Particle vs Wave Interpretations of QM

[Demystifier]

But those questions were not meaningless like these.

That's subjective.

 

[martinbn]

That's subjective.

You don't think that this question is meaningless?!

Is the Moon itself the same thing as its wave function?

 

[Demystifier]

You don't think that this question is meaningless?!

No. Its meaning becomes very clear in specific quantum interpretations such as Bohmian mechanics and many worlds.

 

[Matterwave]

I didn't mean to derail the conversation with a cheeky reference to the moon lol.

But for the record, I am staunchly against the "these questions are meaningless" view.

It was indeed Einstein's rhetorical device to use the moon as an example, but the underlying question is valid. Where does the cut (sometimes called the Heisenberg cut or Von Neumann cut) between microscopic (QM) and macroscopic (Classical) exist? And therefore what constitutes a measurement?

Such questions have led to quite fruitful results in decoherence. See e.g. the original seminal paper from Zeh: https://www.math.tecnico.ulisboa.pt/~jnatar/nonarxivpapers/Zeh_1970.pdf?hl=en-US

 

[gentzen]

I tried reading your post a few times, but I wasn't able to understand your objection in a very precise and clear way. When you say "this" is a mistake, and "this" would be an assumption. What exactly are you referring to with "this"?

I see that you bolded "any time" and "to any desired accuracy" in the earlier quote. Am I to understand that those two are your objections?

If so, could you clarify why you object to "any time"?

What Tumulka implicitly claims by writing "any time" is that you can have a system evolving normally, and you can decide a specific time where you want to know one (or more?) particle positions, to within an accuracy you also decide beforehand, and then you do a measurement that will give you that information.

This is not what we actually experience in the world around us. Hence it is not helpful for connecting the mathematics of BM to our experiences, which is one of the jobs of an interpretation.

For "any desired accuracy" this is true of the standard QM formalism. Ignoring practical experimental considerations and just looking at the pure formalism, you may measure q to any desired accuracy. The Heisenberg uncertainty relations only come into effect when you consider q and p simultaneously.

You have not even defined yet what "measurement" should mean in BM. Therefore, ignoring practical experimental considerations is not a wise first move.

I would like to understand the lack of conceptual clarity that you see.

What is the role of the wavefunction in BM, and what is the role of the trajectories? The claim that the trajectories are directly observable is neither in agreement with our experience, nor does it provide the missing conceptual clarity.

I see nothing wrong in any of the quotes you provided. I agree with both Tumulka and Bell that calling Bohmian mechanics a hidden variables theory is a quirk of history.

And this missing conceptual clarity was Bell's fault, not an omission by Bohm. Bohm discussed with Pauli, Einstein, de Broglie, and others, so what he wrote made sense in its own context. But who was Bell's opponent, when he made those remarks? Rudolf Peierls? Not for this specific point. He could have asked David Bohm, or Basil Hiley, or ... Shimony, Horne & Clauser? But he did not.
Roderich Tumulka on the other hand just spelled out this mistake explicitly, probably in order to increase clarity. And it does increase clarity, because it becomes easier to see that this is actually a mistake.

And that the particle positions are in fact the observed quantities so they are not hidden in that sense.

I really like Demystifier's clarification of this point:

Bohmian mechanics (BM) is a hidden variable theory in the following senses:
(1) It claims that something observable (the particle position) has a value even when it is not observed.
(2) In practice you never directly observe a position of a macroscopic particle such as electron. All you directly observe is an aggregate position of a macroscopic object, typically the position of the pointer of a macroscopic measuring apparatus.

(I am not against BM. I do think it is valuable, not least because it helps to nail-down certain issues, confusions, and mistakes.)

 

[PeterDonis]

This is not what we actually experience in the world around us.

It isn't? Don't we make measurements all the time that work basically the way you describe?

The claim that the trajectories are directly observable is neither in agreement with our experience

If you qualify this as "trajectories of individual quantum particles", I would agree with it, but it's weaker claim than the claim I quoted at the top of this post.

 

[gentzen]

It isn't? Don't we make measurements all the time that work basically the way you describe?

No, we don't measure near instantaneous particle positions for arbitrarily evolving quantum systems. And we also don't measure positions to an accuracy determined by our "means of measurement" alone, independent of the measured situation.

If you qualify this as "trajectories of individual quantum particles", I would agree with it, but it's weaker claim than the claim I quoted at the top of this post.

I don't think that Tumulka has the entire "trajectory" in mind, so I don't want to qualify beyond an isolated position (at a prescripted time) on the trajectory of an "individual quantum particle".

 

[PeterDonis]

we don't measure near instantaneous particle positions for arbitrarily evolving quantum systems.

I don't know what you mean by this. In order to measure any quantum system, we have to have some knowledge of what it's doing.

we also don't measure positions to an accuracy determined by our "means of measurement" alone, independent of the measured situation.

I don't know what this means either, or why it's relevant to the discussion.

I don't think that Tumulka has the entire "trajectory" in mind, so I don't want to qualify beyond an isolated position (at a prescripted time) on the trajectory of an "individual quantum particle".

I don't get this at all. An isolated position is not a trajectory. A trajectory is a continuous curve of such positions. It doesn't have to cover the entire history of the particle, but it does have to cover at least some portion of it beyond one isolated position.

Is there any literature reference that explains the points you're trying to make here?

 

[PeterDonis]

In practice you never directly observe a position of a macroscopic particle such as electron. All you directly observe is an aggregate position of a macroscopic object

Not necessarily. A spot on a detector screen showing the location of a particle impact, while it does have a finite size, is not something I'd describe as "an aggregate position of a macroscopic object", like a pointer. The spot is a pretty direct measurement of the position of the particle when it hit the detector, just with a finite resolution that depends on the "pixel size" of the detector screen.

 

[renormalize]

(2) In practice you never directly observe a position of a macroscopic particle such as electron. All you directly observe is an aggregate position of a macroscopic object, typically the position of the pointer of a macroscopic measuring apparatus.

Did you mean to say "a microscopic particle such as electron"? Even so, I don't understand your comment about only observing "an aggregate position of a macroscopic object". Doesn't a bubble-chamber photo represent a detailed record over time of the actual positions of moving elementary particles?

(https://cds.cern.ch/record/39469)

 

[Matterwave]

I should first make a few disclaimers

1. I am no expert on Bohmian mechanics. Indeed I have not read Bohm's book on the subject. My knowledge comes from the occasional lecture I've seen on the subject.
2. I am no Bohmian. It seems to me that due to gross non-locality, people have really struggled to make BM compatible with relativity which blocks its success.

I apologize if I get the arguments wrong.

You have not even defined yet what "measurement" should mean in BM. Therefore, ignoring practical experimental considerations is not a wise first move.

My comment that you were referring to here was based on standard QM and had no relation to BM.

What is the role of the wavefunction in BM, and what is the role of the trajectories?

The wave function guides the trajectories via the guidance equation. The role of the trajectories is the same as that of standard classical mechanics.

The claim that the trajectories are directly observable is neither in agreement with our experience, nor does it provide the missing conceptual clarity.

I am quite confused by this. Isn't it our most common experience with physics that it gives us a description of how matter moves (a.k.a. trajectories)? Why would real trajectories existing be in disagreement with experience?

Bohmian Mechanics tells us that particle trajectories are real just like trajectories in Classical Mechanics are real, they are just guided by the wave function.

The randomness of QM is pushed to the same level as randomness in Statistical Mechanics or Stochastic Mechanics. I.e. it is due to uncertainties in initial conditions. Conceptually this seems very clear to me.

Perhaps I still don't understand your objections clearly enough.

 

[Demystifier]

Not necessarily. A spot on a detector screen showing the location of a particle impact, while it does have a finite size, is not something I'd describe as "an aggregate position of a macroscopic object", like a pointer. The spot is a pretty direct measurement of the position of the particle when it hit the detector, just with a finite resolution that depends on the "pixel size" of the detector screen.

But you see the pixel, not the particle. The pixel is not the particle.

 

[Demystifier]

Did you mean to say "a microscopic particle such as electron"? Even so, I don't understand your comment about only observing "an aggregate position of a macroscopic object". Doesn't a bubble-chamber photo represent a detailed record over time of the actual positions of moving elementary particles?
View attachment 373100
(https://cds.cern.ch/record/39469)

Of course, I meant "microscopic particle such as electron". Thanks for noting the typo!

The trace we see in the bubble chamber is an aggregate of many small bubbles (about 0.1 mm each), and each bubble is an aggregate of many ($10^{12}$ or more) microscopic atoms. So what we see directly is a macroscopic object, an aggregate of many atoms. The aggregation was caused by travel of the charged elementary particle, but what we see is not the elementary particle itself.

 

[renormalize]

The trace we see in the bubble chamber is an aggregate of many small bubbles (about 0.1 mm each), and each bubble is an aggregate of many ($10^{12}$ or more) microscopic atoms. So what we see directly is a macroscopic object, an aggregate of many atoms.

True, but that's not a fundamental limitation. Instead of photographic film, using a plastic detector like CR-39 yields proton tracks only about $1.4\,\text{nm}$ in diameter, i.e., only a few atoms across. See, for example:
Determination of the proton latent track dimensions in CR-39 detectors using small angle neutron scattering
So the positions of moving elementary particles can be determined to within a $\text{nm}$ or so. That's hardly macro-scopic! And if we can measure its position to that accuracy, I fail to see the relevance of directly "seeing" the elementary particle itself. After all, we say we "see" a virus or even arrays of atoms in an electron-microscope image even though our unaided eyes themselves could never resolve them.

 

[Demystifier]

True, but that's not a fundamental limitation. Instead of photographic film, using a plastic detector like CR-39 yields proton tracks only about $1.4\,\text{nm}$ in diameter, i.e., only a few atoms across. See, for example:
Determination of the proton latent track dimensions in CR-39 detectors using small angle neutron scattering
So the positions of moving elementary particles can be determined to within a $\text{nm}$ or so. That's hardly macro-scopic! And if we can measure its position to that accuracy, I fail to see the relevance of directly "seeing" the elementary particle itself. After all, we say we "see" a virus or even arrays of atoms in an electron-microscope image even though our unaided eyes themselves could never resolve them.

You are missing the point. When you observe a very small object, say by an electron microscope, what you see directly is always something macroscopic. The picture produced by the electron microscope is macroscopic. It represents something microscopic, but the picture itself is macroscopic.

 

[renormalize]

You are missing the point. When you observe a very small object, say by an electron microscope, what you see directly is always something macroscopic. The picture produced by the electron microscope is macroscopic. It represents something microscopic, but the picture itself is macroscopic.

It's certainly likely that I am not understanding your point about "seeing" elementary particles.
So let me instead clearly state my claim: based on observing their trajectories through media like film or plastic, it is possible, in principle, to measure the position of rapidly-moving elementary particles (like protons) to within microscopic, atomic-level, accuracies on the order of nanometers. Do you agree or disagree?

 

[Demystifier]

It's certainly likely that I am not understanding your point about "seeing" elementary particles.
So let me instead clearly state my claim: based on observing their trajectories through media like film or plastic, it is possible, in principle, to measure the position of rapidly-moving elementary particles (like protons) to within microscopic, atomic-level, accuracies on the order of nanometers. Do you agree or disagree?

I agree.

But don't miss the context in which I said what I said. My claim was that the Bohmian position of a microscopic particle is a hidden variable, in the sense that we never observe such a position directly, but only indirectly by seeing a position of something macroscopic. Indeed, someone who disagrees with that claim might think that the bubble chamber shows directly that the microscopic particle has a trajectory, and hence that the bubble chamber provides an evidence that the Bohmian interpretation is on the right track. But you probably agree with me that the trace in the bubble chamber is not an evidence at all for the Bohmian interpretation.

 

[gentzen]

A reference to an actual published peer-reviewed paper would be much better than someone's comment on a blog post. Even well-known physicists will say a lot of things in a informal context that they know they would never get away with in a peer-reviewed paper.

131. Quantum Theory and Determinism PDF
L. Vaidman,
Quantum Stud.: Math. Found. 1, 5-38 (2014)1405.4222
The relevant part is section "10 Multiple Bohmian worlds".

This is copied from https://www.tau.ac.il/~vaidman/lvhp/publication_list.html. While copying from Lev Vaidman's publication page, it is probably a good idea to also copy Vaidman's position on 'Bohmians' vs. David Bohm:
189. Einstein was not wrong about our universe PDF
L .Vaidman,
Philosophical Magazine, DOI: 10.1080/14786435.2026.2643002 (2026)

I am a student of Yakir Aharonov who met David Bohm in Haifa when he left São Paulo. I am grateful to David Bohm not only as the advisor of Aharonov, but also for his research, which continues to be a basis for many of my works. ... This might explain why the dedicated group of ‘Bohmians’ promotes it as a fundamental theory of our universe.
... I also admire Bohmian mechanics for its determinism. However, Bohm himself never considered his theory a final theory explaining our universe. I was privileged to spend a day with David Bohm during the 30th anniversary of the Aharonov–Bohm effect celebrated in South Carolina. We had several hours of discussions in which he expressed his belief that we will never find the final theory of the universe, only a better and better approximation, and that Bohmian mechanics is just a step toward a better theory.

What Vaidman writes seems to be consistent with other reports of David Bohm's opinions:
Against the "nightmare of a mechanically determined universe": Why Bohm was never a Bohmian by Flavio Del Santo, Gerd Christian Krizek:

Why on earth are they calling it Bohmian mechanics? Haven’t they read a word I have written?!

However, one should not take Lev Vaidman as a reliable "interpreter" of BM. His "unreliability" can be found most condensed in
176. Are there observational differences between Bohmian mechanics and other interpretations? PDF
L. Vaidman,
in Physics and the Nature of Reality - Essays in Memory of Detlef Dürr, R.Tumulka, A. Bassi, S. Goldstein, N, Zanghi (eds.) Fundamental Theories of Physics (Springer Nature) (Springer, 2023) PhilSci Archive 21418
especially

For BM I suggest considering two possible postulates. The BM supervenience
postulate I:

The experience of a sentient being supervenes on the Bohmian positions of the particles the sentient being is made of.​

The BM supervenience postulate II:

The experience of a sentient being supervenes on the Bohmian collapsed wavefunction of its degrees of freedom.​

the Bohmian collapsed wave is unambiguously defined only when we have welllocalized branches.
Another possible proposal is supervenience on both Bohmian position and the Bohmian collapsed wave function. However, I feel that every one of the ingredients, Bohmian positions or Bohmian collapse wave function is enough to explain our experience, so this proposal seems to be unreasonably complicated and not necessary.

Neither of those two postulates corresponds to the position of David Bohm. It is probably reasonable to argue that the 'Bohmians' basically subscribe to Vaidman's postulate I.

 

[gentzen]

I don't know what you mean by this. In order to measure any quantum system, we have to have some knowledge of what it's doing.


I don't know what this means either, or why it's relevant to the discussion.

My personal opinion is that Tumulka's claim

It is widespread to call any variables that are not functions of $\Psi$ “hidden variables”; in Bohmian mechanics, the configuration Q is a variable that is not a function of $\Psi$, so it is often called a hidden variable although the particle positions are not hidden at all in Bohmian mechanics, as they can be measured any time to any desired accuracy.

is a mistake. Even so it remains unclear what Tumulka actually wants to claim, I see no way to interpret his claim in a way that would make it correct.
But I see a motivation for making such a claim in the first place: To give a precise physical meaning to the exact coordinates of a trajectory at any time. But my personal opinion is that this is not a promising way to provide that meaning.

As a concrete example of what I try to say: The Bohmian position of an electron in the inner s-orbital of an ion cannot be determined significantly more accurate than the size of that s-orbital, not even with highly focused neutrons, or with highly focused high-energy x-rays (or with yet-to-be-invented two-photon imaging).

I don't get this at all. An isolated position is not a trajectory. A trajectory is a continuous curve of such positions. It doesn't have to cover the entire history of the particle, but it does have to cover at least some portion of it beyond one isolated position.

I tried to come up with an interpretation of Tumulka's statement that he and others might believe to be defensible.

Is there any literature reference that explains the points you're trying to make here?

Yes, there is literature arguing against the sort of interpretation of Bohmian trajectories expressed in Tumulka's statement and in the earlier (easier to defend) statements by Bell. One of these papers I have read is
"Why Bohmian Mechanics? one and two-time position measurements, Bell inequalities, philosophy and physics" by Nicolas Gisin (https://arxiv.org/abs/1509.00767)
Two main references in that paper to earlier work/arguments along the same lines are
[4] B.-G. Englert et al., Z. Naturforsch. 47a, 1175-1186 (1992)
[5] L. Vaidman, Found. Phys. 35, 299-312 (2005)
I remember of having read [5] earlier:
94. The Reality in Bohmian Quantum Mechanics or Can You Kill with an Empty Wave Bullet? PDF
L. Vaidman,
Found. Phys. 35, 299-312 (2005) quant-ph/0312227
Maybe I didn't read it very thoroughly, but I think it is the place were I first learned that David Bohm was not a 'Bohmian':

I get used to the idea of plurality of worlds, but a theory without collapse and with a single world is clearly a better theory of everything. In some sense, Bohmian quantum mechanics is such theory. (Note, however, that Bohm himself never viewed his theory in that way. I had elaborate discussion with him in South Carolina in 1989 in which he explained that his theory is another step in the evolution of physics and there will never be the final theory of everything.)

What is common between Gisin and Vaidman is that both see Bohmian mechanics itself positive.
I now read a bit in [4] "Surrealistic Bohm Trajectories" by Berthold-Georg Englert, Marian O. Scully, Georg Süssmann, and Herbert Walther (https://www.degruyterbrill.com/de/document/doi/10.1515/zna-1992-1201/html) and the reactions (http://znaturforsch.com/aa/v48a/48a1261.pdf http://znaturforsch.com/aa/v48a/48a1263.pdf). This is surprisingly confrontational, and not in favor of Bohmian mechanics. (My motivation to dive deeper into this stuff came from the even more confrontational https://arxiv.org/abs/quant-ph/0001011 and my opinion that the 'Bohmians' don't make such an obvious mistake. A paper in a similar spirit is https://arxiv.org/abs/2502.14449.)

 

[jeffn1]

I have been trying to get a better understanding of what appears to be (to me) a less fantastical interpretation of the Many Worlds Interpretation (without gazillions of universes created every time a photon interacts with something, etc.). So, it seems the Relative State interpretation of MW does not require continued universe creation. Some of what I am reading seems to suggests this view requires a conscious observer and the observations are applicable to that observer. Any thoughts are appreciated.

 

[PeterDonis]

The pixel is not the particle.

I didn't say it was. What I said is that it shows the location of the particle's impact, to within the finite resolution of the pixel. So it seems reasonable to say that it is a measurement of the particle's position at the time of impact, to that resolution.

 

[Matterwave]

I have been trying to get a better understanding of what appears to be (to me) a less fantastical interpretation of the Many Worlds Interpretation (without gazillions of universes created every time a photon interacts with something, etc.).

Note that, at least to my knowledge, there is no claim that universes are created only that it branches in MWI. Why is branching different than creation is a more technical matter and I am not well versed enough to answer this clearly.

I have not read the following book, but it is often cited as a good reference for understanding the actual claims of MWI (instead of the pop sci hyperbole): https://sites.pitt.edu/~dmw121/books-emergent.html

 

[PeterDonis]

Why is branching different than creation is a more technical matter and I am not well versed enough to answer this clearly.

The answer is simple: "branching" is just unitary evolution, and unitary evolution can't create or destroy anything.

 

[Matterwave]

The answer is simple: "branching" is just unitary evolution, and unitary evolution can't create or destroy anything.

Yes, I realize that mathematically MWI is pure unitary evolution of a universal wave function via Schroedinger's equation. Mathematically that is all the interpretation does and indeed that's the whole point.

So I agree, this must be the answer. However, one does hope for a bit more, let's say exposition, of how we should reconcile that pure unitary evolution with our every day experience that we never actually see a live and dead cat simultaneously. How did I make it into the branch where the cat is alive?

But of course, maybe David Wallace wrote such exposition in his book and all I have to do is read it. I can add it to my reading list, but my reading list keeps growing longer so it might take a while lol.

 

[PeterDonis]

one does hope for a bit more, let's say exposition, of how we should reconcile that pure unitary evolution with our every day experience that we never actually see a live and dead cat simultaneously.

Because the branches are decohered, and because in the overall wave function you are entangled with the cat--and both you and the cat are entangled with everything else in the environment--in each decohered branch, you experience whatever is consistent with the state of the cat and everything else within that branch.

How did I make it into the branch where the cat is alive?

The question is meaningless because it is based on a false premise. You are not in one branch or the other. You are in both branches. The you that is in the "cat is alive" branch sees the cat as alive, and the you that is in the "cat is dead" branch sees the cat as dead.

 

[Matterwave]

Because the branches are decohered, and because in the overall wave function you are entangled with the cat--and both you and the cat are entangled with everything else in the environment--in each decohered branch, you experience whatever is consistent with the state of the cat and everything else within that branch.

Maybe if I reread this a few more times it will click. Maybe the only way is to read some more books on the subject.

The question is meaningless because it is based on a false premise. You are not in one branch or the other. You are in both branches. The you that is in the "cat is alive" branch sees the cat as alive, and the you that is in the "cat is dead" branch sees the cat as dead.

Yeah I suppose I walked into that one. I brought my subjective experience into the discussion by my implicit meaning of "I".

 

[PeterDonis]

Maybe if I reread this a few more times it will click.

Bear in mind that, if you find it hard to believe that the MWI actually says this because it seems so outlandish, you're not alone. I find it outlandish too. So do many others. But it is what the MWI actually says, outlandish and all. People who believe the MWI is true do actually believe what I described. If you really push about how outlandish it seems to you, many of them will probably waffle. But if you actually do believe the MWI, those outlandish things are what you're committed to, whether you like it or not.

I brought my subjective experience into the discussion by my implicit meaning of "I".

One of the biggest problems with even trying to talk about the MWI at all is that you have to drastically change the meaning of important words like "I". Our ordinary language simply was not intended to describe such things.

 

[Demystifier]

I didn't say it was. What I said is that it shows the location of the particle's impact, to within the finite resolution of the pixel. So it seems reasonable to say that it is a measurement of the particle's position at the time of impact, to that resolution.

Yes, but I would just not call such a measurement "direct". Even though the spot has the same position as the assumed particle (which is probably the reason why you think of it as "direct"), I call it "indirect" because the spot is a very different object than the particle.

 

[Roberto Pavani]

It's certainly likely that I am not understanding your point about "seeing" elementary particles.
So let me instead clearly state my claim: based on observing their trajectories through media like film or plastic, it is possible, in principle, to measure the position of rapidly-moving elementary particles (like protons) to within microscopic, atomic-level, accuracies on the order of nanometers. Do you agree or disagree

Reading the above quote, I'm puzzled by a possible experiment whose outcome I cannot predict.

Consider a double-slit experiment with protons and a thick plastic detector that records tracks.

My intuition (which may well be wrong) is that the detected positions would still follow the usual interference pattern. However, I do not know what happens to the recorded tracks inside the detector volume.

In my mind, the proton leaves something like a microscopic chalk mark inside the plastic. After many events, one could inspect the resulting 3D pattern of tracks. Would those tracks appear to originate from one slit or the other? Or would they somehow reflect the interference phenomenon as well?

Put differently: is interference reflected only in the statistical distribution of the detected positions, while the individual recorded tracks look completely classical and seem to point back to one slit or the other?

I'm not claiming a contradiction. I'm simply unable to visualize what such a detector would actually record.

Note that I'm specifically interested in a thick plastic detector placed at the central maximum of the interference pattern. I am not asking about the entire pattern. Even this single region seems sufficient to analyze. What I cannot visualize is the 3D shape of the ensemble of tracks recorded inside the detector: would it look like a single forward-going bundle, two converging populations, a cone-like distribution, or something else?

 

[PeterDonis]

a thick plastic detector that records tracks.

Meaning, tracks from the proton source, through the slits, and to the detector screen? If so, then this...

My intuition (which may well be wrong) is that the detected positions would still follow the usual interference pattern.

...is not correct. Recording the tracks, at least if it means what I said above, records which-path information, which removes the interference.

However:

I'm specifically interested in a thick plastic detector placed at the central maximum of the interference pattern.

How would such a detector "record tracks"? If this is all you meant, then I don't understand what you mean by "recording tracks".