my standards D'Alembert's principle, Hamilton's principle, Newton's laws are all fits to the category of 'theory', since even if they are about the same topic they have different math behind them.

Interpretation, however would be something like the history of Newton's first law: originally it was a statement of the behavior of isolated bodies, then slowly it was transformed to the definition of inertial systems. The underlying math is the same, however the translation to actual language became different.

In this context the debate about the interpretation of QM would be more about the frustration caused by the conflict of language and complex math what prevents the clear description of principle with common language than about different theories of the same topic - since there is no fundamentally different math for the topic...

#### Pleonasm

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.
I would like to think that an explanatory model positing hidden variables, like Pilot wave, would be a theory in and of itself, and not just an interpretation. Nature would have an additional feature to itself.

Contrast these two alternative world views of Quantum Mechanics:

1. Standard model/collapse of the wave function: Subatomic nature behaves in a lawful manner, subject to our probabilistic day-to-day knowledge of it. There are no hidden variables to account for it all.

2. Pilot-wave: Subatomic nature behaves in a lawful manner, subject to our probabilistic day-to-day knowledge of it. There are hidden variables account for it.

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#### Ian J Miller

As to what qualifies as a different theory, what about different premises, even if some of the basic maths are the same? As an example, how about this. Start with the usual expression for the wave function phase, and assume with the pilot wave there is a wave that causes the effects that require QM. Now, take the 2-slit experiment and as premise 1, assume the wave causes the effect. If so, the wave has to arrive at more or less the same time as the particle, and therefore the phase velocity of the wave should equal the expectation particle velocity. Given the phase velocity = E/p, our hidden variable is now an energy, not position. The value here is that for stationary states, the wave properties define the energy and you do not have to solve insoluble differential equations. For example, for the chemical bond, if you assume the waves add linearly, but between the nuclei two new waves are created for the new interactions, the energy of the hydrogen molecule, for example, given that nucleus/electron interactions are equal for the two electrons, now comes out as 1/3 the Rydberg energy, to a first approximation. Does that qualify as a theory? You have a method with no arbitrary parameters.

#### PeterDonis

Mentor
I would like to think that an explanatory model positing hidden variables, like Pilot wave, would be a theory in and of itself, and not just an interpretation. Nature would have an additional feature in it.
If the model makes different predictions for some experiments, then it is a different theory, not an interpretation. But a model that just says "there are hidden variables", but keeps all of the experimental predictions the same, is an interpretation.

#### PeterDonis

Mentor
what about different premises, even if some of the basic maths are the same?
If the math is the same, the theory is the same, because all of the predictions will be the same. Telling a different story in ordinary language about why you picked that particular math doesn't make it a different theory.

#### Dale

Mentor
I would like to think that an explanatory model positing hidden variables, like Pilot wave, would be a theory in and of itself, and not just an interpretation. Nature would have an additional feature in it.
Definitely not. A prime example is Lorentz aether theory which posits that nature has an additional feature (the aether), but is generally considered an interpretation of S.R. rather than a new theory precisely because it makes no new predictions.

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