How many interpretations of QM do you speak?

[Sambuco]

No, the quantum field and the wave function are not related like this for Hobson. The non-relativistic wave function is not considered as "real" by Hobson.

In section III.B of this paper, he said:

"The Schroedinger field is the non-relativistic version of the Dirac equation's relativistic field. It follows that the Schroedinger matter field, the analogue of the classical EM field, is a physical, space-filling field. Just like the Dirac field, this field is the electron."

Lucas.

 

[Morbert]

- Consistent histories (@Morbert, Where should I start?).

The best places to start are

https://quantum.phys.cmu.edu/CQT/

https://press.princeton.edu/books/hardcover/9780691004358/understanding-quantum-mechanics

 

[gentzen]

"The Schroedinger field is the non-relativistic version of the Dirac equation's relativistic field. It follows that the Schroedinger matter field, the analogue of the classical EM field, is a physical, space-filling field. Just like the Dirac field, this field is the electron."

I read this as a statement about the relation between to the non-QFT single particle Dirac equation, and the non-QFT single particle Schroedinger equation. And as a (true) statement about second quantization in the wider context of that paragraph.

It is not a claim that the n-particle wave function occuring in non-relativistic QM would be "real".

 

[PeterDonis]

It follows that the Schroedinger matter field, the analogue of the classical EM field, is a physical, space-filling field.

The problem with this is that the term "space-filling" can't possibly be right, except for the obviously unphysical case of a single spinless quantum system alone in the universe. The "Schrodinger field" for any system more complicated than that is not a function on ordinary 3-dimensional space; it's a function on the configuration space of the system. For 3N spinless "particles", for example, this is a function on a 3N-dimensional space. So whatever the "Schrodinger field" is, it can't be interpreted the way the classical EM field is interpreted.

 

[Sambuco]

I read this as a statement about the relation between to the non-QFT single particle Dirac equation, and the non-QFT single particle Schroedinger equation. And as a (true) statement about second quantization in the wider context of that paragraph.

It is not a claim that the n-particle wave function occuring in non-relativistic QM would be "real".

It seems he is trying to say something like that, but it is really confusing. Indeed, in the conclusions, he says:

"Thus Schroedinger's Ψ(x,t) is a spatially extended field representing the amplitude for an electron (i.e. the electron-positron field) to interact at x rather than an amplitude for finding, upon measurement, a particle. In fact, the field Ψ(x,t) is the so-called "particle." Fields are all there is."

I suppose that could be interpreted the way you say, although it would be good for Hobson to consider cases where things aren't so simple, since, as @PeterDonis said in post #34, everything becomes complicated when there is more than one particle.

Lucas.

 

[gentzen]

Thus Schroedinger's Ψ(x,t) is a spatially extended field representing the amplitude for an electron (i.e. the electron-positron field) to interact at x rather than an amplitude for finding, upon measurement, a particle.

Yes, that is how one has to use QM as an instrumentalist in practical computations. This is the trouble with the word "measurement". However, what PeterDonis dislikes about this "to interact at x" interpretation is that you have to consider superpositions of such "to interact at x" events at some point (just like in MWI).

(Simple example: The electron interacts with the valence electrons in a crystal, and can cause ionization events. But the secondary electrons "created" during those ionization events can interfere with other secondary electrons that could have been "created". Not an overly important effect, but still a measurable effect.)

Also, the update after that "interaction at x" of the electron wavefunction is not really obvious. One can work out how it should be done, but it remains instrumentalism, or "let me calculate and explain". Not really "shut up and calculate" if you ask me, because what you should calculate is not obvious without explanations.

 

[PeterDonis]

what PeterDonis dislikes about this "to interact at x" interpretation is that you have to consider superpositions of such "to interact at x" events at some point

No, that's not what I was saying. What I was saying is that as soon as you have more than one spinless particle, the wave function is not a function of $x$, if $x$ is interpreted as a position in ordinary space. It's a function on configuration space, which is a 3N-dimensional space--for two spinless particles, it's a 6 dimensional space, 3 dimensions for each particle. In terms of "particle positions", for two spinless particles it's a function of two positions--the position of each of the two particles. Even a single such function, not a "superposition" of anything, is still not a function of "position" in ordinary space.

 

[Nugatory]

It's a symptom, indicating that we haven't yet found a natural interpretation

There remains the (rather discouraging) possibility that there is no natural interpretation.

 

[Sambuco]

(Simple example: The electron interacts with the valence electrons in a crystal, and can cause ionization events. But the secondary electrons "created" during those ionization events can interfere with other secondary electrons that could have been "created". Not an overly important effect, but still a measurable effect.)

Incidentally, I find this topic particularly interesting because part of my work involves developing models for total dose in MOSFETs, and the charge generation stage is always modeled using semi-empirical expressions.

Lucas.

 

[Demystifier]

In section III.B of this paper, he said:

"The Schroedinger field is the non-relativistic version of the Dirac equation's relativistic field. It follows that the Schroedinger matter field, the analogue of the classical EM field, is a physical, space-filling field. Just like the Dirac field, this field is the electron."

Lucas.

It's not clear what it means that the Dirac field is "physical", given that this field operator is not self-adjoint, so it is not even an observable.

 

[martinbn]

It's not clear what it means that the Dirac field is "physical", given that this field operator is not self-adjoint, so it is not even an observable.

To me it is clear. It represents a physical object, the field. On the other hand an observble cannot be real in this sense, it only represents some property of something that is real.

 

[Demystifier]

It represents a physical object

So "physical" means that it represents a physical object? But isn't it circular, given that you didn't say what "physical object" means?

 

[Matterwave]

"Thus Schroedinger's Ψ(x,t) is a spatially extended field representing the amplitude for an electron (i.e. the electron-positron field) to interact at x rather than an amplitude for finding, upon measurement, a particle. In fact, the field Ψ(x,t) is the so-called "particle." Fields are all there is."

It seems to me that the two instances of word "field" here are different mathematical objects.

In section III.B Hobson writes:

“Fields are all there is” suggests beginning the quantum theory of matter from Schroedinger’s equation, which mathematically is a field equation similar to Maxwell’s field equations, and quantizing it. ... Dirac invented, for just this purpose, a covariant generalization of Schroedinger’s equation for the field $\Psi(x,t)$ associated with a single electron. ... The resulting quantized matter field $\Psi_{op}(x,t)$ is called the “electron-positron field.” It’s an operator-valued field operating in the anti-symmetric Fock space.

But then surely Hobson knows that the (single particle, spinless) (Schroedinger) wave function (which Hobson calls a field), dressed in QFT language, is actually:

$$\psi_1(x) = \langle 0 | a(x) | \Psi_1\rangle$$

(See eqn 4.66 in https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=3211&context=physics_facpub)

Here, the $a(x)$ are the operator-valued fields which would be identified as "the fields" in section III.B of Hobson. Then in the conclusion, Hobson is switching to identifying the $\psi_1(x)$ as the "spatially extended field". (Some translation has to be done from Hobson's notation to Torre's)

In a multiparticle context (where you can see @PeterDonis objection very clearly) the (Schroedinger) wave function looks like:

$$\psi(x_1, x_2, ..., x_n) = \frac{1}{\sqrt{n!}}\langle 0 | a(x_1)a(x_2)...a(x_n)|\Psi\rangle$$

So, firstly, it's clear that $\psi$ is no longer a function in space, but a function on configuration space and secondly, on the right hand side, there's $n$ instances of the operator-valued fields $a$ (not to mention they get sandwiched between Fock states).

Which thing in the above equation does Hobson want to make the "physically real field"? It's not clear to me if this is an oversight from Hobson or if he's using this vagueness for rhetorical effect.

 

[martinbn]

So "physical" means that it represents a physical object? But isn't it circular, given that you didn't say what "physical object" means?

Anything that exists objectively out there (in space and time) and interacts with other such things. Or whatever the exact formulation in philosophy is.

 

[gentzen]

It's not clear what it means that the Dirac field is "physical", given that this field operator is not self-adjoint, so it is not even an observable.

If you haven't tried before to make sense of Art Hobson's claim, starting from an isolated quote from one of his papers is not a good idea. Especially not if those quotes were selected by Sambuco/Lucas to highlight his confusion.

Those "there is nothing special here to see" beliefs a la van Kampen typically come from people who know how to use QM or even QFT in an instrumentistic way to arrive at feasible computations that allow comparison to experiment after fitting of "some" unknown parameters. Typically this even comes with the belief that those parameters should in principle be computable from first principles, but the programs one can use for doing that themselves have semi-empirical stuff in them all over the place. Not because it would be unavoidable, but because that is how one ends up with feasible computations.

 

[Demystifier]

I think Art Hobson wants to get rid of the so called "wave-particle duality". Insisting that fields are more fundamental than particles is indeed a reasonable way towards this goal, but he seems to be wrong in thinking that "wave-particle duality" is the only conceptual problem in quantum foundations.

 

[WernerQH]

Quantum "objects" are neither waves nor particles. But what are they? In my view, the biggest conceptual hurdle is that we think of the world as composed of objects (which is of course natural in the classical world that we perceive).

 

[martinbn]

Quantum "objects" are neither waves nor particles. But what are they? In my view, the biggest conceptual hurdle is that we think of the world as composed of objects (which is of course natural in the classical world that we perceive).

That is a strange question! What do you expect as an answer? If the quantum fields are the fundamental building blocks, you cannot describe them in terms of anything else more fundamental. No particles nor waves will help you. You use them, the quantum fields, to describe everything else.

 

[gentzen]

Quantum "objects" are neither waves nor particles. But what are they?

They are objects in a suitable compact closed category. Especially, there exists a tensor product from the underlying monoidal category (or tensor category), which allows to put together different objects.

Great, so we can put together the photon field, the electron-positron field, the quark field, the Higgs field, the neutrino field, ... into one bigger object.

Yeah, but often we would like to just have single electrons or protons as objects, and put those together with the tensor product. This works "a bit" in non-relativistic QM. The Bohmians worked out that it actually works really well and much better than one would have expected.

The Bohmians didn't succeed to make it work equally well for QFT. This indicates to me that there is a "conceptual hurdle" here, similar to what you suggest:

In my view, the biggest conceptual hurdle is that we think of the world as composed of objects (which is of course natural in the classical world that we perceive).

However, my guess is rather that the hurdle is our unwillingness to have processes which change the number or nature of the involved objects. This unwillingness comes from our classical conception of time as a continuum, together with the expectation that the objects evolve continuously as a function of time. This creates a topological hurdle to change the number or nature of the involved objects.

Once we allow the number or nature of the involved objects to change, we are faced with the task of finding a suitable generalization of unitary processes. Surprisingly, a suitable notion of causality turns out to work best, at least if we are willing to live with the consequence that this breaks time symmetry.

 

[Sambuco]

Those "there is nothing special here to see" beliefs a la van Kampen typically come from people who know how to use QM or even QFT in an instrumentistic way to arrive at feasible computations that allow comparison to experiment after fitting of "some" unknown parameters. Typically this even comes with the belief that those parameters should in principle be computable from first principles, but the programs one can use for doing that themselves have semi-empirical stuff in them all over the place. Not because it would be unavoidable, but because that is how one ends up with feasible computations.

You have described my daily routine (well, except for the quantum field theory part), but I must say I do not share a stance like van Kampen’s. My "problem" with Hobson’s work is that it seems to me as very imprecise. I get the impression that he is attempting to get rid of a problematic notion of particles through a field-only approach, yet without adopting a specific interpretation (many-worlds, hidden variables, objective collapse, and so on). To do so, he posits the existence of a spatially distributed field. The proposal itself is certainly interesting, but two issues arise: first, the problem he seeks to solve does not exist in any of the standard interpretations, so that his proposal addresses a problem that exists only because he fails to tackle the central issue (the measurement problem). Second, by not assuming a definite ontology, his concept of a field becomes ambiguous: at times he speaks of the "Schrödinger field", which is valid in real space only for a single, non-entangled particle, while later mentioning the "electron-positron field," the quantum version of which is an operator-valued field. He also draws analogies to the classical electromagnetic field that do not hold true in general terms. In my opinion, he should provide a clear description of what he is referring to when he speaks of a field located in physical space.

Lucas.

 

[Sambuco]

In my view, the biggest conceptual hurdle is that we think of the world as composed of objects (which is of course natural in the classical world that we perceive).

This unwillingness comes from our classical conception of time as a continuum, together with the expectation that the objects evolve continuously as a function of time.

I fully agree with both of you. In fact, that line of thought is what leads me to interpretations like RQM.

Lucas.

 

[Paul Colby]

My fluency hovers somewhere between 0.5 and 0.75 Copenhagen Interpretations.

 

[gentzen]

Which interpretations are you familiar with, and at which level?

I am familiar with instrumentalistic interpretations of QM, including orthodox QM, "let me calculate and explain", and to a certain extend also "shut up and calculate". I have an advanced understanding of how density matrices arise, how to work with them, including various ways to get back to pure states again.
I can compute, in non-relativistic QM, in Fock-space multi-particle QM in second quantization, but not really in QFT. I know how some topics relevant for my daily work (like the random-phase-approximation) look in perturbative Feynman diagram QFT.
I have some feeling for when people of various backgrounds will start to protest, but have not yet found a good way to handle those protest. This is also an important aspect of "let me calculate" occuring in instrumentalistic interpretations.

I am a proponent of the consistent histories interpretation. I accept that it is an incomplete interpretation, that one can still improve it to make it a bit more complete, but that some of its issues will most likely stay as they are for a very long time. My current research in CH consists of testing "paid pro LLM models" on my proposed entropy bound. However, neither me nor Claude Opus is brave enough to directly aim for a full proof, instead focusing on consolidating achievable intermediary results and understanding.

After I understood CH good enough, I was very motivated to better understand Bohmian mechanics, to understand how it treats some of the points where CH is weak. I am not a Bohmian, and am sceptical of Bohmians who believe too much in John Bell. Lev Vaidman's perspective on BM is less biased, but even he tries to stay too close to the "wishes" of those Bohmians. For me, both CH and BM are toy models, and I can benefit the most from them when I try to reconcile what they do with instrumentalistic interpretations. Especially, neither demoting the wave function completely to merely nomological status, nor elevating it to a wave function of the universe a la MWI is helpful for an instrumentalist like me. What the instrumentalist needs is a conditional density matrix of the quantum subsystem under investigation.

OK, finally I have to talk about the thermal interpretation. The TI goes beyond the density matrix, instead working directly with the q-expectations encoded in it, and also basing the interpretation on those q-expectations. That von Neumann-algebra or generalized probability theory perspective is not easy. At some point I understood why it was important to define q-expectations also for non-self-adjoint operators. So this "people of various backgrounds will start to protest" problem gets much worse, so one goes back to first work-out the instrumentalistic perspective on the density matrix "nicely".

And finally the reason why I decided to write this post, namely as participant in the Applied Category Theory Munich Meetup I read

2024-12-12	Bob Coecke and Aleks Kissinger, Picturing Quantum Processes, Chapter 5.
2024-11-14	Bob Coecke and Aleks Kissinger, Picturing Quantum Processes, Chapter 4.
2024-10-17	Bob Coecke, Kindergarten Quantum Mechanics

and also continued my study of Bob Coecke's work later on my own. (https://en.wikipedia.org/wiki/Categorical_quantum_mechanics could have been a nice link for my previous post, but I am only familiar with Bob Coecke's work.)

Oh well, maybe I would also have to mention my study of N David Mermin both for QM interpretations and quantum computing (and also for ... many other physics topics). I am a Mermin fanboy. My knowledge of quantum computing hardware and theory also influences my perspectives on interpretation of QM, especially concerning the role of locality (yes, QM is local in a suitable sense) and entropy.

 

[WernerQH]

They are objects in a suitable compact closed category. Especially, there exists a tensor product from the underlying monoidal category (or tensor category), which allows to put together different objects.

Thanks, but this isn't at all what I had in mind. I wanted a physical answer, but anticipated that nothing satisfactory would be forthcoming. Yes, "What are they?" was a rhetorical question. I think that "objects" are not a very useful category in the microcosmos, something which we simply imposed from our experiences in the classical world. We just assume that the objects of everyday life are composed of smaller objects.

However, my guess is rather that the hurdle is our unwillingness to have processes which change the number or nature of the involved objects.

I don't understand what kind of unwillingness you have in mind. I feel comfortable with processes like absorption or emission of photons.

This unwillingness comes from our classical conception of time as a continuum, together with the expectation that the objects evolve continuously as a function of time.

Perfect! That's the classical preconception, the "expectation that objects evolve continuously as a function of time" that I think is unwarranted. There's more to quantum theory than Schrödinger's equation (unitary evolution).

Once we allow the number or nature of the involved objects to change, we are faced with the task of finding a suitable generalization of unitary processes. Surprisingly, a suitable notion of causality turns out to work best, at least if we are willing to live with the consequence that this breaks time symmetry.

I'm not sure what you are hinting at. For me these "objects" aren't real, only their interaction events are. Photons and electrons enter QED as correlation functions ("propagators"). They help us describe the correlations between microscopic events. QED is a machinery for calculating correlation functions. The vertices in a Feynman diagram can be connected in multiple ways, and all possible diagrams have to be evaluated and added to arrive at a probability (amplitude) of a particular pattern of events. Electrons are identical, which means there is no fact of the matter that "this" electron emitted the photon absorbed by "that" electron. The lines in Feynman diagrams do not represent real objects, but are just an aid to calculations. If only interactions of photons and electrons are real, if photons and and electrons are derived from a more basic substrate (discrete events), then gauge theory could even become more intuitive: a change of gauge affects both the electron's and the photon's wave function.

To summarize: for me "objects" are just patterns of microscopic events in spacetime. I think of the world-line of an electron not as continuous, but as a dotted line (on a time scale of $\hbar/mc^2 \sim 10^{-21}\ \rm s$).

 

[WernerQH]

his proposal addresses a problem that exists only because he fails to tackle the central issue (the measurement problem)

@Demystifier -- is there a measurement problem? Is a language (interpretation) in which "measurement" (let alone a "measurement problem") cannot even be formulated, defective or superior? Or does your polyglot stance allow you to remain agnostic? There is and there is not a measurement problem? ;-)

 

[gentzen]

I'm not sure what you are hinting at.

I am hinting at

But still, if Bohr's "claim of causality" has really such a simple interpretation, then he has essentially given up on causality. On the other hand, Heisenberg always defended QM for still respecting causality, if the fundamental limitations of our knowledge (imposed by QM) are properly taken into account.
Let me repeat here, what I learned recently about "Bob Coecke's" causality postulate:

I did research time-symmetric and retrocausal type interpretations quite intensely. I also studied "Picturing Quantum Processes" by Bob Coecke and Aleks Kissinger, because the calculus looks nicely time-symmetric too. Luckily for me, it turns out that Bob Coecke (et al?) found out how that time-symmetry gets broken (I think I know how to apply this "solution" to Consistent Histories): By "his" causality postulate:

So, we can more fundamentally interpret the causality equation as follows:
If a state is discarded, it may as well never have existed.

We can also interpret (6.32) directly:
If the output of a process is discarded, it may as well have never happened.
which is a straight generalisation of the interpretation we gave for causal states in Section 6.2.3.

We motivated causality with this motto:
if the output of a process is discarded, it may as well have never happened.
... (6.55)
This also means that if a processes is happening somewhere else, and its output never reaches us, we don’t need to care about it. As we already noted, this is crucial to being able to even do science, in that it allows us to safely ignore parts of the universe that won’t affect us.

Thus, the causality postulate (6.64) for a generic process guarantees that:
probabilities can be consistently assigned to branches.

Definition 8.8 is just a minor update to our original slogan for causality:
If we discard/delete all of the quantum/classical outputs
of a quantum process, it may as well have never happened.
Thus we have succeeded (as promised) in extending the interpretation of causality for quantum maps of Section 6.2.4, to quantum processes which may also involve classical inputs and outputs.

(I know I should make screenshots from his book to show just how seamless and natural that postulate works. In the meantime, I also tried to find out where he first published "his" causality postulate. I learned that it is actually not "his" postulate, but from Chiribella et al: the postulate itself in 2009, and the realization that this is actually "the causality postulate" in 2010.)

or a bit more compact at

The point of Englert is that Bell's theorem only applies to theories "similar to Bohmian mechanics" in suitable ways:
[...]
In such theories, it makes sense to think about locality in the way Bell did.

However, you should not ignore that in quantum theory, different ways to think about locality or causality might be more appropriate. Here is an example, how such a more appropriate way can look like:

10.2.1 Causality​

Causality is an extremely important postulate for quantum theory which nevertheless has an extremely simple interpretation:

If the output of a process is discarded, it may as well have never happened.​

10.4 Historical notes and references​

[...]
Causality, although it plays a very central role in this book, was the last one to enter the picture. Its importance became clear from the information theoretic axiomatization of Chiribella et al. (2010, 2011).

Chiribella, G., D’Ariano, G. M., and Perinotti, P. 2010. Probabilistic theories with purification. Physical Review A, 81(6), 062348.
Chiribella, G., D’Ariano, G. M., and Perinotti, P. 2011. Informational derivation of quantum theory. Physical Review A, 84(1), 012311.

From
Coecke B, Kissinger A. Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press; 2017.

 

[gentzen]

I'm not sure what you are hinting at. For me these "objects" aren't real, only their interaction events are.

In Picturing Quantum Processes, what is real are processes. The objects are where processes start and end. Your interaction events would be processes too, if you don't insist that they have to happen at a precise point in time (or rather even a precise point in spacetime).

However, objects are not "unreal" either, and you still have to decide for yourself which processes or division of a process into subprocesses should be real, and which are just a convenient calculational intermediate representation. So PQP doesn't really help too much with ontology. But it definitvely helps with causality and locality.

 

[WernerQH]

I was curious and looked at "Picturing Quantum Processes" a while ago. But it doesn't appeal to me. (Maybe because I'm definitely not an instrumentalist. Rather a realist.) I think of QFT as a microscopic theory, and Feynman diagrams as a more direct way of "picturing quantum processes".

So PQP doesn't really help too much with ontology. But it definitvely helps with causality and locality.

I think of QFT as definitely non-local, and of causality as a classical "preconception", because we "know" that time only evolves forward.

 

[gentzen]

I think of QFT as definitely non-local, and of causality as a classical "preconception", because we "know" that time only evolves forward.

Some form of locality is needed for being able to even do science:

This also means that if a processes is happening somewhere else, and its output never reaches us, we don’t need to care about it. As we already noted, this is crucial to being able to even do science, in that it allows us to safely ignore parts of the universe that won’t affect us.

I have not yet thought about whether that causality condition "If the output of a process is discarded, it may as well have never happened." implies that time only evolves forward. Probably not, because there are those cups and caps processes in PQP, and the causality condition doesn't really forbid them.

I was curious and looked at "Picturing Quantum Processes" a while ago. But it doesn't appeal to me. (Maybe because I'm definitely not an instrumentalist. Rather a realist.)

Of course it doesn't appeal to you. It doesn't appeal to me either:

Concerning 17, today I watched/read Basic ZX-calculus for students and professionals. I wanted to understand how Bob Coecke encoded both classical and quantum information in the same diagram-calculus, by using doubled diagrams for one of them. But I didn’t want to have to read his 900+ pages book Picturing Quantum Processes.
[...] try to understand where Bob Coecke arrived at with his stuff. I think I understand it better now, but I still don’t understand quantum information.

Here 17 was

17. Quantum physics, which turns 100 this year, is arguably the most metaphysical of all empirical discoveries. It’s worthy of returning to again and again in life, asking: but how could the world be that way? Is there a different angle that we missed?

And his ZX-calculus doesn't even stay in the physical quantum processes "subspace" of his category. It encodes arbitrary linear maps, and the proof that it does so makes it clear why this was hard to avoid. It is the causality condition which enforced physical quantum processes.

(Category theory is a typical mathematical way to try to avoid classical "preconceptions". It has its own rules, but can nevertheless represent most of mathematics. So you have a consistent context to work in, but you are not restricted to the typical classical ontologies. That is why I bring it up, when Scott raises his 17, or you raise your "similarly burdened with metaphysical preconceptions that we haven't yet clearly identified" or your "In my view, the biggest conceptual hurdle is that we think of the world as ...". And I always bring it up as those "compact closed category", because that is the part where our intuition "starts to protest". It really wants our world to be described by a "cartesian closed category".)

 

[Demystifier]

@Demystifier -- is there a measurement problem? Is a language (interpretation) in which "measurement" (let alone a "measurement problem") cannot even be formulated, defective or superior? Or does your polyglot stance allow you to remain agnostic? There is and there is not a measurement problem? ;-)

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