I A skeptic's view on Bohmian Mechanics

[DrChinese]

Is there one?

I don't think so. On the other hand, demystifier is on record saying "... it cannot be said that there exists a well-defined relativistic QM." There's always an out!

http://xxx.lanl.gov/pdf/quant-ph/0609163v2

 

[zonde]

No. Bohmian mechanics is nonrelativistic and non-field, and its dynamics has not even a notion of spacelike separation that would be well-defined.

Are you saying that Bohmian mechanics allow FTL communication (that spacelike separated observables do not commute)?

 

[ShayanJ]

Are you saying that Bohmian mechanics allow FTL communication (that spacelike separated observables do not commute)?

Bohmian mechanics is like quantum mechanics, defined on the absolute space and time of Newton. There is no notion of space-like separated events in Newton's view!

 

[zonde]

This is a definition that simply mixes locality with realism making them indistinguishable while at the same time claiming it has nothing to do with realism and erroneously endorsing it to Bell. It is terribly confused.

Ok, then here are some of Bell's own words:
"It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of “local causality” or “no action at a distance”. Of course, mere correlation between distant events does not itself imply action at a distance, but only correlation between the signals reaching the two places. These signals, in the idealized example of Bohm, must be sufficient to determine whether the particles would go up or down. For any residual undeterminism could only spoil the perfect correlation. It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis."

And please try not to use "realism" in QM context unless you mean "not solipsism" because it's very confusing what you mean with it. (is it determinism here? or causality? or particles having spin at all times?)

 

[zonde]

Bohmian mechanics is like quantum mechanics, defined on the absolute space and time of Newton. There is no notion of space-like separated events in Newton's view!

Hmm, we can say that there can be no photon or any massive particle that has trajectory trough both events if they are spacelike separated by definition.

 

[PeterDonis]

we can say that there can be no photon or any massive particle that has trajectory trough both events if they are spacelike separated by definition.

So what is the definition of "spacelike separated" in Newtonian mechanics? There isn't one--the concept simply does not exist in Newtonian mechanics.

 

[A. Neumaier]

Is there one?

This answer

That's because wave functions, described by relativistic wave equations (such as Dirac or Klein-Gordon equation), do not propagate faster than c.

to the comment

So I would ask any Bohmian why there is a limit - in a nonlocal theory - to entanglement which exactly matches the limits given by c.

seems to suggest that there is one. But no reference is given...

 

[atyy]

Well, you said "I agree", so I thought that's what you got from what I said!
Anyway, that's exactly what I wanted to say. The physics community now is divided. The majority of physicists are happy with quantum mechanics and see no problem in it and just want to use it. There are some people who see some problems and want to solve them. These are not only Bohmians. Everyone who does some research on foundational issues is in this camp. So its not that there are problems that only Bohmians see, its just that Bohmians have their own way of looking at these problems. And I really don't see anything different here and that's what confusing me. Why everyone treats Bohmian mechanics so much different than other interpretations? Its not better than others but its not worse too!

Bohmian Mechanics is different from all other interpretations because it removes the weirdness from QM. That's why people don't like it. You can't write any more popsci books about how weird QM is. It's a PR and financial disaster for physics.

 

[atyy]

There is a lot of rigorous statistical mechanics done in mathematical physics. See, e.g., the nice book by Ruelle. The only approximation made there is the thermodynamic limit, replacing numbers like $N=10^{23}$ by infinity. One can then even estimate the relative error made by this replacement, and it is of the order $N^{-1/2}$, hence very tiny. Thus there is no barrier of the kind you seem to suggest. At least rigorously proving the validity of QM to 11 decimal places is in principle feasible.

Does this book explain why a priori probability density in the phase space is uniform? Or is it just an axiom?

I'm not sure what Ruelle's book exactly states, not the present state of the art. However, in general, the rigourous proofs are not sufficient either because the time needed for convergence to reach equilibrium is far longer than what is observed (eg. comments on ergodic theorems at the end of https://ocw.mit.edu/courses/physics...-fall-2013/lecture-notes/MIT8_333F13_Lec7.pdf), or when the convergence to equilibrium is fast enough it is restricted to some special class of dynamical systems (eg. Axiom A type https://en.wikipedia.org/wiki/Axiom_A or http://www.ihes.fr/~ruelle/PUBLICATIONS/[42].pdf) for which there is no proof that that class includes most physical systems.

Interesting comments on Axiom A systems here: https://arxiv.org/abs/1604.07672v1 and http://www.scholarpedia.org/article/Chaotic_hypothesis.

 

[ShayanJ]

it removes the weirdness from QM.

No it doesn't. The weirdness of QM is encapsulated in its violation of Bell-type inequalities. Bell guaranteed that we can't think about the microscopic world using our intuition from the macroscopic world. Any theory that violates Bell-type inequalities still has some of that weirdness and BM is no exception. Its true that in BM particles have definite positions and momenta at all times, but you have the quantum potential with its weird behavior and probably other weird things.

As I said, I myself don't like BM because I like a smart nature that can handle its business without giving that much attention to its details. I really don't like BM to be the actual mechanism behind the nature and I don't think it is. But this is not a physical argument and I won't let this undermine my ability to assess actual physical arguments for and against BM. What I don't like is when some people think that "I don't like it" is actually a physical argument!

 

[atyy]

No it doesn't. The weirdness of QM is encapsulated in its violation of Bell-type inequalities. Bell guaranteed that we can't think about the microscopic world using our intuition from the macroscopic world. Any theory that violates Bell-type inequalities still has some of that weirdness and BM is no exception. Its true that in BM particles have definite positions and momenta at all times, but you have the quantum potential with its weird behavior and probably other weird things.

As I said, I myself don't like BM because I like a smart nature that can handle its business without giving that much attention to its details. I really don't like BM to be the actual mechanism behind the nature and I don't think it is. But this is not a physical argument and I won't let this undermine my ability to assess actual physical arguments for and against BM. What I don't like is when some people think that "I don't like it" is actually a physical argument!

The Bell inequalities say reality is nonlocal. Reality is not weird unless you think nonlocality is weird.

 

[PeterDonis]

Everyone, "weird" and similar adjectives are subjective judgments, not scientific terms. Please keep the discussion on topic.

 

[ShayanJ]

The Bell inequalities say reality is nonlocal. Reality is not weird unless you think nonlocality is weird.

I think Bell's assumptions are a good description of what we'd call non-weird. Its not something subjective, Newtonian mechanics is not weird. But relativity is, and any theory that violates Bell-type inequalities is. Weird means non-intuitive and strange to our common sense and our intuition and common sense come from years of living as macroscopic beings dealing with other macroscopic beings and always moving much slower than light w.r.t. each other.
So for me, the fact that you can somehow rewire your mind so that you call relativity, non-locality, etc. intuitive and appealing to common sense doesn't mean that they're not weird. They're weird for a macroscopic being moving much slower than light.
I should mention that I have no problem with relativity and I really love it and have succeeded in developing an intuition for it but as I said that's not natural for a human being.

 

[PeterDonis]

I think Bell's assumptions are a good description of what we'd call non-weird.

Yes, but it's still your opinion and not something that's amenable to scientific testing. So, as I said, it's off topic. This thread is supposed to be about scientific aspects of Bohmian mechanics, not who does or does not think it is "weird". Please bear that in mind.

 

[atyy]

So I would ask any Bohmian why there is a limit - in a nonlocal theory - to entanglement which exactly matches the limits given by c. You never see 2 entangled particles unless they were in contact (limited by c) with some other system that gave rise to the entanglement. I would think that non-local mechanism would give rise to entanglement of all kinds of other things where c is not a limiting factor, if it is also the "out" that explains quantum non-locality. (And yes I know BM is supposed to be equivalent to QM, but this question still seems open to me.)

This part is put in by hand, but it is not restricted to Bohmian Mechanics, and we can restrict ourselves to Copenhagen QM. If we take the Wilsonian view of QFT (in the Copenhagen interpretation), then QED should be thought of as conceptually arising from a non-relativistic quantum mechanical system such as lattice QED. There are also other ways in which relativistic QED can arise from a non-relativistic lattice theory with different degrees of freedom than just a discretization of QED. In these systems, technically, FTL is permitted. In practice they are not. These are governed by Lieb Robinson bounds: https://arxiv.org/abs/0808.2495.

Within BM, in addition to emergent relativity via a Lieb-Robinson bound, the other assumption that is important is quantum equilibrium. In particular cases, this can be justified analogously to how equilibrium statistical mechanics can arise from Newtonian mechanics.

The two key ideas are:
1. Quantum equilibrium allows BM to approximate non-relativistic QM as closely as needed.
2. Lieb Robinson bounds allow non-relativistic QM to approximate relativistic QM as closely as needed.

Taken together these are at the physics level of rigour (but the Lieb-Robinson bound has been made very rigourous), and the major flaw in this argument is that even at the physics level of rigour the argument does not yet seem to go through for chiral fermions interacting with non-abelian gauge fields. I believe it is fine for QED and quantum gravity.

 

[A. Neumaier]

what Ruelle's book exactly states, not the present state of the art.

Its an old book, thus it definitely doesn't tell the state of the art. But in math, old books don't become obsolete, truth is truth at all times.
Most results, however, are not based on the ergodic theorem, so what you write is not so relevant.

 

[A. Neumaier]

What I don't like is when some people think that "I don't like it" is actually a physical argument!

Why did you then complain when I argued that physicists make choices based on with what they can feel happy? It is not a physics argument but an argument why one is prepared to consider certain assumptions or arguments as fruitful. Fruitful is also a subjective aspect, but very important in the development of science!

 

[atyy]

Its an old book, thus it definitely doesn't tell the state of the art. But in math, old books don't become obsolete, truth is truth at all times.
Most results, however, are not based on the ergodic theorem, so what you write is not so relevant.

You are clearly not familiar with the work you cite! Ruelle's resulst are axiom A results!

 

[Demystifier]

If by real you mean EPR real, they are not.

So, if I understood you correctly, the first spin is EPR real (because it is measured by Alice), the second spin is also EPR real (because it is measued by Bob), but both spins together are not EPR real (because nobody observed both spins). Is that what you are saying?

 

[Demystifier]

So my point is that non-realism has nothing to do with saying "nothing exists". It only has to do with saying: "no initial configuration determines the observed outcome."

I think this should be called non-determinism.

We live in a subjective universe, and how we choose to observe actively shapes the reality we see.

This is non-realism. But I never understood why so many people think that non-determinism and non-realism is the same.

 

[Demystifier]

But no reference is given...

Any book or review paper on BM, or the original Bohm's two papers from 1951.

 

[Demystifier]

I'd be interested to know what happens in a relativistic version of Bohmian mechanics. Do the microscopic particle positions respect Einstein causality, or is the latter considered to be a statistical effect?

It is a statistical effect. See e.g.
https://arxiv.org/abs/1205.1992

 

[A. Neumaier]

You are clearly not familiar with the work you cite! Ruelle's resulst are axiom A results!

He wrote several books, which you conflate. You seem to refer to his book Thermodynamic Formalism. The Mathematical Structures of Equilibrium Statistical Mechanics whereas I was referring to https://www.amazon.com/dp/9810238622/?tag=pfamazon01-20.

 

[RockyMarciano]

So, if I understood you correctly, the first spin is EPR real (because it is measured by Alice), the second spin is also EPR real (because it is measued by Bob), but both spins together are not EPR real (because nobody observed both spins). Is that what you are saying?

No. You keep conflating the broadest philosophical meaning and the EPR meaning of "real". Neither Alice's nor Bob's measures are separately EPR real as is shown by the experiments of BI violation. But if Alice or Bob make a measurement these are of course real in the sense that it is not something just in their mind, by definition of measurement in science.

This is non-realism. But I never understood why so many people think that non-determinism and non-realism is the same.

Because they are the same in the EPR definition of realism as deterministic. They are of course not the same in the philosophical definition of realism I gave that you normally use when referring to realism.

 

[A. Neumaier]

It is a statistical effect. See e.g.
https://arxiv.org/abs/1205.1992

Thanks. I didn't know this paper. When viewed in the large $N$ limit, does your many-particle relativistic quantum mechanics reproduce macroscopic continuum mechanics? Or is it just a proposal studied for its own sake?

 

[A. Neumaier]

You keep conflating the broadest philosophical meaning and the EPR meaning of "real".

This is not a thread to discuss and correct notions of ''real'' but one on Bohmian mechanics. Please keep your remarks on topic.

 

[Demystifier]

When viewed in the large $N$ limit, does your many-particle relativistic quantum mechanics reproduce macroscopic continuum mechanics?

Yes (but not in a way you naively expect).

 

[RockyMarciano]

This is not a thread to discuss and correct notions of ''real'' but one on Bohmian mechanics. Please keep your remarks on topic.

I was answering a direct question by the official Bohmian around here.Either the question is on topic and then the answer is, or the question is off topic and then you should make your comment addressing the question.

 

[A. Neumaier]

Yes (but not in a way you naively expect).

In which way, then?

 

[A. Neumaier]

I was answering a direct question by the official Bohmian around here. Either the question is on topic and then the answer is, or the question is off topic and then you should make your comment addressing the question.

I did it already: https://www.physicsforums.com/posts/5665529/ and posts #95-#97. But you didn't listen.

Single posts easily slide away from a topic. But a post already off-topic (and in response to one of your comments that was already off-topic) doesn't justify answering a direct question in it in the same thread. If you want to answer to something off-topic you can always open a new thread to do so, and copy the link to the originating post there.

 

[RockyMarciano]

Ok, then here are some of Bell's own words:
"It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of “local causality” or “no action at a distance”. Of course, mere correlation between distant events does not itself imply action at a distance, but only correlation between the signals reaching the two places. These signals, in the idealized example of Bohm, must be sufficient to determine whether the particles would go up or down. For any residual undeterminism could only spoil the perfect correlation. It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis."

This is just playing semantically with the distinction between inferences and assumptions. The premise of BI that measurements in the same direction determines perfect anticorrelation measurements pressumes simultaneous existence of the spin measurement angles at certain initial time t, therefore determinism despite of how common sense this premise might appear. The fact is that this premise is implied by "no action at a distance" i.e. classical locality principle when applied to spacelike separated regions. So here the classical notion of locality based on simultaneity is used, i.e. the classical determinism with an initial state at time t=0 with a Cauchy surface of simultaneous measurements outcomes.

And please try not to use "realism" in QM context unless you mean "not solipsism" because it's very confusing what you mean with it. (is it determinism here? or causality? or particles having spin at all times?)

In the context of EPR, EPR realism is clearly well defined, so why not use it? The meaning "not solipsism" is the broadest philosophical meaning and this is indeed confusing in the quantum context of EPR.

 

[Demystifier]

In which way, then?

Classical fluid consists of many classical mutually non-entangled particles. Quantum mechanically, each of these particles can be considered to have it's own wave function, the width of which is of the order of Bohr radius. By Ehrenfest theorem, the "center" of each of these wave packets moves by classical laws. In BM, each of these wave packets is filled with a few pointlike particle (depending on the kind of atom one talks about). Within packet the Bohmian motion of the particles is highly non-classical. Nevertheless, since each particle is confined within the packet (the center of which moves classically), this non-classical motion looks pretty classical at large macroscopic distances.

 

[RockyMarciano]

I did it already: https://www.physicsforums.com/posts/5665529/ and posts #95-#97. But you didn't listen.

And then in #99 you asked a question as off-topic from the OP as the ones Demystifier have been asking me.

 

[A. Neumaier]

And then in #99 you asked a question as off-topic from the OP as the ones Demystifier have been asking me.

It is my thread and my question in #99 was about an aspect of Bohmian mechanics quite related to the title. But you answered in #131 again an offtopic post by zonde to one of your off-topic posts and contribute in this way to the pollution of the thread.

 

[A. Neumaier]

Classical fluid consists of many classical mutually non-entangled particles. Quantum mechanically, each of these particles can be considered to have it's own wave function, the width of which is of the order of Bohr radius. By Ehrenfest theorem, the "center" of each of these wave packets moves by classical laws. In BM, each of these wave packets is filled with a few pointlike particle (depending on the kind of atom one talks about). Within packet the Bohmian motion of the particles is highly non-classical. Nevertheless, since each particle is confined within the packet (the center of which moves classically), this non-classical motion looks pretty classical at large macroscopic distances.

I don't see how starting from your relativistic multiparticle version, this gives macroscopic continuum mechanics. Reference?

 

[RockyMarciano]

It is my thread

Ok, if it comes down to this I'm out.

 

[Demystifier]

I don't see how starting from your relativistic multiparticle version, this gives macroscopic continuum mechanics. Reference?

I've just explained it in the post above, but in a sketchy way. If you don't see it I would need to write a long article with all details for you, which I don't plan to do. There is no reference because it is considered obvious, not only in the BM community, but also in the clasicallity-from-decoherence community.

 

[A. Neumaier]

There is no reference because it is considered obvious, not only in the BM community, but also in the clasicallity-from-decoherence community.

Strange. In statistical mechanics, it is considered nontrivial to derive macroscopic continuum mechanics from microscopic multiparticle theory, but apparently in BM everything trivializes so that none of the difficult things must be done. It is this attitude that was criticised by Reinhard Werner in the article quoted in post #1,

The Bohmian perspective seems to be the opposite. You don’t care about the hard problem, but only about that last, utterly trivial bit.

 

[Demystifier]

In statistical mechnaics, it is considered nontrivial to derive macroscopic continuum mechanics from microscopic multiparticle theory, but apparently in BM everything trivializes so that none of the difficult things must be done.

It is of course non-trivial (either with or without BM) to do it rigorously. But it is trivial if you don't insist on rigor.

Anyway, you might be interested in
https://arxiv.org/abs/quant-ph/0112005

 

[Demystifier]

I don't see how starting from your relativistic multiparticle version, this gives macroscopic continuum mechanics. Reference?

I have noticed that many of your questions about BM totally miss the point. To exaggerate a bit, many of your questions sound to me like: OK, string theory is the theory of everything, so how string theory explains the protein folding? Reference?

BM is supposed to be a fundamental theory, but it does not mean that it can easily answer all possible macroscopic questions. See
http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf

 

[A. Neumaier]

BM is supposed to be a fundamental theory

Therefore I ask the questions that I expect a fundamental theory to solve. I am not interested in foundations that are not even trying to address these questions. They are fake foundations, in my view.

I have noticed that many of your questions about BM totally miss the point.

You effectively tell me that I shouldn't be interested in Bohmian mechanics. I had noticed this myself over the course of years. But I still ask these questions so that others can see it, too.

 

[dextercioby]

Ok, if it comes down to this I'm out.

Don't feel offended, Arnold is trying to do something never achieved before: keeping a thread about interpretations of QM as much as possible on-topic and philosophy-free. Almost succeeding.

 

[Demystifier]

You effectively tell me that I shouldn't be interested in Bohmian mechanics.

I am not sure whether you are really interested in BM (or only interested in disproving* BM), but if you are, it seems to me that you are interested for wrong reasons. From a Bohmian point of view, standard QM is an effective theory emerging from more fundamental BM. For many high-level questions it is much more appropriate to use effective theory instead of fundamental theory. Different physical questions need different effective theories. See the paper "More is different" by Anderson I linked above. So yes, in a way I am telling you that you shouldn't be interested in Bohmian mechanics, just as I would tell you that you shouldn't be interested in quantum electrodynamics if you asked me about radiation from antenna (for which classical electrodynamics is a much better tool).

(*I have never seen that you said anything positive about BM. In all these years you either criticize it, or ask questions which sound like "Ha, I bet you can't answer this one!".)

 

[A. Neumaier]

I am not sure whether you are really interested in BM (or only interested in disproving* BM)

I am highly interested in good and strong foundations of quantum mechanics. As part of my efforts there I look at what each interpretations contributes to the understanding of the questions that I find good foundations should settle. In particular, I ask questions, give answers, and criticize in this spirit.

(*I have never seen that you said anything positive about BM.

This is because I share the sentiment of Reinhard Werner expressed in the quotes in post #1 that, unfortunately, there is very little positive to say about BM. Querying for possible positive things that I might have overlooked only confirms that. These queries are dismissed with comments such as

In all these years you either criticize it, or ask questions which sound like "Ha, I bet you can't answer this one!".

 

[A. Neumaier]

unfortunately, there is very little positive to say about BM.

I have even less positive to say about Many Worlds. It has not even a mathematical basis but is pure speculation.

 

[A. Neumaier]

I don't think so. On the other hand, demystifier is on record saying "... it cannot be said that there exists a well-defined relativistic QM." There's always an out!
But now
http://xxx.lanl.gov/pdf/quant-ph/0609163v2

It is a statistical effect. See e.g.
https://arxiv.org/abs/1205.1992

he thinks there is one. Though it is a nonstandard one that does not make the same predictions as QED. That's why I had asked

When viewed in the large $N$ limit, does your many-particle relativistic quantum mechanics reproduce macroscopic continuum mechanics? Or is it just a proposal studied for its own sake?

I don't see how starting from your relativistic multiparticle version, this gives macroscopic continuum mechanics. Reference?

Because this is the least test a theory different from QED must pass to be taken seriously. Unfortunately, the answer I got was only

There is no reference because it is considered obvious, not only in the BM community, but also in the classicality-from-decoherence community.

although the question is about the relativistic multiparticle theory itself and not the Bohmianization of it. Bohmian mechanics may be confident that they predict the same relativistic results as the theory that they Bohmianize, but if the latter makes wrong predictions then the Bohmian version makes the same wrong predictions.

Thus it is important to have clarified the status of the unbohmianized version. And in contrast to what demystifier claims, the classicality-from-decoherence community has never studies this relativistic quantum theory. Not because they consider it obvious (where is the reference that justifies this claim?) but because they consider it an exotic proposal.

 

[Demystifier]

there is very little positive to say about BM

If so, why are you still so much interested in it? Why do you waste your time? Why don't you just ignore it?

I often criticize Copenhagen, MWI, or minimal ensemble, but I would never do that if I didn't also see many positive things about those. On the other hand, I spend no time to criticize thermal interpretation.

 

[A. Neumaier]

Why don't you just ignore it?

I had answered this already:

As part of my efforts there I look at what each interpretations contributes to the understanding of the questions that I find good foundations should settle. In particular, I ask questions, give answers, and criticize in this spirit.

 

[rubi]

Here is another objection that I realized in the last thread, which unfortunately got hijacked and locked.

Apparently, Bohmian mechanics needs to model the complete system, including the apparatus and the environment, in order to (perhaps) agree with the QM predictions. In response to a question by @stevendaryl, Demystifier replied:

When the measurement setup is changed, then it is $P(\lambda)$ that gets modified.

I agree that this must happen in BM, but it seems to me that this makes BM superdeterministic. In a deterministic theory, the assumption $P(\lambda,\vec a,\vec b) = P(\lambda)$ is usually taken to model the free choice of the experimenters. If BM can only reproduce QM by taking the measurement process into account, it appears to deny this free choice.

 

[Demystifier]

I agree that this must happen in BM, but it seems to me that this makes BM superdeterministic. In a deterministic theory, the assumption $P(\lambda,\vec a,\vec b) = P(\lambda)$ is usually taken to model the free choice of the experimenters. If BM can only reproduce QM by taking the measurement process into account, it appears to deny this free choice.

I'm glad that you asked it. Indeed, there is no free choice in BM because it is a fully deterministic theory. However, it is not superdeterministic theory. In a superdeterministic theory the initial conditions are fine tuned in order to simulate a law which does not really exist as a law. (For instance, 't Hooft studies superdeterministic local hidden variables for QM, where the appearance of non-locality is simulated by fine tuned initial conditions for local hidden variables.) There is no such fine tuning of initial conditions in BM. Similar to classical mechanics, BM is fully deterministic but not superdeterministic.