A very interesting paper on orthodox quantum mechanics

[A. Neumaier]

TL;DR

based on what a majority textbooks says

Beck, G. (2025). How to be an orthodox quantum mechanic.
https://arxiv.org/abs/2504.20597

From the abstract:

to answer [...] what is the orthodox interpretation of quantum mechanics? [...] we review a collection of 42 textbooks on quantum mechanics, encompassing the most popular and prominent works of this nature.

From the conclusion:

To an orthodox quantum mechanic, individual particles exist in wave-like superpositions, when left to their own devices, and assume their observed properties (and appear as particles) when forced to by outside interference. When this happens, the individual particle’s properties are subject to the uncertainty principle as a form of measurement uncertainty and the state is inevitably changed by the uncontrolled disturbance inherent in measurement.

 

[Peter Morgan]

tl;dr summary: We will not here consider quantum field theory whatsoever.

I suppose that's part of what orthodoxy requires: we can ignore QFT because it's the same as QM.

 

[gentzen]

I suppose that's part of what orthodoxy requires: we can ignore QFT because it's the same as QM.

The "we ignore" part is certainly true. The reasoning why it gets ignored is probably not so much that it is the same as QM, but that the need for "asymptotic states" and renormalization doesn't fit well with Heisenberg's subjective Copenhagen interpretation.
And investigating whether Bohr's pragmatic orthodox interpretation has less trouble with it is avoided, because who knows what exactly is the orthodox interpretation anyway.
However, the minimal statistical interpretation has no problem with QFT. But part of the orthodoxy is to avoid being to close to the minimal statistical interpretation.

 

[A. Neumaier]

who knows what exactly is the orthodox interpretation anyway.

By the paper cited, we now know much better than we used to know....

 

[A. Neumaier]

tl;dr summary: We will not here consider quantum field theory whatsoever.

I suppose that's part of what orthodoxy requires: we can ignore QFT because it's the same as QM.

Orthodoxy is what is (by most textbooks) imparted to students when they have to learn quantum mechanics. That automatically excludes quantum field theory.

 

[pines-demon]

But part of the orthodoxy is to avoid being to close to the minimal statistical interpretation.

Don't worry Ballentine made it to the list.

 

[Peter Morgan]

The "we ignore" part is certainly true. The reasoning why it gets ignored is probably not so much that it is the same as QM, but that the need for "asymptotic states" and renormalization doesn't fit well with Heisenberg's subjective Copenhagen interpretation.
And investigating whether Bohr's pragmatic orthodox interpretation has less trouble with it is avoided, because who knows what exactly is the orthodox interpretation anyway.
However, the minimal statistical interpretation has no problem with QFT. But part of the orthodoxy is to avoid being to close to the minimal statistical interpretation.

I take the minimal statistical interpretation of QM to be qualitatively different from QFT insofar as there is no idea of a collection of identically prepared systems (an ensemble) in QFT (the second paragraph of the Beck orthodoxy preprint very nearly insists that there must be a concept of a system.) For QFT, there is only a measurement operator associated with a region of space-time & a state over the algebra generated by those measurement operators on the theory side and only a dataset as measurement results on the side of experiment.
As for classical signal analysis, I take it that the data in a dataset does not in the first instance have 'particles' (or call them 'systems' for generality) and 'particle properties' as their causes: if there is a track in a bubble chamber we might be as OK with saying "look, a particle track" as we are with saying "look, a table", but very often we have only many isolated data items in a dataset, so that saying "look, a particle" when we have only an isolated data item seems to me tendentious.

Orthodoxy is what is (by most textbooks) imparted to students when they have to learn quantum mechanics. That automatically excludes quantum field theory.

Before that, a few minutes ago, I was about to post that I think it was worth pointing out this aspect of Beck's preprint, but for this thread it's perhaps better not to go to too deep into QFT. Undergraduates and graduate students are sadly expected to learn QFT on the basis of interpretations of QM that I think do not extend very well to QFT.

 

[bhobba]

The reasoning why it gets ignored is probably not so much that it is the same as QM, but that the need for "asymptotic states" and renormalization doesn't fit well with Heisenberg's subjective Copenhagen interpretation.

Yes, EFT is a issue for the orthodox interpretation.

Even worse is if you take the relativistic limit of QFT, you still have the necessity of antiparticles, which is the main point of a paper I have posted a few times:
https://arxiv.org/abs/1712.06605

Actually, there are several different, but equivalent formulations of ordinary QM:
https://faculty1.coloradocollege.edu/~dhilt/hilt44211/AJP_Nine formulations of quantum mechanics.pdf

None are equivalent to the non-relativistic limit of QFT, but interpretation F seems able to incorporate antiparticles the most naturally.

Thanks
Bill

 

[Peter Morgan]

Actually, there are several different, but equivalent formulations of ordinary QM:
https://faculty1.coloradocollege.edu/~dhilt/hilt44211/AJP_Nine formulations of quantum mechanics.pdf

I would add 'Algebraic QM', which can be found in textbook form in https://arxiv.org/abs/1211.5627, by François David, (published as "The formalisms of quantum mechanics", Springer 2015, https://doi.org/10.1007/978-3-319-10539-0 ).
For me algebraic QM holds interest because I think it is a more direct transposition of algebraic QFT to the QM context.
For a briefer presentation in a compendium article, there is also
Landsman N P 2009 "Algebraic quantum mechanics" Compendium of Quantum Physics ed D
Greenberger, K Hentschel and F Weinert (Berlin: Springer), https://doi.org/10.1007/978-3-540-70626-7_3.

Algebraic QM of course cannot be thought to be orthodoxy, but I suppose François David thinks it should be.

 

[A. Neumaier]

Don't worry Ballentine made it to the list.

But his book is nearly as far as possible from the consensus textbook orthodoxy; see the last paragraph of p.20 in Beck's paper!

 

[gentzen]

Don't worry Ballentine made it to the list.

But his book is nearly as far as possible from the consensus textbook orthodoxy; see the last paragraph of p.20 in Beck's paper!

Wow, I had read Ballentine's orthodoxity measure as 0.88, but actually it is -0.88. Which makes total sense to me.

 

[gentzen]

I take the minimal statistical interpretation of QM to be qualitatively different from QFT insofar as there is no idea of a collection of identically prepared systems (an ensemble) in QFT (the second paragraph of the Beck orthodoxy preprint very nearly insists that there must be a concept of a system.)

If you compute the scattering between two incoming particles, or the lifetime of some excited state, then you are looking at a simple physical situation with few degrees of freedom. This is the kind of situation which is normally well described by the idealization of (an ensemble of) identically prepared systems.

OK, you think it is wrong to talk of incoming particles, and instead want to talk of an incoming beam and a target, or of two crossing beams. OK, but the detection events will still be isolated events. So why go to the trouble to avoid talking of incoming particles (or of a system), when the detection will be particle like anyway, and QFT computations themselves have no issues with talking of particles either.

For QFT, there is only a measurement operator associated with a region of space-time & a state over the algebra generated by those measurement operators on the theory side and only a dataset as measurement results on the side of experiment.

What is true is that detection events cannot be correlated to incoming particles, but only to coincident particle detections (in case one is interested in this quasi-particle aspect).
Still, all this is mostly unrelated to the minimal statistical interpretation, so you seem to construct issues and complication where I can see none.

 

[pines-demon]

What was Weinberg take on interpretations? he scores a bit low in orthodoxy.

 

[Peter Morgan]

If you compute the scattering between two incoming particles, or the lifetime of some excited state, then you are looking at a simple physical situation with few degrees of freedom. This is the kind of situation which is normally well described by the idealization of (an ensemble of) identically prepared systems.

Certainly QFT as we have it is effective to an extraordinary degree and I have no problem with discussing asymptotic states, but I think there are alternatives. If one thinks that something very fundamental has to change for us to make progress or even perhaps to understand what we're doing, then my feeling is that hesitating about saying "here is a particle" as an axiom is one possibility. Axiom #1 in QM —at least in all the orthodox QM interpretations— is something like "there are systems and they correspond to Hilbert spaces", whereas algebraic QM & QFT say "no, let's wait a while before we say that". Whether my specific alternatives are useful is another matter, but I'm not the only person trying to rethink QM & QFT, so that's OK, but I feel somewhat encouraged by a data analysis and signal analysis way of thinking having no particle language in the first instance, even while acknowledging that introducing particles as causes of events reduces the computational complexity of the data analysis task.

OK, you think it is wrong to talk of incoming particles, and instead want to talk of an incoming beam and a target, or of two crossing beams. OK, but the detection events will still be isolated events. So why go to the trouble to avoid talking of incoming particles (or of a system), when the detection will be particle like anyway, and QFT computations themselves have no issues with talking of particles either.

Not beams, for me. I've been looking at the math of QFT, particularly as we see it in the Wightman axioms (which is the starting point for perturbative interacting QFTs), where we find that the operator-valued distribution we begin with is not a measurement operator: for measurement operators we have to 'smear' the operator-valued distribution with test functions, $\hat M_f=\int\hat\phi(x)f(x)d^4x$. $f(x)$ is a formal description of what kind of measurement $\hat M_f$ is. Signal analysis has an almost identical idea, called a "window function". For the free ElectroMagnetic field, the math of QFT straightforwardly derives that if we could measure $\hat M_f$ in the vacuum state, with $f(x)$ a real-valued function, the resulting statistics of those EM field measurements would be Gaussian, with the variance being a functional of $f$, $\langle 0|\hat M_f^*\hat M_f|0\rangle$. From this a castle can be built, which despite being non-interacting and all just in the imagination is a different starting point for more imagination.

What is true is that detection events cannot be correlated to incoming particles, but only to coincident particle detections (in case one is interested in this quasi-particle aspect).
Still, all this is mostly unrelated to the minimal statistical interpretation, so you seem to construct issues and complication where I can see none.

Some proportion of the people who see the whole of one of my talks or who read my published articles are intrigued but I think it's true that nobody can see how to use it productively. My bad! I don't know how many people go through my work carefully and regret wasting their time. In any case, nobody has looked at my work, said "let's tell everybody", and been able to make it happen, so I know I'm not getting everything right.
The issues and complications —the two clouds that have been on the horizon for a whole century— that I think this kind of approach allows us to rethink are the measurement and renormalization problems. In particular, I am not aware of any other approach that gets us enough out of the box to make both these problems look significantly different. [I never last long on Physics Forums. I start writing these ridiculous long posts and I usually have to take a six month break after about a week.]

 

[javisot]

TL;DR Summary: based on what a majority textbooks says

Beck, G. (2025). How to be an orthodox quantum mechanic.
https://arxiv.org/abs/2504.20597

From the abstract:

From the conclusion:

A very interesting article. I've been wondering about this for a while.

Personally, I've noticed that physicists sometimes talk about the "textbook," "the consensus in QM," or "the mathematics of QM," referring to a sort of complete, consensual, non-interpretive description of QM, without referring to anything concrete. Something like the average of all QM textbooks.

Is this orthodox and average description truly complete or incomplete? That would be another possible debate. It's been interesting to see some information on this, thanks.

 

[bhobba]

But his book is nearly as far as possible from the consensus textbook orthodoxy; see the last paragraph of p.20 in Beck's paper!

Although well thought of by many, including me, it is not an orthodox approach.

That said, it is the book I recommend studying before seriously looking into interpretations. QM from just two axioms (well, the way Ballintine does it anyway, which is my favourite). And when you add in the second axiom basically follows from the first by Gleason, we are left with the central mystery. Actually, there is more to it, but before embarking on the interpretation journey, taking the time to work it out for yourself is a good warm-up (compare it to the seven axioms posted in the forum). Of course, Ballentine incorporates the statistical interpretation in the textbook.

Thanks
Bill

 

[gentzen]

Some proportion of the people who see the whole of one of my talks or who read my published articles are intrigued but I think it's true that nobody can see how to use it productively. My bad! I don't know how many people go through my work carefully and regret wasting their time. In any case, nobody has looked at my work, said "let's tell everybody", and been able to make it happen, so I know I'm not getting everything right.

That is not the point.
You construct issues and complications for the minimal statistical interpretation where I can see none.
Somehow you seem to have issues with talk of system or particles, and seem to think that those invalidate the minimal statistical interpretation. But that interpretation is much simpler: We have a theory which only predicts probabilities, and the minimal statistical interpretation describes the canonical situation where the classical frequentist interpretation of probability can be used. That's all.

 

[gentzen]

If one thinks that something very fundamental has to change for us to make progress or even perhaps to understand what we're doing, then my feeling is that hesitating about saying "here is a particle" as an axiom is one possibility.

And another possibility it to try to understand what we are doing, currently. Like the article mentioned in the OP.

Or also

David Schmid, Yìlè Yīng, Matthew Leifer (2025). Copenhagenish interpretations of quantum mechanics.
https://arxiv.org/abs/2506.00112

From the abstract:

We define a class of Copenhagenish interpretations encompassing modern interpretations that follow the Copenhagen spirit. These interpretations are characterized by four postulates: Observers Observe, Universality, Anti- -ontology, and Completeness. We explain why such interpretations are not equivalent to the textbook (or orthodox) interpretation, nor to the view that one should shut up and calculate, nor to strict operationalism.

 

[bhobba]

What was Weinberg take on interpretations? he scores a bit low in orthodoxy.

See:



I haven't watched it myself - about to.

It would seem he thinks none are any good. I believe his folk theorem clarifies a great deal.

Added Later:

The Lindblad equation (interesting take):
https://arxiv.org/abs/1204.2016

Thanks
Bill

 

[Peter Morgan]

That is not the point.
You construct issues and complications for the minimal statistical interpretation where I can see none.
Somehow you seem to have issues with talk of system or particles, and seem to think that those invalidate the minimal statistical interpretation. But that interpretation is much simpler: We have a theory which only predicts probabilities, and the minimal statistical interpretation describes the canonical situation where the classical frequentist interpretation of probability can be used. That's all.

I think the distinction is that I see a dataset where you see an ensemble of particles. It would be only a small issue if there were not clouds to worry about and perhaps it is, as you think, not an issue. ¯\_(ツ)_/¯

 

[Peter Morgan]

David Schmid, Yìlè Yīng, Matthew Leifer (2025). Copenhagenish interpretations of quantum mechanics.
https://arxiv.org/abs/2506.00112

I had only seen v1 of that, so thank you for the push.

 

[gentzen]

I think the distinction is that I see a dataset where you see an ensemble of particles.

Why do you think that I see an ensemble of particles? I see an experiment depending on some knobs, that I can repeat as often as I want, and where I can set the knobs different for each repetition, if I want.

The ensemble are those repetitions, not the particles (which may or may not play a role in the experiment).

 

[PeterDonis]

The ensemble are those repetitions

This is how Ballentine presents the statistical interpretation--the ensemble is basically the abstract set of all instances of a given preparation process, what you are calling setting the knobs. There is no claim about the quantum systems being prepared and experimented on having any particular nature ("particles" or "waves" or anything else).

 

[Peter Morgan]

Why do you think that I see an ensemble of particles? I see an experiment depending on some knobs, that I can repeat as often as I want, and where I can set the knobs different for each repetition, if I want.

The ensemble are those repetitions, not the particles (which may or may not play a role in the experiment).

Apologies, I hadn't understood you to be espousing a minimal statistical Interpretation different from that of Ballentine. What you have just described is significantly closer to how I think about QM than I think Ballentine's approach is. I think the standard definition of the word ensemble is that it does refer to an ensemble of systems, as here, https://en.wikipedia.org/wiki/Ensemble_(mathematical_physics), not to an ensemble of repetitions / data without systems as causes of those repetitions or that data.
My understanding has been that Ballentine's position has not changed that much from his position in 1970, say, in his article in Rev Mod Phys, as here, with my emphasis,

I believe that his 1998 book takes the same view.
If you're in favor of a dataset interpretation as something distinct from Ballentine's ensemble interpretation, you might perhaps find at least a few ideas in my most recent talk of interest, “A Dataset & Signal Analysis Interpretation of Quantum Mechanics” (Announcement, YouTube, PDF) Colloquium, School of Engineering and Physical Science, North South University, Dhaka, May 18th, 2025. Nobody likes all of that and nobody could possibly think it's complete, but so far nobody has told me that watching it was a complete waste of their time. I am told by a Yale undergraduate who dived into my work after a research seminar that I gave in Yale Physics on May 1st that this, on May 18th, is the most accessible version. The PDF has links to the published articles on which the talk is based and final preprint versions can be found by straightforward searches on arXiv.

 

[PeterDonis]

Ballentine's position

In his textbook, he gives basically the same description you quoted, but he also says that an equivalent way of looking at the quantum state is as representing an ensemble of preparations all done according to the same preparation process. Since the preparation process is describable in ordinary classical terms, it seems like a better place to anchor the meaning of the quantum state than in a "quantum system" that we can't observe directly anyway.

 

[mad mathematician]

TL;DR Summary: based on what a majority textbooks says

Beck, G. (2025). How to be an orthodox quantum mechanic.
https://arxiv.org/abs/2504.20597

From the abstract:

From the conclusion:

Well being orthodox in Q theory interpretations means usually to adhere to Copenhagen interpretation, as far as I can tell.

 

[Demystifier]

I take the minimal statistical interpretation of QM to be qualitatively different from QFT insofar as there is no idea of a collection of identically prepared systems (an ensemble) in QFT (the second paragraph of the Beck orthodoxy preprint very nearly insists that there must be a concept of a system.) For QFT, there is only a measurement operator associated with a region of space-time & a state over the algebra generated by those measurement operators on the theory side and only a dataset as measurement results on the side of experiment.

I don't think there is any difference between QM and QFT in that sense. You can certainly think of QFT in terms of ensemble, after all Ballentine in his book has a chapter on quantum optics, which is a QFT. More generally, for any interpretation of QM there is a corresponding generalization to QFT.

 

[martinbn]

The quote from the conclusion. This one

To an orthodox quantum mechanic, individual particles exist in wave-like superpositions, when left to their own devices, and assume their observed properties (and appear as particles) when forced to by outside interference. When this happens, the individual particle’s properties are subject to the uncertainty principle as a form of measurement uncertainty and the state is inevitably changed by the uncontrolled disturbance inherent in measurement.

Reads like the typical pop science QM exposition of the wave particle duality.

 

[Demystifier]

The quote from the conclusion. This one

Reads like the typical pop science QM exposition of the wave particle duality.

Pop science QM is written by actual physicists. They give the best explanation they can under the constraint of not using equations. So when a physicist gives such an explanation of QM in a pop science text, that's because he/she thinks it's essentially correct.

 

[martinbn]

Pop science QM is written by actual physicists. They give the best explanation they can under the constraint of not using equations. So when a physicist gives such an explanation of QM in a pop science text, that's because he/she thinks it's essentially correct.

Yeah, right!