How many interpretations of QM do you speak?

[WernerQH]

Category theory is a typical mathematical way to try to avoid classical "preconceptions".

I don't think it is of so much use for physicists. You might be able to check if your concepts are used consistently, but not whether they are appropriate and useful in a particular context. Let me return to the preconceptions that you mentioned: causality and locality.

We have a strong desire to explain things. The correlations in Bell-type experiments are explained "naturally" by a common source that creates photons with opposite polarizations. Crucial in that explanation is the idea that photons do not change their polarization as they travel from the source to the detectors. (Classically it is firmly established that the polarization of a beam of light does not depend on the distance of the detector, leaving aside effects of birefringence and Faraday rotation.) But the violation of Bell's inequalities shows that it is impossible to assign definite polarization states to individual photons. And it is questionable whether polarization can really be called a property of a photon, because the results depend as much on the properties of the detector as on those of the photon. To say the polarization was "measured" is actually misleading. Given only that it was detected by an H-oriented detector, it could have had, with some probability, any other polarization except V. The polarization of a photon is always inferred (really attributed) a posteriori, knowing how it was produced and how it was detected. Of course, classically there exist perfectly polarized beams of light. As EPR said, if "we can predict with certainty [...] then there exists an element of physical reality corresponding to this physical quantity". The classical beam of light seems to be composed of photons all having the same polarization. But in the quantum picture we must not mistake a very special case for the generic case. As @Demystifier emphasized in the other thread, a polarization state refers to an ensemble of photons, not to an individual photon. It is a statistical concept.

Why do we believe in photons? It is because of our metaphysical belief in causality and continuity. We imagine something that travels continuously from the "source" to the "detector", carrying information. But these "objects" lead to contradictions. We can't clearly define their properties, and have long discussions on "entanglement". For me, the obvious conclusion is to reject the idea of those travelling objects. There must be microscopic currents in the source and in the detectors, and these currents exhibit correlations. I don't know how to explain these correlations to someone who insists that physics must be causal and local. But at least QED allows us to describe and predict these correlations.

 

[WernerQH]

In some of the languages (interpretations) there is no measurement problem, but in most of them there is. Personally, I think there is.

I share John Bell's view that the words "system" and "measurement" should not be used in expositions of the fundamentals of quantum theory. I also think that quantum theory is a miscroscopic theory, and that quantum "mechanics" is a misnomer. It suggests that quantum theory is a more general theory that must include classical mechanics as a limiting case. But the idea that a macroscopic object could be at two different places at the same time is too absurd for me to stomach.

 

[jeffn1]

I share John Bell's view that the words "system" and "measurement" should not be used in expositions of the fundamentals of quantum theory. I also think that quantum theory is a miscroscopic theory, and that quantum "mechanics" is a misnomer. It suggests that quantum theory is a more general theory that must include classical mechanics as a limiting case. But the idea that a macroscopic object could be at two different places at the same time is too absurd for me to stomach.

Hobson looks replace the term "measure/measurement" with the term "detect/detection". Hobson's problem, as understand it, is that measurement suggests a key role for a human observer/consciousness etc. Bell's objection seems to be a bit different: one of his objections is that measurement "refers[] to some preexisting property of the object in question." From what I have read, Bell would look to replace the terms "measurement" with the term "experiment". I would think Hobson would view that as a step backward.

 

[Demystifier]

From what I have read, Bell would look to replace the terms "measurement" with the term "experiment".

That's true, but that's not the main issue for Bell. The main issue is that measurement/experiment should not be referred to in the fundamental principles or axioms of a physical theory.

 

[Matterwave]

It is interesting to discuss Bell's "Against Measurement". He clearly thinks "measurement", "observable" (he wants "beable", which is NOT the same thing as observable), "macroscopic", and many other words are too loose for foundations.

But for measurement in particular (and why, I guess, he chose measurement for the title) he is railing against, as @jeffn1 quoted, its additional implication of "there's some real physical property with a value underneath I'm simply revealing". If you apply this reasoning and say realist interpretations must abide by this understanding of "measurements", you immediately run into the no-go result that Bell himself showed was essentially a corollary of Gleason's theorem demanding contextuality (in his paper "On the Problem of Hidden Variables in Quantum Mechanics"). Bell showed an alternative way to get to the same result as the Kochen-Specker theroem (https://en.wikipedia.org/wiki/Kochen–Specker_theorem). No hidden variable theory can reproduce the predictions of quantum mechanics if it is required to assign definite values, regardless of measurement set up (non-contextually), to all quantum mechanical observables (at least for 3 or more state systems).

 

[WernerQH]

From what I have read, Bell would look to replace the terms "measurement" with the term "experiment".

Not quite. He added:

However, the idea that quantum mechanics, our most fundamental physical theory, is exclusively even about the results of experiments would remain disappointing.

"Experiment" is more appropriate than "measurement", because it also includes (state) preparation, and is not assumed to happen "in an instant". It is important to consider an entire process, from beginning to the end. In this respect Consistent Histories provides a useful change of perspective. It is misleading to think of a "system" that is in some definite "state" at every instant -- a stochastic description should be non-markovian. (The time-dependent Schrödinger equation creates the opposite impression. It is not the whole story!)

 

[jeffn1]

Hobson and Bell seem to be using (or more accurately criticizing the use of) the word "measurement" in different contexts. Hobson seems to be referring use of the word in relation to the "collapse" of the wave function. So, he wants to replace it with a term that is less person-centric: "detection". Bell seems to be criticizing it a different context/emphasis, which, frankly I have to read up on a bit.

 

[gentzen]

Hobson seems to be referring use of the word in relation to the "collapse" of the wave function. So, he wants to replace it with a term that is less person-centric: "detection".

I don't think that comparing Hobson to Bell is helpful. As I said before, van Kampen is a more appropriate reference point. Hobson wants to collapse the wavefunction even in scenarios without a sufficiently permanent record of the "results". So he proposes to speak of "to interact at x". If you look at typical semi-empirical calculations, you can see where he is coming from. Maybe this is just the difference between "for all practical purposes" vs "for some practical purposes".

You can look at where Bell criticizes van Kampen to see the most important difference: For van Kampen, if the loss of phase information (for some given time or space separation after the interaction) is severe enough, the use of the Born rule is justified, and "explains" all that needs to be explained. For Bell, without sufficiently permanent records, "disjointness" cannot be explained, and hence "measurement" has not been explained either. Bell believes that van Kampen just made a simple mistake, and cannot understand that he may be unable to appreciate where van Kampen is coming from.

 

[RUTA]

I believe there is a historical precedent: Maxwell's electrodynamics. For more than four decades it was not fully understood. The mathematical equations were there (and highly successful), but people kept trying to understand what this theory actually describes. For them an interpretation of Maxwell's equations meant constructing a mechanical model for the "ether". Today the ether has been replaced by the electromagnetic field, and we have understood that the concept of an ether was fraught with metaphysical preconceptions. I'm convinced that the photon concept (and quantum theory in general) is similarly burdened with metaphysical preconceptions that we haven't yet clearly identified.

In 1996, Rovelli made the same analogy:

[Q]uantum mechanics will cease to look puzzling only when we will be able to derive the formalism of the theory from a set of simple physical assertions ("postulates", "principles") about the world. Therefore, we should not try to append a reasonable interpretation to the quantum mechanics formalism, but rather to derive the formalism from a set of experimentally motivated postulates.

The reasons for exploring such a strategy are illuminated by an obvious historical precedent: special relativity. ... Special relativity is a well understood physical theory, appropriately credited to Einstein’s 1905 celebrated paper. The formal content of special relativity, however, is coded into the Lorentz transformations, written by Lorentz, not by Einstein, and before 1905. So, what was Einstein’s contribution? It was to understand the physical meaning of the Lorentz transformations.

That is, he challenged the foundations of physics community to reconstruct the Hilbert space kinematics of QM like Einstein reconstructed the Lorentz transformation kinematics of Maxwell's equations. Hardy was the first to successfully answer Rovelli's challenge in 2001 with his paper, "Quantum Theory from Five Reasonable Axioms," and the "first fully rigorous, complete reconstructions" were published in 2011 by Chiribella, D'Ariano & Perinotti and by Masanes & Mueller. Silberstein, McDevitt and I completed the quantum reconstruction program in 2022 by justifying the empirically discovered fact whence Hilbert space kinematics (Bohr's "quantum postulate" aka Darrigol's "discreteness requirement" aka Khrennikov's "quantum action invariance principle" aka Brukner & Zeilinger's "Information Invariance & Continuity" aka the observer-independence of h) with the relativity principle exactly like Einstein justified the empirically discovered observer-independence of c whence the Lorentz transformations with the relativity principle. We have published papers (listed in YouTube video) and a book with Oxford UP (Einstein's Entanglement, 2024), but the most up-to-date exposition of this is in my July 2026 talk at IQSA ().

 

[WernerQH]

What is quantum theory about? Is it about quantum objects and measurements performed on them? Or Hilbert spaces? For me the most pressing question is about its ontology, not about a more "coherent" presentation of the formalism.

 

[gentzen]

What is quantum theory about?

Initially, it was a theory like thermodynamics, which described things like specific heat, conductivity, spectroscopic measurements, interactions of molecular beams with electric and magnetic fields, ...
The main difference to a theory like thermodynamics was that it could no longer be interpreted in terms of classical concepts, which became dominant following the successes of Newton's mechanics and its generalizations.
It wasn't the first such theory, special and general relativity had run into trouble with those classical concepts before.

However, Dirac's theory of the electron, the discovery of the positron predicted by it, and the later successes of QFT and particle physics turned it into something more fundamental, at the basic level of everything which exists in our world.

However, there is a paradox: QM as a theory is mathematically consistent and well understood, but it doesn't predict "by itself" the things QFT does. QFT explains and predicts more than QM, but it is "less consistent" than QM, and mathematically still not well understood.

Which raises the question whether "quantum theory" is about those things that QFT talks about.

Is it about quantum objects and measurements performed on them?

QM is about quantum objects that we as the user of the theory are allowed (and required) to define ourselves. It gets validated by how accurately it predicts results of experiments, and explains observable phenomena like specific heat or conductivity (as a function of temperature).

Phenomena like superconductivity are already in the intersection of QM and QFT. QM alone cannot predict it, but once known (from experiments) or predicted by QFT, QM can be used to describe it and work with it.

Or Hilbert spaces?

No, that is not overly important.

For me the most pressing question is about its ontology, not about a more "coherent" presentation of the formalism.

Time works different in QM than it does in QFT. But an ontology without a close connection to time is hard to imagine. So maybe it can make sense to try to understand QM and its possible ontologies (like various variants of BM, CH, MWI, ...) independent of QFT. Finding an ontology for a mathematically consistent theory is normally easier than trying the same for a theory whose consistency is still an open question.

 

[Matterwave]

Bell seems to be criticizing it a different context/emphasis, which, frankly I have to read up on a bit.

His essay "Against Measurement" sums up his views pretty nicely. :)

 

[Matterwave]

No, that is not overly important.

I wonder if you would expand on this. :)

In my (perhaps overly naive) reading, when someone says "Hilbert spaces" in relation to QM they usually mean the full machinery (e.g. including the operator algebra) which leads to the "quantum weirdness". So it would seem to be quite important from that respect as it gives rise to the "difficult to interpret" results. Perhaps you read "Hilbert space" much more narrowly? I am just curious~

 

[gentzen]

I wonder if you would expand on this. :)

I look at the actual predictions, and how they are derived. For example, I was talking about "specific heat" in my answer to WernerQH. If you look at some models for it, like Einstein solid model, Debye model, or Born-von-Kármán-model, you won't find much talk about Hilbert spaces or operator algebras there.

Those model predate Hilbert spaces, but it was unknown whether those models are mathematically consistent, before modern QM got discovered. But what is important is that modern QM is mathematically consistent and well understood, not that Hilbert spaces are used in introductory QM textbooks. Even more so since those textbooks already try to prepare the students to stop obsessing over consistency, as a preparation to widespread semi-empirical methods and QFT.

 

[javisot]

Those model predate Hilbert spaces, but it was unknown whether those models are mathematically consistent, before modern QM got discovered. But what is important is that modern QM is mathematically consistent and well understood, not that Hilbert spaces are used in introductory QM textbooks.

However, what matterwave says is also correct; one way we express that "weirdness" of QM is reflected in that these quantum objects evolve in a Hilbert space, not in a 3+1 dimensional one.

 

[Matterwave]

I look at the actual predictions, and how they are derived. For example, I was talking about "specific heat" in my answer to WernerQH. If you look at some models for it, like Einstein solid model, Debye model, or Born-von-Kármán-model, you won't find much talk about Hilbert spaces or operator algebras there.

I see. So would you say that for you, the phenomenology is the most important part? I can certainly understand that perspective.

But what is important is that modern QM is mathematically consistent and well understood, not that Hilbert spaces are used in introductory QM textbooks.

A lot of the mathematical consistency (rigor? I read this as rigor as well) comes from the Hilbert spaces (and actually, if we are being more specific, Rigged Hilbert spaces) though, doesn't it? For example, for us to say an expression like $\hat{O}|\psi\rangle$ makes sense at all we need to understand the structure of the Hilbert space and the actions of operators on rays in the Hilbert space.

 

[gentzen]

I see. So would you say that for you, the phenomenology is the most important part? I can certainly understand that perspective.

How would you reply to

What is quantum theory about? Is it about quantum objects and measurements performed on them? Or Hilbert spaces? For me the most pressing question is about its ontology, not about a more "coherent" presentation of the formalism.

?

My reply was to distinguish between QM and QFT, and to highlight how QM gets used and verified. QM gets verified by the phenomenology, while QFT gets verified by its predictions of new phenomena (often new particles) and extremely accurate predicted "constants".

Note especially that WernerQH and me talked about quantum objects in this thread, and that he rejects the idea of those objects:

But these "objects" lead to contradictions. We can't clearly define their properties, and have long discussions on "entanglement". For me, the obvious conclusion is to reject the idea of those travelling objects.

The defining feature of those quantum objects in QM was not that they evolve in some space, but that they can be put together by a tensor product to form larger objects. Except that it is a bit more complicated, because Fermions and Bosons are "special". (Looks like putting larger objects together is not as associative as I hoped, when taking care of Fermions and Bosons.)

 

[gentzen]

However, what matterwave says is also correct; one way we express that "weirdness" of QM is reflected in that these quantum objects evolve in a Hilbert space, not in a 3+1 dimensional one.

The Hilbert space is not overly helpful for understanding that weirdness. It is helpful for understanding the trouble with Fermions and Bosons. But when you really want to work with them, after you understood the trouble and are ready to move on, Fock space is more helpful.

Of course, if one insists that Hilbert space implicitly is a placeholder for all those mathematical details, then at some point you can equate me dismissing the importance of Hilbert spaces with me dismissing the importance of all mathematical details.

 

[PeterDonis]

Fock space is more helpful.

Fock space is a Hilbert space.

 

[PeterDonis]

Moderator's note: An off topic subthread has been deleted.

 

[Matterwave]

How would you reply to

What is quantum theory about? Is it about quantum objects and measurements performed on them? Or Hilbert spaces? For me the most pressing question is about its ontology, not about a more "coherent" presentation of the formalism.

My reply would have been quite different than yours, but we all think in different ways! I was interested in your view on "Hilbert space". To be very clear, I have not tried to be critical, I am merely curious.

I suppose that even though my training was always in physics, I tend to gravitate towards the more mathematical side of things.

To answer that specific question, I would probably say:

Quantum theory is about the science of the very small. It is formulated using formalism built on top of Hilbert spaces, but it is not ultimately "about Hilbert spaces". Like any empirical science, Quantum Theory is concerned with making specific predictions that tie to experiment. This forms the main crux of quantum theory but it is not all that quantum theory should be about. The foundations of quantum theory, e.g. the measurement problem, is an important, though difficult, topic.

 

[Lord Jestocost]

What is quantum theory about?

About what we can know and infer from experimentally accessible, physical phenomena.

 

[WernerQH]

QM is about quantum objects that we as the user of the theory are allowed (and required) to define ourselves.

I've been wasting my time! The point I've been trying to make didn't get across -- people just don't heed John Bell's recommendation to ban the word "system" (= "object") from the foundations of quantum theory. :-) It is precisely the use of this word with its unfortunate classical connotations that makes quantum theory appear paradoxical and "weird". If quantum mechanics is hard to understand for most people, then quantum field theory even more so. But I think it's just the other way round: once you've understood what QFT is all about, QM becomes almost obvious. ;-)

Maxwell's ether was paradoxical. The aberration of star light was an established fact and an ether wind the "obvious" consequence. But it failed to show up. The mechanical properties of the ether were paradoxical and hard to reconcile with the familiar physics. The ether became obsolete, once the attention turned to the electromagnetic field. It wasn't really a "mechanical explanation" of how light propagates, but a mere description, based on an abstract creation of Faraday's and Maxwell's minds. But it was so successful that nowadays hardly any physicist hesitates to call the electromagnetic field real.

I believe that QFT becomes easier to understand if it is not viewed as a theory of quantum objects or an abstract quantum field, but rather a statistical theory of localized (microscopic!) events scattered over the arena of spacetime. These events occur in patterns, some of which may resemble particles, others waves. Some of these patterns can be identified as "objects", but their existence is not continuous in time. @Sambuco gave a memorable quote of Schrödinger

In other words we assume—following a habit of thought that applies to palpable objects—that we could have kept our particle under continuous observation, thereby ascertaining its identity. This habit of thought we must dismiss. We must not admit the possibility of continuous observation. Observations are to be regarded as discrete, disconnected events.

and Rovelli wrote

Perhaps the rivers of ink which have been expended discussing the nature of the 'continuous' over the centuries, from Aristotle to Heidegger, have been wasted. Continuity is only a mathematical technique for approximating very finely grained things. The world is subtly discrete, not continuous. The good Lord has not drawn the world with continuous lines: with a light hand, he has sketched it in dots, like Seurat.

To be a bit more specific, using the fluctuation/dissipation theorem the emissivity (in $\rm W\,m^{-3}\,Hz^{-1}\,sr^{-1}$) of a radiating medium can be expressed as a Fourier integral over its current density fluctuations: $$
\epsilon = \frac {\mu_0 \omega^2} {8 \pi^2 c} \sum_{\mu,\nu=1,2,3} e_\mu^* e_\nu \int_{-\infty}^\infty dt \int d^3x \ e^{-i(kx-\omega t)} \langle j_\nu(0,0) j_\mu(x,t) \rangle \quad .
$$ (See, for instance, Landau-Lifshitz vol IX, section 75 on the photon Green's function in a medium.) Classically, current density was thought of as a continuous field. But in quantum statistical physics it is possible to read this as an expectation value of a sum over discrete current pulses. Dividing by $\hbar\omega$ it yields the number of photons emitted per volume and time in a specific direction and frequency interval. Similarly, the absorption coefficient at a particular frequency can be written $$
\kappa = \frac {\mu_0 c} {2 \hbar\omega} \sum_{\mu,\nu=1,2,3} e_\mu^* e_\nu \int_{-\infty}^\infty dt \int d^3x \ e^{-i(kx-\omega t)} \langle j_\mu(x,t) j_\nu(0,0) - j_\nu(0,0) j_\mu(x,t) \rangle \quad .
$$ Multiplied by $c$ this is the rate of absorption processes (minus the rate of stimulated emissions). It is tempting to identify $j_\mu(x,t) j_\nu(0,0)$ as representing an absorption, and $j_\nu(0,0) j_\mu(x,t)$ an emission process. It is noteworthy that a photon is not created in an instant. Between times $0$ and $t$ the photon is "in limbo". This seems to be what Barandes calls indivisible or non-markovian dynamics. (Modelling quantum phenomena as stochastic processes is an excellent idea, but unfortunately Barandes spoils it by introducing "trajectories" in configuration space. Does Barandes work count as a QM interpretion? I don't think so.)

@Demystifier - sorry for drifting away from this thread's original topic.

 

[Matterwave]

About what we can know and infer from experimentally accessible, physical phenomena.

How does this answer distinguish quantum theory from any other empirical science?

 

[Demystifier]

@Demystifier - sorry for drifting away from this thread's original topic.

No problem, it's a natural organic development often ocurring in many threads.