Against "interpretation" - Comments

[PeterDonis]

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 modeled 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

 

[PeterDonis]

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]

(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:

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.

 

[Dale]

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:

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).

 

[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.

 

[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.

Ah, that's a bit sad
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...

 

[Rive]

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.

 

[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]

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]

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]

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.

 

[Ian J Miller]

If you introduce new premises, the maths are not the same. For my example above, I have introduced the phase velocity of the wave equalling the particle velocity. That does not occur in any book or paper on QM of which I am aware, apart from anything I have written, such as the above. What it does is provide a method for calculating properties that standard theory can not dowiht0put introducing "validation corrections" (See Pople's Noble lecture).

 

[PeterDonis]

If you introduce new premises, the maths are not the same.

True, but the math might also be inconsistent. See below.

For my example above, I have introduced the phase velocity of the wave equalling the particle velocity.

But you have not shown that this leads to a consistent model, or given a reference to one. In the pilot wave version of standard (non-relativistic) QM, you can't arbitrarily set the phase velocity of the pilot wave; it's not a free parameter, it's determined by the Schrödinger Equation.

 

[Ian J Miller]

True, but the math might also be inconsistent. See below.
But you have not shown that this leads to a consistent model, or given a reference to one. In the pilot wave version of standard (non-relativistic) QM, you can't arbitrarily set the phase velocity of the pilot wave; it's not a free parameter, it's determined by the Schrödinger Equation.

The Schrödinger equation defines the energy of the particle, and it applies even if there is no wave with physical properties. But if the wave is not at the slits, how can it affect what the particle does when it goes through? Accordingly, what I have written above is not the standard pilot wave, nevertheless it gives results in accord with observation for molecules.

 

[Dale]

If you introduce new premises, the maths are not the same.

What matters is whether or not the experimental predictions are the same. Same predictions -> same theory.

 

[Pleonasm]

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.

I suppose it depends on the context. In a philosophy context, a theory of the world is what one thinks constitutes the world. A world of hidden variables as opposed to no hidden variables would constitute two difference universes cosmetically. I write cosmetically, because they would in this case be operationally identical nevertheless. Perhaps a physics context doesn't give a damn about this, but it would seem overly reductionist.

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.

How do you square "definitely not" with "generally concidered". Is statement 1 a personal opinion expressed?

 

[Dale]

In a philosophy context

This forum is a scientific context.

How do you square "definately not" with "generally concidered". Is statement 1 a personal expression?

Everything I write is a personal expression. I believe that expression to be consistent with the professional scientific literature as referenced earlier in this thread.

Btw, spell check might be helpful, or at least copy and paste. Both of your manual quotes introduced spelling errors that were not in my original. At first I thought you were trying to make fun of me.

 

[PeterDonis]

if the wave is not at the slits, how can it affect what the particle does when it goes through?

Because the pilot wave version of standard non-relativistic QM has an explicitly nonlocal interaction between the pilot wave and the particles. This feature is a key reason why nobody has yet been able to come up with a consistent relativistic version.

what I have written above is not the standard pilot wave

Then your model is under-specified, because you have not given the complete statement of all the entities and dynamics, and therefore we don't know what your model predicts for all experiments that we have predictions from standard QM for. So it's impossible to tell whether it is a different theory from standard QM, or just a different interpretation.

 

[PeterDonis]

I suppose it depends on the context.

Sure, it could, but in this context we care about the physics definition, not about any philosophical definition. This is a physics forum.

 

[Pleonasm]

This forum is a scientific context.

How one defines "theory" as opposed to "interpretation" is ultimately a philosophical question. It's just semantics at the end of the day.

My point was that your initial statements are contradictions. You wrote "definitely not" to my claim, only to follow it up with a "generally not" example. This is a contradiction.

 

[Pleonasm]

FWI, I know of a working physicist who is of the opinion that the pilot wave model is a theory, not just an interpretation. It doesn't seem to be self-evident to him at least.