Minimal vs Instrumental vs Ensemble

[Morbert]

TL;DR Summary

Terms like "minimal interpretation" and "ensemble interpretation" and "instrumentalist interpretation" are sometimes used interchangeably. This thread makes notes of some distinctions made in literature.

I've recently had a look back at the review by Home and Whitaker as well as Asher Peres's book "Quantum Theory: Concepts and Methods". Both "minimal interpretation" and "ensemble interpretation" refer to categories of interpretations rather than interpretations themselves. Specifically, you can have an ensemble interpretation that is not minimal, and a minimal interpretation that is not an ensemble interpretation. Below is a table considering a minimal instrumentalist interpretation, a pre-assigned-values (PIV) ensemble interpretation, and the minimal ensemble interpretations. The table does not fully describe each interpretation. It only highlights some points of distinction between them.

Some remarks:

Both instrumental and ensemble interpretations could be considered anti-realist insofar as the the state of a system does not represent an actually-existing thing. Ensembles are infinite, as "finite ensembles, in fact, constitute individual systems, and quantum mechanics is not supposed to make predictions about individual systems. So an ensemble must be an infinite affair." (Sudbery). Even ensembles where members are pre-assigned values is still fictitious due to this infinite character. Similarly, the instrumentalist Peres describes the quantum system as a useful abstraction that does not exist in nature, characterized by the probabilities of outcomes of every conceivable test on a system.

Home + Whitaker consider a state $|\psi\rangle = \sum_r \langle r|\psi\rangle|r\rangle$ and say that, according to a PIV ensemble interpretation, this represents an infinite ensemble of systems, each with a value $r$. And according to the minimal ensemble interpretation, it represents an ensemble of systems each in linear combination of $|r\rangle$ states. The latter seems recursive and inconsistent to me. I have argued against it in previous threads but perhaps it is accepted.

There is disagreement in literature to the significance of the collapse postulate. As such the last column in the table is the least definitive.

Interpretation	Quantum states refer to	Probabilities are	Is probability ascribed to single events?	Do ensembles have structure?	The collapse postulate
Minimal instrumentalist interpretation	Macroscopic preparation procedures	The likelihood of outcomes of macroscopic tests	Yes	N/A	No significance is attributed to the interpolation of the wavefunction across repeated measurements.
Pre-assigned-value ensemble interpretation	Infinite ensembles of identically prepared systems	Portions of the ensemble with the corresponding property	No	Yes	The postulate describes the division of the ensemble into subensembles, each represented by possible states after collapse
Minimal ensemble interpretation	Infinite ensembles identically prepared systems	Relative frequencies for macroscopic tests over the ensemble	No	No	The postulate describes the creation of subensembles, each represented by possible states after collapse

 

[Demystifier]

What exactly is minimal in the minimal interpretation?

 

[kered rettop]

What exactly is minimal in the minimal interpretation?

Not the number of posts about it, that's for sure

I'm going to hazard a guess because the meaning seems - to me, that is - to be perfectly clear from the context of, say, @vanhees71's posts. Usual disclaimers: it's not intended to be a definitive answer; I may very well be missing something; maybe your question is intended to be slightly provocative; maybe Van Hees employs an idiosyncratic lexicon etc etc. However, I think it rather likely that a lot of users will have taken it to mean much the same thing as me and been perfectly happy with it - until now.

I think it's fair to say that the postulates of the maths are accepted. These come down to: a recipe for the state evolution, usually couched in terms of a Hilbert space, and another recipe, for probabilities, usually expressed as the Born Rule. Minimalist means there are no additional postulates, of course. And, in the spirit of minimalism, if it turns out that the second postulate is derivable from the first, then it changes nothing except that we have some redundancy. Maybe a minimalist would relegate it from a postulate to a theorem.

But the above does not say which, if any, of the mathematical gizmos represent things that are real. A minimalist interpretation will have to assert the reality of observational outcomes in some way, otherwise the theory remains a bit of pure mathematics having no bearing on reality. And claims about reality are metaphysics, in this case necessary metaphysics, in order to bridge the gap between the maths and the lab.

So, in the minimalist interpretation, we have a maths with as few postulates as possible and permission from the metaphysics to use it to make predictions. In other words "shut up and calculate".

It should be noted that other interpretations do assert the reality of the unobservable wave function and try to account for observations within that framework. In that respect MWI is arguably minimalist, but it fails the test if it invokes decoherence theory in its account. Not because decoherence is an additional postulate but because it requires an environment or something equivalent. Therefore, formally, the environment needs to be postulated.

Of course if you suffer from a pathological desire to interpret QM as describing reality in additional ways - and I most certainly do so suffer - then the minimalist interpretation will not appeal. It has nothing to say on the matter. My personal opinion is that there needs to be a clear explanation of how something that may not even exist (the wave function) can give rise to things that most definitely do (observational outcomes). However, it would appear that minimalism is not even agnostic about the onticity of the wave function, it just doesn't talk about it. Presumably because it doesn't need to.

Well, that took longer to write than I expected. Is it what you asked, or even helpful? Probably not.

 

[vanhees71]

I don't know, whether my "lexicon" is "idiosyncratic", only because I insist in defining what's meant by the words I used. For me the greatest obstacle in discussing the foundations of quantum mechanics is the mess philosophers and, even worse, philosophy-inclined physicists, create by using words without clear definitions of their meaning. The worst is "localicy" and "non-locality". Instead of using the clear and definite meaning given in mathematical terms when formulating relativistic QFT, they have all kinds of nebulous different meanings, but that's not so much the point of the here discussed question, about what's "minimal" in the "minimal interpretation".

For me the main point of this interpretation is that it just takes the probabilistic interpretation of the quantum state seriously, i.e., it says that these probabilities is all there is in our description of Nature, as far as it is objectively observable. For me that makes the quantum physics clean and simple as a natural science. Whether or not it is "complete", I'm pretty agnostic about. The history of physics shows that so far no physical theory has been complete. Whether QT is, is not so clear. For sure there's no satisfactory QT including the gravitational interaction, but that's indeed a physical problem and not a philosophical one.

 

[kered rettop]

I don't know, whether my "lexicon" is "idiosyncratic", only because I insist in defining what's meant by the words I used.

I was not suggesting there's a problem with you insisting on being clear! Sorry, if "idiosyncratic lexicon" sounded derogatory, it wasn't intended that way at all, quite the opposite, in fact. My sense of humour again, I'm afraid.

 

[Morbert]

What exactly is minimal in the minimal interpretation?

As far as I can tell, a minimal interpretation is one that strives to limit its conceptual machinery to the macroscopic. So the instrumentalist is probably as minimal as you can get. Wading a little further, we might introduce the notion of an ensemble of microscopic systems, but then make this as minimal as possible by refusing to commit to any inherent structure of this ensemble etc.

 

[Demystifier]

Well, that took longer to write than I expected. Is it what you asked, or even helpful? Probably not.

Your explanation of minimal interpretation is not minimal.

 

[kered rettop]

Your explanation of minimal interpretation is not minimal.

True. But it's very cute.

 

[bhobba]

To me, minimal is not introducing things beyond formalism. The ensemble interpretation is minimal; the DBB interpretation is not, e.g. it says a wave guides an actual particle.

It is not an important distinction, in my opinion. Like all formalisms, it says more about a person's view of the world than anything else.

QM is just a mathematical model implied mainly by Gleason's theorem, and the reality is in Quantum Field Theory. That says more about my worldview than anything else. I find interpretations interesting, but it is an area of slow progress.

Copenhagen is an instrumentalist view, but it is not minimal. It makes the claim the state is the complete description of the system. Einstein objected to this, saying it was incomplete. In my opinion, it is also incomplete, but for different reasons than Einstein did.

Thanks
Bill

 

[gentzen]

The way I would interpret Ballentine is that his statistical interpretation is minimal, because it does not assign probabilities to single events. One of its advantages is that it is Lorentz invariant, and also applies to QFT in its current "strange" state. That it only was proposed in 1970, after Bell had written his crucial papers, is interesting. And indeed, Ballentine quotes Bell in his paper.

Neither a straightforward Copenhagen interpretation, nor other straightforward minimal instrumentalist interpretation, are Lorentz invariant in that straightforward way. A straightforward Copenhagen interpretation of QFT (in its current state) seems to fail, and I haven't thought about whether other minimal instrumentalist interpretations work better in that respect. One could interpret QBism as an interpretation of the Copenhagen interpretation, which at least succeeds in restoring Lorentz invariance. (But my impression is that it still won't work for QFT, at least I don't see how.)

One issue with vanhees71's adaption of Ballentine's interpretation is that he seems to make claims in addition to Ballentine (like that it would assign probabilities to single events, and other non-ensemble like situations). Also, when Demystifier brought up a "rather simple" mistake by Ballentine, it resulted in quite a mess. Just observing that mess hurted me inside. (In fact, vanhees71's claims have triggered quite some "research like" activity on my part, often in connection with CH, because calculation is so easy and straightforward there. But I am always unsure how much "research like" activity of that kind is actually compatible with PF's rules on "personal research".) I would even say that some of vanhees71's positions, clarifications and explanations are correct and do go beyond Ballentine, but he always preceedes those with "of course", which I find annoying.

 

[Morbert]

@gentzen What is the difficulty with minimal instrumentalist interpretation re/ Lorentz invariance and QFT?

 

[vanhees71]

One issue with vanhees71's adaption of Ballentine's interpretation is that he seems to make claims in addition to Ballentine (like that it would assign probabilities to single events, and other non-ensemble like situations). Also, when Demystifier brought up a "rather simple" mistake by Ballentine, it resulted in quite a mess. Just observing that mess hurted me inside. (In fact, vanhees71's claims have triggered quite some "research like" activity on my part, often in connection with CH, because calculation is so easy and straightforward there. But I am always unsure how much "research like" activity of that kind is actually compatible with PF's rules on "personal research".) I would even say that some of vanhees71's positions, clarifications and explanations are correct and do go beyond Ballentine, but he always preceedes those with "of course", which I find annoying.

I don't think I have another view on the meaning of probabilities than Ballentine. Of course the state must have an operational meaning for the single quantum system, and this operational meaning, as I understand it, is that it describes a preparation procedure on a single system. This implies that there are probabilities for the outcome of measurements done on this single system. Now you can test wheter QT predict these probabilities correctly only by repeating the experiment often enough, i.e., you have to prepare a sufficiently large statistical sample, to be able to test the observed "relative frequencies" with the predicted probabilities including a statistical error estimate. In this sense the quantum state only describes statistical properties of statistically samples of equally prepared quantum systems (aka "ensembles").

 

[PeterDonis]

I don't think I have another view on the meaning of probabilities than Ballentine.

You contradict yourself:

Of course the state must have an operational meaning for the single quantum system, and this operational meaning, as I understand it, is that it describes a preparation procedure on a single system. This implies that there are probabilities for the outcome of measurements done on this single system.

This is not what Ballentine says. Ballentine says there is no such thing as "probabilities for the outcome of measurements done on [a] single system". Probabilities are only meaningful in terms of statistics done on the results of measurements on a large number of identically prepared systems. He says much the same thing about states. See Chapter 2 of his book.

 

[gentzen]

@gentzen What is the difficulty with minimal instrumentalist interpretation re/ Lorentz invariance and QFT?

If some instrumental interpretation interpretation ascribes probabilities to single events, and those single events happen at a specific point in time, than that specific point in time seems to create problems with the typical "asymptotic in- and out-states only" QFT. For Lorentz invariance of instrumental interpretations, a global time parameter creates problems, but those are easier to avoid than the problems with QFT.

 

[Morbert]

If some instrumental interpretation interpretation ascribes probabilities to single events, and those single events happen at a specific point in time, than that specific point in time seems to create problems with the typical "asymptotic in- and out-states only" QFT. For Lorentz invariance of instrumental interpretations, a global time parameter creates problems, but those are easier to avoid than the problems with QFT.

Event would be in the probability theory sense of pertaining to outcomes. E.g. If a test involves rolling a die, then "landing on an even number" would be a valid event, with an associated probability. In QFT the relevant events would presumably be things like detector excitation rates.

 

[gentzen]

Event would be in the probability theory sense of pertaining to outcomes. E.g. If a test involves rolling a die, then "landing on an even number" would be a valid event, with an associated probability. In QFT the relevant events would presumably be things like detector excitation rates.

Without time, you cannot track the evolution of a single system through time. The Copenhagen interpretation is perfectly happy with tracking such an evolution. But if you cannot track single systems anymore, then you are back to Ballentine's minimal statistical interpretation.

 

[Morbert]

Without time, you cannot track the evolution of a single system through time. The Copenhagen interpretation is perfectly happy with tracking such an evolution. But if you cannot track single systems anymore, then you are back to Ballentine's minimal statistical interpretation.

Why would you need to track the evolution of a single system? An instrumentalist would instead be concerned with a test on the single system, and the events pertaining to possible outcomes of that test. What would necessitate an interpretation like Ballentine's would be e.g. a frequentist interpretation of probabilities. Are you saying that typical QFT quantities like cross sections necessitate a frequentist interpretation?

 

[gentzen]

Why would you need to track the evolution of a single system? An instrumentalist would instead be concerned with a test on the single system, and the events pertaining to possible outcomes of that test. What would necessitate an interpretation like Ballentine's would be e.g. a frequentist interpretation of probabilities. Are you saying that typical QFT quantities like cross sections necessitate a frequentist interpretation?

No, the "frequentist" part is not important. The point is rather whether you have to wait until the experiment is over, before you can make conclusions from your classical measurement results, or whether you can update your conclusions (about the single system) on the fly, and maybe even adjust some control signals suitably (i.e. a time dependent reaction).

For example, the typical envisioned applications of quantum computers are perfectly happy with statistics for finished runs only. But if you want to make predictions about what happens in the universe, then it is a bit annoying to have to wait until "the experimental run" is over.

Maybe it is again easiest to use CH to illustrate the trouble. Assume you use the time-symmetric version, which basically means that you can have post-selection. But the post-selection will only happen after a single run is over, i.e. you don't yet know during the run itself, whether it will be accepted as valid at all, or in which category it will fall. But your conclusions need that category to work, so they are not yet available during the run.

 

[Morbert]

No, the "frequentist" part is not important. The point is rather whether you have to wait until the experiment is over, before you can make conclusions from your classical measurement results, or whether you can update your conclusions (about the single system) on the fly, and maybe even adjust some control signals suitably (i.e. a time dependent reaction).

For example, the typical envisioned applications of quantum computers are perfectly happy with statistics for finished runs only. But if you want to make predictions about what happens in the universe, then it is a bit annoying to have to wait until "the experimental run" is over.

So does you concern exclude conventional tests of QFTs? Ones that involve things like particle accelerators, event displays etc? I.e. Ones readily described by preparation and macroscopic data?

Maybe it is again easiest to use CH to illustrate the trouble. Assume you use the time-symmetric version, which basically means that you can have post-selection. But the post-selection will only happen after a single run is over, i.e. you don't yet know during the run itself, whether it will be accepted as valid at all, or in which category it will fall. But your conclusions need that category to work, so they are not yet available during the run.

Well to borrow a turn of phrase: Show me an experiment (real or thought) and I'll show you a minimal, instrumentalist interpretation of it.

 

[gentzen]

So does you concern exclude conventional tests of QFTs? Ones that involve things like particle accelerators, event displays etc? I.e. Ones readily described by preparation and macroscopic data?

Wait, which concern are you talking about? The predictions of QFT are tested by the minimal statistical interpretation, and everybody is happy with that. And you can just accept the minimal statistical interpretation as a valid instrumentalist interpretation, so no concerns there either.

The interesting question is how a straightforward Copenhagen interpretation applies to QFT. Sure, you can take the "finished classical results" of some QFT experiment and plug them into Copenhagen. Or you plug important QFT corrections into some non-relativistic quantum model, and use Copenhagen for that model. Which is actually cool, in certain ways, but QFT was still somehow outside, and not fully integrated. But here, at least it was integrated on the quantum level.

Well to borrow a turn of phrase: Show me an experiment (real or thought) and I'll show you a minimal, instrumentalist interpretation of it.

Wait, we start to talk past each other, no? My point was that straightforward instrumentalist interpretations like the Copenhagen interpretation just avail themselves to suitable time parameters. Those time parameters easily generate trouble with QFT and Lorentz invariance. The trouble with Lorentz invariance is typically solvable with a bit more care, but the trouble with QFT is different.
The point of the two examples was to illustrate the trouble for the minimal statistical interpretation, and what missing access to a "true" time parameter means in practice.

 

[Morbert]

Wait, which concern are you talking about? The predictions of QFT are tested by the minimal statistical interpretation, and everybody is happy with that. And you can just accept the minimal statistical interpretation as a valid instrumentalist interpretation, so no concerns there either.

I mean your concern re/ a minimal instrumentalist interpretation not involving infinite ensembles. Do you think such an interpretation of these standard tests of QFTs is not possible? I.e. If we are instrumentalists, we must invoke infinite ensembles?

The interesting question is how a straightforward Copenhagen interpretation applies to QFT. Sure, you can take the "finished classical results" of some QFT experiment and plug them into Copenhagen. Or you plug important QFT corrections into some non-relativistic quantum model, and use Copenhagen for that model. Which is actually cool, in certain ways, but QFT was still somehow outside, and not fully integrated. But here, at least it was integrated on the quantum level.

Wait, we start to talk past each other, no? My point was that straightforward instrumentalist interpretations like the Copenhagen interpretation just avail themselves to suitable time parameters. Those time parameters easily generate trouble with QFT and Lorentz invariance. The trouble with Lorentz invariance is typically solvable with a bit more care, but the trouble with QFT is different.
The point of the two examples was to illustrate the trouble for the minimal statistical interpretation, and what missing access to a "true" time parameter means in practice.

Here I am taking "Copenhagen interpretation" to mean some interpretion protocol insisting on explicit finite time-evolution, and hence something difficult to apply to asymptotic times. I think that is an interesting question, but that instrumentalism is a more general concept relating operators to macroscopic apparatus. I think these two questions should be separated.

 

[gentzen]

I mean your concern re/ a minimal instrumentalist interpretation not involving infinite ensembles. Do you think such an interpretation of these standard tests of QFTs is not possible? I.e. If we are instrumentalists, we must invoke infinite ensembles?

No, there is no need to invoke infinite ensembles. What I tried to clarify is totally unrelated to finite or infinite ensembles. I tried to express this by

No, the "frequentist" part is not important.

To quibble over "infinite ensembles" versus "finite empirical sample" (or whatever was the correct name) feels like a fight over words to me, probably vanhees71 would call it "philosophy".

 

[PeterDonis]

there is no need to invoke infinite ensembles.

If this is what you mean by "minimal", then your claim in post #10 that Ballentine's interpretation is minimal is wrong, since Ballentine explicitly defines "ensembles" to be infinite. See Chapter 2 of his book.

 

[PeterDonis]

To quibble over "infinite ensembles" versus "finite empirical sample" (or whatever was the correct name) feels like a fight over words to me

It certainly doesn't to Ballentine, since he goes to some trouble to distinguish the two in his book.

 

[gentzen]

No, there is no need to invoke infinite ensembles.

If this is what you mean by "minimal", then your claim in post #10 that Ballentine's interpretation is minimal is wrong, since Ballentine explicitly defines "ensembles" to be infinite. See Chapter 2 of his book.

That was my reply to "If we are instrumentalists, we must invoke infinite ensembles?" Even if those "infinite ensembles" would be an important characteristics of instrumentalism for Ballentine, that would still be unrelated to what he means by "minimal," or how I interpreted him:

The way I would interpret Ballentine is that his statistical interpretation is minimal, because it does not assign probabilities to single events.

 

[PeterDonis]

Even if those "infinite ensembles" would be an important characteristics of instrumentalism for Ballentine, that would still be unrelated to what he means by "minimal,"

This doesn't make sense. You can't pick and choose isolated parts of an interpretation, whether it's Ballentine's or anyone else's. You need to consider the whole thing.

 

[physika]

and everybody is happy with that.

That statement sounds familiar...

 

[vanhees71]

You contradict yourself:This is not what Ballentine says. Ballentine says there is no such thing as "probabilities for the outcome of measurements done on [a] single system". Probabilities are only meaningful in terms of statistics done on the results of measurements on a large number of identically prepared systems. He says much the same thing about states. See Chapter 2 of his book.

You misread what I wrote. I wrote about the operational sense of the quantum state, and that's a preparation procedure on a single system. It implies only the knowledge about the probabilities for the outcomes of measurements on the so prepared system, which can be tested only on ensembles (or rather "statistical samples" which approximate the theoretical ensembles sufficiently). Indeed, see Chpt. 2 of Ballentine's book!

 

[vanhees71]

Why would you need to track the evolution of a single system? An instrumentalist would instead be concerned with a test on the single system, and the events pertaining to possible outcomes of that test. What would necessitate an interpretation like Ballentine's would be e.g. a frequentist interpretation of probabilities. Are you saying that typical QFT quantities like cross sections necessitate a frequentist interpretation?

Yes, or how else than just "collecting enough statistics" do you think the HEP physicists measure cross sections?

 

[vanhees71]

If this is what you mean by "minimal", then your claim in post #10 that Ballentine's interpretation is minimal is wrong, since Ballentine explicitly defines "ensembles" to be infinite. See Chapter 2 of his book.

We all know that in reality we deal with "statistical samples" and not infinite theoretical "ensembles". Also there are standard statistical procedures to estimate the corresponding uncertainties related to finite samples vs. infinite theoretical ensembles. That's how empirical science works! If your rigorous point of view were right, one couldn't use QT at all to describe Nature, which obviously is not the case. To the contrary, the most accurate observations/measurements in physics are involving generic QT features like the Lamb shift of the hydrogen atom, the anomalous magnetic moments of electrons/muons, etc.

 

[PeterDonis]

I wrote about the operational sense of the quantum state, and that's a preparation procedure on a single system.

Not according to Ballentine. You really should read his book before claiming that your interpretation is the same as his.

Indeed, see Chpt. 2 of Ballentine's book!

If you think Ballentine says that "the operational sense of the quantum state" is "a preparation procedure on a single system", then please provide an explicit quote from that chapter that does so. I can't find one.

We all know that in reality we deal with "statistical samples" and not infinite theoretical "ensembles".

Ballentine discusses this. If you want to claim that your interpretation is the same as his, you need to provide explicit quotes from his book that say so. I can't find any.

 

[Morbert]

@gentzen Again I will have to ask you for an example experiment, as your issue is unclear to me.

 

[Morbert]

Yes, or how else than just "collecting enough statistics" do you think the HEP physicists measure cross sections?

Statistical samples are a necessary part of many experiments. But these statistical samples might still be compatible with, say, an interpretation of quantum probabilities as propensities of individual systems, as opposed to relative frequencies of infinite ensembles.

 

[Morbert]

fwiw Asher Peres is the most "instrumentalist" physicist I know of and he heavily uses the notion of an ensemble.

Before we examine concrete examples, the notion of probability should be
clarified. It means the following. We imagine that the test is performed an infinite number of times, on an infinite number of replicas of our quantum system, all identically prepared

Even if a formal distinction can be made between instrumentalist minimal, and minimal ensemble, there might not be any physicists advocating the former rather than the latter.

 

[gentzen]

@gentzen Again I will have to ask you for an example experiment, as your issue is unclear to me.

Is it unclear to you, whether my issue is really an issue, or unclear where I see a potential issue? It is not fully clear to me either, whether my issue is really fundamental, or just an apparent issue. I described my issue as:

The point is rather whether you have to wait until the experiment is over, before you can make conclusions from your classical measurement results, or whether you can update your conclusions (about the single system) on the fly, and maybe even adjust some control signals suitably (i.e. a time dependent reaction).

A good example for a time dependent reaction might be quantum teleportation. I described before why this seems to be problematic for Bohmian mechanics:

And Quantum State Teleportation where the measurement result dependent unitary transformations applied to particle 3 work fine for Copenhagen, but not for Bohmian mechanics (this is the paragraph just above section 6 Conclusion in the link above):

Simply by noting the actual position ($x_0$) of the measuring device, the observer, near particles 1 and 2, immediately knows which wavepacket $x_0$ has entered, and therefore which state is active for particle 3. The observer then sends this classical information to the observer at 3 who will then apply the appropriate unitary transformation $U_1\dots U_4$ so that the initial spin state of particle 1 can be recovered at particle 3.

To see that this is incompatible with Bohmian mechanics, note that what is described here would be a backaction of the trajectories on the wavefunction, which is not possible (or at least not included) in Bohmian mechanics.

I had written a description of quantum teleportation from a QBist perspective (which I see as instrumentalistic). I can paste it, if you want. But mostly it was just long. The point of that description was that there are time dependent quantum states, and actions dependent on those time dependent states. But the actions are based on subjective beliefs about quantum states, not on objective quantum states. At least that is the QBist perspective.