The Refutation of Bohmian Mechanics

[Varon]

To further clarify, the issues you (Varon) raise are what I mean by deBB tapdancing around the issues that killed its contemporary non-standard theories.

You love to use high class slang. But I don't know what "tapdancing" mean. Pls. use standard straight english. What are you saying?

 

[Dmitry67]

As I said many times, pure MWI with its minimal set of assumptions cannot explain the Born rule. Some additional assumptions must be taken. In my view, Bohmian mechanics is just one such set of assumptions. So in this sense - yes, Bohmian mechanics is MWI in denial. Or more precisely, Bohmian mechanics is the most intuitive (and perhaps most natural) completion of the MWI program.

Yes, both theories can be interpreted as examples of more general theory with N types of fundamental particles.

in MWI N=0
in dBB N=1
N>1 can be attacked based on Occam razor, but such generalisation is useful because it shows a fundamental problem with dBB (while MWI has problem with the Born rule): why my copies, mades of empty waves, are not conscious?

So dBB does not 'solve' the Born rule, it just replaces one problem (Born rule) with another (some axiom about existence). While we can hope that somehow the first problem will be solved (emerge on level of macroscopic objects or even on the level of consiousness), for dBB alternative there is no such hope - it is just an axiom.

 

[Varon]

Yes, both theories can be interpreted as examples of more general theory with N types of fundamental particles.

in MWI N=0
in dBB N=1
N>1 can be attacked based on Occam razor, but such generalisation is useful because it shows a fundamental problem with dBB (while MWI has problem with the Born rule): why my copies, mades of empty waves, are not conscious?

So dBB does not 'solve' the Born rule, it just replaces one problem (Born rule) with another (some axiom about existence). While we can hope that somehow the first problem will be solved (emerge on level of macroscopic objects or even on the level of consiousness), for dBB alternative there is no such hope - it is just an axiom.

Dmitry67, as a lone proponent of Many Worlds here. I think you must be familiar with Albert and Loewer and Lockwood's Many Minds Interpretation (variant of Many worlds) that attempt to solve the Born Rule as well as choosing of the preferred basis). What can you say about them? I've been studying their works since yesterday and my head spinning already. Do you believe what they are saying may be possible? (hope Bohmians and the don't care pragmatists can at least comment too... I initially wanted to make a separate thread for this but just include it here)

Quoting from Lockwood paper "'Many Minds' Interpretations of Quantum Mechanics"

"A many minds theory, as I understand it, is a theory which takes completely at face value the account which unitary quantum mechanics gives of the physical world and its evolution over time. In particular, it allows that, just as in special relativity there is a fundamental democracy of Lorentz frames, so in quantum mechanics there is a fundamental democracy of vector bases in Hilbert space. In short, it has no truck with the idea that the laws of physics prescribe an objectively preferred basis. For a many minds theorist, the appearance of there being a preferred basis, like the appearance of state vector reduction, is to be regarded as an illusion. And both illusions can be explained by appealing to a theory about the way in which conscious mentality relates to the physical world as untinary quantum mechanics describes it."

[skipping many paragraphs...]

"What Albert and Loewer actually suggest, of course, is that, associated with each living brain, there is a continuous infinity of minds, each independently evolving, according to the same stoachstic law. That we are dealing with a continuous infinity, here, is sufficient to ensure that each brain is not only certain to be inhabited, in every Everett branch, but certain to be inhabited by a continuous infinity of minds. Morever, there is no problem about understanding the quantum-mechanical probabilities, in the context of this theory. For these probabilities are put in by hand simply by stipulating that each mind obeys an irreducibly probabilities law of evolution, which mirrors the predictions of the quantum-mechanical statistical algorithm."

 

[Misericorde]

You love to use high class slang. But I don't know what "tapdancing" mean. Pls. use standard straight english. What are you saying?

High class slang, that's a new one on me, sorry if I've been confusing. Tap dancing is a kind of dance that involves a lot of fancy moves with the feet, so the metaphor is dodging around the major issues with words or small compromises.

To put it another way, instead of tapdancing, let me say: deBB has compromised again and again except in its central preference of position, to the point where it has only survived as a kind of weak MWI. I apologize for being confusing!

 

[Misericorde]

Yes, both theories can be interpreted as examples of more general theory with N types of fundamental particles.

in MWI N=0
in dBB N=1
N>1 can be attacked based on Occam razor, but such generalisation is useful because it shows a fundamental problem with dBB (while MWI has problem with the Born rule): why my copies, mades of empty waves, are not conscious?

So dBB does not 'solve' the Born rule, it just replaces one problem (Born rule) with another (some axiom about existence). While we can hope that somehow the first problem will be solved (emerge on level of macroscopic objects or even on the level of consiousness), for dBB alternative there is no such hope - it is just an axiom.

This is the exact means by which it has "tapdanced" Varon; it keeps adding to the problem without solving anything. Instead of wave-particle duality you have a pilot wave. Position is preferred, MWI is implied, and so on, and this is all on top of the formalism.

I'd say:

It's deBB that's 1, Formalism that's 0, and MWI is somewhere in between.

 

[Dmitry67]

Varon, I know there are some attempts to derive the Born rule in MWI, so far I think they are far from being final. In any case, I hope an appearence of the Born rule is emergent somehow on the macroscopic level or on conscious level.

I *almost* share Many Minds view: yes, no 'measurement devices' observe anything: they just transfer the decoherence. Photon is decoherenced with the photosensor, it transfers it to the hand of the voltmeter, photons transfer that information to our retina. All elements of that chain can be in superposition, and the only final and ultimate agent for the observation is our consciousness. Superposition ends not when it is measured (it just puts measurement device in a correlated superposition), it ends when we see it, when we feel it.

World is a very strange place, there is no preferred basis physically, but there are some special ones of the systems with qualia. However, to extract a system from the environment, we need a basis, so it is recursive. Ultimately, Born rule can be also an illusion, created by our consicousness, like the moment NOW.

However, I believe that consicousness can be physically studied (to some extent) so Many Minds should not have any additional assumtions - everything must be derived from pure MWI.

 

[Dmitry67]

Position is preferred

I had also attacked dBB based on that
Demystifier's response was, if I remember it correctly, that the opposite to knowing position exactly is knowing the momentum exactly. Then position is not localized at all. But in the Universe there are no global frames.

 

[Varon]

Varon, I know there are some attempts to derive the Born rule in MWI, so far I think they are far from being final. In any case, I hope an appearence of the Born rule is emergent somehow on the macroscopic level or on conscious level.

I *almost* share Many Minds view: yes, no 'measurement devices' observe anything: they just transfer the decoherence. Photon is decoherenced with the photosensor, it transfers it to the hand of the voltmeter, photons transfer that information to our retina. All elements of that chain can be in superposition, and the only final and ultimate agent for the observation is our consciousness. Superposition ends not when it is measured (it just puts measurement device in a correlated superposition), it ends when we see it, when we feel it.

World is a very strange place, there is no preferred basis physically, but there are some special ones of the systems with qualia. However, to extract a system from the environment, we need a basis, so it is recursive. Ultimately, Born rule can be also an illusion, created by our consicousness, like the moment NOW.

However, I believe that consicousness can be physically studied (to some extent) so Many Minds should not have any additional assumtions - everything must be derived from pure MWI.

What I can't understand in this Many Worlds is what if the observers are machines or video camera in a laboratory experiment system without humans. What would serve as Many Minds then? Or would it be invalid? What difference if humans observe them versus automated machines? Random choice? But we could design machine that can initiate random choice too. Pls. elaborate.

 

[Misericorde]

I had also attacked dBB based on that
Demystifier's response was, if I remember it correctly, that the opposite to knowing position exactly is knowing the momentum exactly. Then position is not localized at all. But in the Universe there are no global frames.

I agree with your view; I've never understood why deBB is taken as even remotely mainstream. Your point about MWI and Occam's Razor is enough for me frankly.

 

[Demystifier]

Why do you think is the Position observable preferred in Bohmian mechanics?

I have already answered it in post #188.

 

[Dmitry67]

What I can't understand in this Many Worlds is what if the observers are machines or video camera in a laboratory experiment system without humans. What would serve as Many Minds then? Or would it be invalid? What difference if humans observe them versus automated machines? Random choice? But we could design machine that can initiate random choice too. Pls. elaborate.

This is why I said I *ALMOST* accept Many Minds, but I am still on MWI ground.
Unitary evolution is objective, so when room is isolated from the environment, there is no difference if there are any consious beings inside. But until someone conscious had opened the door, there is simply no basis to be used... well, you can use any basis, but results will be different for each one, and there is no rule to favor one versus the other.

Mathematically we can use ANY basis, but consciousness breaks the symmetry between all possible ones, dividing them into 2 categories: those who feel and the dead and arbitrary ones. As our experience is limited to a very narrow subset of them, we make an extremely 'unfair sampling' of nature. Just for example, pick any random point in cosmos. With 99.99999999999999% probability it will be intergallatic void. But we never experience such places!

For some reason consciousness can break the symmetry between all possible basis, like it breaks the symmetry of time, dividing it into future, past and now. Interestingly enough, the special role of the moment called NOW is denied by the modern Block Time approach, so "flow of time" and "NOW" are called illusions, created by our consciousness. I agree, but what other notions we got used to are also just illusions?

So here is my answer: I don't believe that consciousness affects the physical processes or plays a special role in the evolution of the Universe. Universe does not care about consciousness. However, conciousness is responsible for an unfair sampling of the observations, put to the extreme.

 

[Demystifier]

However, conciousness is responsible for an unfair sampling of the observations, put to the extreme.

Very interesting hypothesis. Of course, I'm not asking for a proof, but can you at least give some arguments which would make it a bit more plausible?

 

[Dmitry67]

I had provided one (about intergalactic void). Of course, you can call it AP, but AP is usually used in a narrower sense - for the selection of initial conditions, like the parameters of the standard model.

I always wanted to share one crazy thought. May be now it is time. It is an indirect, not a direct argument for what I had said above, and I don't claim that it is true; but it can show how deep the rabbit hole can go.

************

I use MWI framework. There are all sorts of branches: with higher 'probability', and with tiny probability. There are even branches where some absurd laws are respected, for example, Uranium atom decay faster on Saturdays. Let's call such 'law' a meta-law (as it is not fundamental and can't be derived, in principle, from QM)

Let's call the branches where meta-laws exist 'meta-branches'. Now assume that physical laws of our world are not 'enough' for the consciousness to exist. However, when some very special meta-laws are plugged in, consciousness is possible.

In such case, only meta-branches would be observed (no matter how tiny their probability is), and the fundamental laws can be very different from what we tend to think. Am I crazy?

 

[Misericorde]

I had provided one (about intergalactic void). Of course, you can call it AP, but AP is usually used in a narrower sense - for the selection of initial conditions, like the parameters of the standard model.

I always wanted to share one crazy thought. May be now it is time. It is an indirect, not a direct argument for what I had said above, and I don't claim that it is true; but it can show how deep the rabbit hole can go.

************

I use MWI framework. There are all sorts of branches: with higher 'probability', and with tiny probability. There are even branches where some absurd laws are respected, for example, Uranium atom decay faster on Saturdays. Let's call such 'law' a meta-law (as it is not fundamental and can't be derived, in principle, from QM)

Let's call the branches where meta-laws exist 'meta-branches'. Now assume that physical laws of our world are not 'enough' for the consciousness to exist. However, when some very special meta-laws are plugged in, consciousness is possible.

In such case, only meta-branches would be observed (no matter how tiny their probability is), and the fundamental laws can be very different from what we tend to think. Am I crazy?

I don't think that's crazy, just not verifiable; it's a natural if exotic philosophical extension of existing concepts. I enjoy your view, although I don't share it, while we're playing with the notion of MWI why not explore the exotic probabilities? In some ways, your idea emphasizes for me why MWI and all interpretations fall short, because they can be taken to extremes so far beyond what physics is even designed to answer or probe.

 

[Dmitry67]

Another (purely emotional) argument against dBB.

Look at SR/GR and QM as 'steps' toward the truth. Every major step was more and more contre-intuitive, and "common sense reasoning" had less and less value. Even MWI is not technically a new 'step', it perfectly fits that scheme. On the contrary, dBB looks so 'human made', artificial - return to the old good billiard ball physics. Soooo comfortable for our common sense reasoning... This is why I think it can't be true...

 

[Demystifier]

Now assume that physical laws of our world are not 'enough' for the consciousness to exist. However, when some very special meta-laws are plugged in, consciousness is possible.

Am I crazy?

No, you are just not specific enough.

 

[Dmitry67]

No, you are just not specific enough.

I don't claim it is true, I am just showing a range of theories MWI/QM can be 'compatible' with.

P.S
I have a question for you about dBB. I remember once there was a discussion about Bell/EPR and no-conspiracy assumption. You replied that you don't see an exact difference between superdeterminism and no-conspiracy. I was thinking about it, I believe I can tell what the difference is.

Conspiracy is some set of boundary conditions, defined at Universe time t>0. Such boundary conditions can be very simple (that area is void at that time) or complicated so you have to write a complicated function to evaluate if it is true (whenever EPR experiment is performed, the results should yeild the specific condition...). Details are not important, the only important thing is that the boundary condition is defined for regions of spacetime at t>0.

Another word for Conspiracy is Destiny.

Q: Do you believe that in dBB there are no boundary conditions defined at Universe time t>0? So do you claim that ALL boundary conditions of dBB are defined strictly at t=0? (Big bang?)

 

[Demystifier]

Your questions require a careful answer:
I believe in nonrelativistic BM all initial conditions are specified at the same time t, but not necessarily at t=0. And I don't see any conspiracy in it.

 

[Ilja]

Bohmian Mechanics as MWI in denial?

My main objection against MWI is that it needs, in fact, some additional structure: It clearly needs some subdivision of the universe into subsystems. But there is nothing in the universe which could be used as a natural candidate. The subsystems we observe in everyday life, and which are also widely used in examples and discussions, like, in particular, minds, clearly do not have the fundamental character which would be necessary - they exist only in states of the universe which are extremely close to our actual state. What is my state in a universe where the Earth does not even exist? A nonsensical question.

But this vague subdivision into subsystems is an additional structure which is not necessary in dBB. It also needs additional structure, but of a different type, the one into configuration and momentum. That's a subdivision which is fundamental already in classical mechanics. It shows up in the equations: H=p^2/2m + V(q), quadratic in momentum but not in the configuration variables, a property which survives even for some relativistic fields, and there is no known system where such a subdivision would be problematic.

 

[mfb]

The subdivision occurs naturally as evolution of the wave function. This is called decoherence.
If you just take a wave function and unitary evolution, you directly arrive at MWI. You get the branching structure in all (relevant) chaotic systems. If you do not "want" those branches, you have to add a structure - collapses (e.g. Copenhagen), particles (dBB) or something else.

 

[Ilja]

The subdivision occurs naturally as evolution of the wave function. This is called decoherence. If you just take a wave function and unitary evolution, you directly arrive at MWI.

Sorry, but no, there is nothing natural there. You need an additional structure - a subdivision of the universe into subsystems. Only if you assume such a subdivision as given, you obtain all the other things, like branching and so on.

If you do not "want" those branches, you have to add a structure - collapses (e.g. Copenhagen), particles (dBB) or something else.

No. You also need additional structure in MWI - the subdivision of the universe into subsystems.

 

[The_Duck]

You also need additional structure in MWI - the subdivision of the universe into subsystems.

What do you mean by this? Why is it true, and what sort of subsystems are you talking about?

 

[mfb]

No, you do not need subdivisions of any sort. Any wave function which somehow looks like a classical system (or a superposition of several classical systems) will produce branches if something like a measurement process happens.

The "somehow" / "something" are on purpose, as the result is very general and applies to a wide range of systems / processes.

 

[bohm2]

You also need additional structure in MWI - the subdivision of the universe into subsystems.

Some like Maudlin have criticized MWI for opposite reasons; for not having an appropriate micro-ontology to appropriately ground macro-level stuff. I'm guessing this is one of the major reasons Maudlin favours the Bohmian model (at least one particular version of it)? An interesting paper by David Wallace discussing some of these problems for MWI and his attempts to adress these criticisms/problems:

(Maudlin (2010), in particular, criticises the Everett interpretation for having an inappropriate micro-ontology to appropriately ground macro-level facts; Hawthorne (2010) raises some similar concerns.) In particular, normally our concepts of space and time are treated as constant between higher-level and lower-level theories, so that for (e.g.) some higher-level object to exist in spacetime region K it must be instantiated not just by any old objects and properties in the lower-level theory, but by objects and properties themselves located in K. As such, getting some understanding of the relation between spacetime and the microscopic ontology might well be crucial for the larger Everettian project. This project will be my concern for the remainder of the article.

A prolegomenon to the ontology of the Everett interpretation
http://philsci-archive.pitt.edu/8892/1/alyssa_volume.pdf

Personally, the biggest problem for BM for me is the "problem of empty waves":

For every branch of the wavefunction containing the actual particle trajectories, there are countless other branches corresponding to every other potential ‘world’ which would have been realized had the particle positions been different. The effects of decoherence soon disable the influence of other branches on the particle trajectories, leaving much of the wavefunction redundant. Nonetheless these redundant branches are an essential element of BM...This criticism of BM has led several authors to argue that BM is little more than a version of the many-worlds interpretation in which the particle trajectories are a way to select one particular world...It has also led Durr, Goldstein, and Zanghi to suggest that the wavefunction should be regarded as nomological, with a role analogous to the Hamiltonian in classical mechanics.

For example Deutsch has claimed that “pilot-wave theories are parallel-universes theories in a state of chronic denial”.

Hidden variable interpretation of spontaneous localization theory
http://arxiv.org/PS_cache/arxiv/pdf/1104/1104.1938v1.pdf

For a very interesting chapter on Maudlin's position see Chapter 4: "Can the World be only wave function":

I quite agree that the question raised is crucial, and arises even in the predictable case. I also agree that the Bohmian should insist—as all Bohmians I know of do!—that predictability has nothing to do with it: even in the predictable case, the state of the wavefunction alone, the wavefunction without any particles at all (if any sense can be made of that) is not sufficient to account for the result of any measurement. For if the result of a measurement consists in, say, a pointer pointing a certain way, and if the pointer is made of particles, then if there are no particles there is no pointer and hence no outcome.

Many Worlds? Everett, Quantum Theory, and Reality
http://bacon.umcs.lublin.pl/~lukasik/wp-content/uploads/2010/12/Many.Worlds.EverettQuantum.Theory.and.Reality.pdf

 

[Ilja]

What do you mean by this? Why is it true, and what sort of subsystems are you talking about?

In http://arxiv.org/pdf/0901.3262v2.pdf I have described this in some detail and constructed an explicit counterexample to the hope that one can derive it somehow given only the Hamilton operator.

Some quotes from Zurek (arXiv:quant-ph/9805065, arXiv:0707.2832):

“One more axiom should [be] added to postulates (i) - (v): (o) The
Universe consists of systems.

“Both the formulation of the measurement problem and its resolution through the appeal to decoherence require a Universe split into systems. Yet, it is far from clear how one can define systems given an overall Hilbert space of everything and the total Hamiltonian.

[A] compelling explanation of what are the systems — how to define them given, say, the overall Hamiltonian in some suitably large Hilbert space — would be undoubtedly most useful.

It would be indeed useful, but, unfortunately for MWI, it is not possible. At least not without any additional physical structure.

No, you do not need subdivisions of any sort. Any wave function which somehow looks like a classical system (or a superposition of several classical systems) will produce branches if something like a measurement process happens.

The "somehow" / "something" are on purpose, as the result is very general and applies to a wide range of systems / processes.

I disagree. Without any additional structure it is not even well-defined what means "something like a measurement process".

 

[Quantumental]

In http://arxiv.org/pdf/0901.3262v2.pdf I have described this in some detail and constructed an explicit counterexample to the hope that one can derive it somehow given only the Hamilton operator.

Some quotes from Zurek (arXiv:quant-ph/9805065, arXiv:0707.2832):



It would be indeed useful, but, unfortunately for MWI, it is not possible. At least not without any additional physical structure.

So have you talked to him about this?
Last time I saw an interview with Zurek he was fairy confident in MWI, though he also said that it might be that you can get "it from bit" some other way.

 

[Ilja]

So have you talked to him about this?

No. The quotes are from the papers I have cited.

 

[Quantumental]

No. The quotes are from the papers I have cited.

From what I can tell he does not agree with you that this is not possible...
It seems he is perfectly fine with it?

 

[Ilja]

From what I can tell he does not agree with you that this is not possible...
It seems he is perfectly fine with it?

I don't even know if he has read my papers, so I cannot tell what he thinks about them.

I think my counterexamples show clearly that MWI needs additional structure. A strange fundamental "subdivision into systems" can provide such an additional structure. Once
Zurek has independently proposed such a subdivision as a natural postulate, it seems
reasonable to guess that he will not give it up.

But it is clearly an additional structure, which is not necessary in the Bohmian approach,
so that the "BM is MWI in denial" argument is clearly invalid.

 

[Quantumental]

But it is clearly an additional structure, which is not necessary in the Bohmian approach,
so that the "BM is MWI in denial" argument is clearly invalid.

Why isn't the structure in the WF enough? I mean given functionalism there should be worlds in the empty pilot waves too?

 

[Ilja]

Why isn't the structure in the WF enough? I mean given functionalism there should be worlds in the empty pilot waves too?

I don't understand this functionalism. A function on something does not mean the existence
of this something. What do I think about unicorns? This depends on the unicorns - I have
a special preference for the invisible pink unicorn, while I consider other unicorns as boring.

So, it is a function of the state of unicorns, and it really exists in my mind. So, does it follow that unicorns exist?

The argument about the missing subdivision of the world into systems is of another type. This structure is necessary because, if one thinks about it, one can easily detect that all the MWI considerations assume that such a subdivision exists. And my example shows that different subdivisions lead to different physical predictions for the same Hamilton operator.

 

[Quantumental]

I don't understand this functionalism. A function on something does not mean the existence
of this something. What do I think about unicorns? This depends on the unicorns - I have
a special preference for the invisible pink unicorn, while I consider other unicorns as boring.

So, it is a function of the state of unicorns, and it really exists in my mind. So, does it follow that unicorns exist?

What?
That is not functionalism at all.
The point is: if the wavefunction has a ontological existence as a pilot wave in the de-Broglie Bohm interpretation, then why doesn't the pilot wave give rise to worlds ?
If the pilot wave funciton exactly like a structure, then why isn't it structure?

The argument about the missing subdivision of the world into systems is of another type. This structure is necessary because, if one thinks about it, one can easily detect that all the MWI considerations assume that such a subdivision exists. And my example shows that different subdivisions lead to different physical predictions for the same Hamilton operator.

I'd love to learn more about this...

 

[Ilja]

What?
That is not functionalism at all.
The point is: if the wavefunction has a ontological existence as a pilot wave in the de-Broglie Bohm interpretation, then why doesn't the pilot wave give rise to worlds ?
If the pilot wave funciton exactly like a structure, then why isn't it structure?

My artificial unicorn-example was of similar nature. My ideas about unicorns have ontological
existence in any theory which assumes that human ideas correspond to states of neurons in the human's brain. So these ideas exist there, as a structure of my neurons.

But it does not follow that this structure of my neurons, even if it can be described by a function on the space of imaginable unicorns, gives rise to unicorns.

I'd love to learn more about this...

http://lanl.arxiv.org/abs/0901.3262 is the basic construction. The same Hamilton operator,
but nonetheless different physical predictions, because of different operators p,q or a different subdivision into systems.

http://lanl.arxiv.org/abs/0903.4657 is some argumentation why various quantum interpretations which are pure - that means, without any additional structure - are not viable.

 

[ImaLooser]

But it does not follow that this structure of my neurons, even if it can be described by a function on the space of imaginable unicorns, gives rise to unicorns.

I came directly from watching a video of imaginary unicorns to this. Golly.

Really.

 

[mitchell porter]

T. Seletskaia has pointed out to me Arnold Neumaier's paper "Bohmian mechanics contradicts quantum mechanics", discussed earlier in this thread.

So far as I can see, no-one made the analogy with momentum... If you want this sort of disagreement between Bohmian mechanics and quantum mechanics, you can just consider momentum. The distribution of momenta, exhibited by the Bohmian trajectories corresponding to a generic wavefunction, is not the same as the probability distribution for the momentum observable, predicted by QM for the same wavefunction.

To get a Bohmian, ontological, realist explanation of the quantum momentum operator, you have to include a physical interaction which "measures" the momentum, and you must consider the overall wavefunction for "original system" + "second system which interacts with the first". This is the sort of wavefunction considered e.g. in studies of measurement-induced decoherence; but here you are to consider the Bohmian trajectories corresponding to this overall wavefunction. When you do this, you once again have predictive agreement between QM and BM.

All this would be well-known to modern Bohmians. What's interesting here is that Arnold has found an analogous problem just involving position, which was supposed to be the part of Bohmian mechanics which matches with quantum mechanics in a direct and uncomplicated way. However, to find this problem, he had to consider correlations between position at different times. So we can refine our understanding as follows:

The single-time distribution for position is the same in Bohmian mechanics and quantum mechanics. The multi-time correlations for unmeasured position in Bohmian mechanics are not the same as the multi-time correlations for position in quantum mechanics, just as the distribution for the unmeasured momentum in Bohmian mechanics is not the same as the distribution for momentum in quantum mechanics. However, if there is a physical interaction such as is required for measurement, then multi-time correlations for measured position, and a distribution for measured momentum, are produced, which are the same as in QM. (This was the point of Marchildon's response.)

While I agree with Arnold's critics, who say that he is ignoring Bohmian measurement theory, I still think it's interesting to grasp the ways in which physical ontology, according to Bohmian mechanics, behaves differently than "quantum appearances" or "quantum intuition" suggest. Though I would not be surprised to learn that this is all old news for Bohmians who have specialized in issues of time (dwell time, time of flight, etc).

 

[Demystifier]

However, if there is a physical interaction such as is required for measurement, then multi-time correlations for measured position, and a distribution for measured momentum, are produced, which are the same as in QM.

Let me just repeat and emphasize the most important sentence of your post.