A Would this experiment disprove Bohmian mechanics?

[Boing3000]

The claim that paths exist in any sense, even if they are hidden, is so serious that it literally refutes all of QM if correct.

How could it "refutes" QM if it make the same prediction. Similarly, how could the existence of X dimensional "strings" refute QM.
That's not how physics work. Classical mechanics is no refuted either by QM. It extends it to some other domain.

I think it's shocking something like this could be taken seriously.

 

[bolbteppa]

How could it "refutes" QM if it make the same prediction. Similarly, how could the existence of X dimensional "strings" refute QM.
That's not how physics work. Classical mechanics is no refuted either by QM. It extends it to some other domain.

Classical mechanics is very viciously refuted by quantum mechanics...

Classical mechanics (both non-relativistic and relativistic) literally claims that a mechanical system is completely described by knowing the positions and velocities/momenta of all particles/fields in the system at each instant of time (Landau vol. 1 sec. 1), i.e. it is in principle possible to know the coordinates and momenta of a particle at each moment in time and so know the path of the particle (which is described by knowing the positions and velocities at each point along the path) - knowing this is to know everything about the behavior of a mechanical system - in other words paths exist and based on this the question is then what the rules are to actually find the path of a given particle in a given situation, and on this basis we can set up either the POLA (global formulation) or some modification of Newton's laws (local formulation).

No matter what games you play, if paths exist there simply must be equations which describe those paths, or at least approximate the true paths if they're 'really' described by discrete equations or fractal equations or something insane, you'd still have something less than probability, and so we could in principle just set up F = ma where the form of F is simply not what we get according to say the assumptions one uses in a POLA formulation for forming the action (based on symmetry principles) which leads to F = ma. This is a chaotic world but it's a classical world. To deny this is to deny mathematics.

The very first claim of quantum mechanics (Landau vol. 3 sec. 1) is that paths just don't exist, this is a statement of the uncertainty principle, because if they did we could just use some formulation of classical mechanics to describe those paths, i.e. we could just set up differential equations for the curves the particles 'really follow' and call these differential equations the true formulation of F = ma, and we should in principle be able to know why our measurements are not getting the right results. Again, it is to simply deny mathematics to claim this is not possible if you allow for the concept of paths to exit. Since a path is described by positions and velocities, and we know classical mechanics should exist in some sense, and we can do things like measure the positions of particles at given instants (e.g. electrons in gas chambers, and we can measure at successive instants and we simply find it ends up in places such that no concept of a path could exist, again Landau vol. 3 ch. 1), we can see it may be possible to still set up some new theory which reduces to classical mechanics in some to-be-defined limit of less accurate measurements...

Because all we've done is destroy classical mechanics, we have no theory, so one needs to then set up a theory, which is postulating the Born rule or something equivalent (which is why claims of being able to derive the Born rule are as ridiculous as saying one can derive something from nothing), again very plausible from experiments which show paths don't exist, but they should exist the less accurately we measure...

The claim that Bohmian mechanics makes, that paths are 'hidden', is simply so radical it either has to be true or not true, and it literally refutes the most basic claim of quantum mechanics, of course a theory which steals equations from a well-defined theory and calls them axioms will end up with the solutions of those equations, nowhere else in science does one take seriously the stealing of equations and call this a theory...

That said, the first Bohm paper is worth reading.

String theory, a quantum theory, is completely different, in no way analogous to comparing classical and quantum mechanics...

 

[Nugatory]

Classical mechanics is very viciously refuted by quantum mechanics...

That argument is based on a misconception about what it means to say that a physical theory is correct.
https://www.physicsforums.com/insights/classical-physics-is-wrong-fallacy/
https://chem.tufts.edu/answersinscience/relativityofwrong.htm

It is also a complete hijack of the original poster's question, so this thread is the wrong place to continue the discussion.

 

[Demystifier]

That said, the first Bohm paper is worth reading.

May I ask why do you think so?

By the way, many misunderstandings of Bohmian mechanics (BM) stem from reading only the first and not the second Bohm's paper. The true essence of BM can only be found in the second paper, which explains what happens during the measurement and why BM makes the same measurable predictions as standard QM. About 99% of "disproofs" of BM arise from ignoring the Bohm's crucial insight about the measurement process in the second paper.

 

[vanhees71]

I always thought BM is completely superfluous from just reading Bohm's paper. Just this weekend I've found an excellent new German textbook on BM by D. Dürr, where it becomes much more convincing. I think now that BM for non-relativistic QM it's a true alternative interpretation to the minimal statistical interpretation without changing the phenomenological content of standard non-relativistic QM. Unfortunately there seems not to be a convincing Bohmian reinterpretation of relativistic QFT and the Standard Model. I think a good English textbook by the same author is

D. Duerr, S. Teufel, Bohmian Mechanics, Springer (2009)

 

[Demystifier]

I always thought BM is completely superfluous from just reading Bohm's paper. Just this weekend I've found an excellent new German textbook on BM by D. Dürr, where it becomes much more convincing. I think now that BM for non-relativistic QM it's a true alternative interpretation to the minimal statistical interpretation without changing the phenomenological content of standard non-relativistic QM. Unfortunately there seems not to be a convincing Bohmian reinterpretation of relativistic QFT and the Standard Model. I think a good English textbook by the same author is

D. Duerr, S. Teufel, Bohmian Mechanics, Springer (2009)

I am very very glad to see that you changed your opinion about non-relativistic BM. May I ask what was the crucial insight in this book that changed your opinion? Was it mathematical rigor or was it something else?

By the way, I would recommend to ignore Chapter 16 (in the English book). It's technically correct, but physically can be very misleading.

 

[vanhees71]

The mathematical rigor is just at the right level in this book. I never though BM to lack mathematical rigor, but I didn't get what it adds to the solution of the apparent interpretational problems of QT since I had the impression they just put in what they want to find out and add Bohmian trajectories which are not observable anyway. That's wrong in the approach by Dürr at all. There the (many-body!) wave function is not a probability amplitude as in the standard minimal interpretation to begin with but a "pilot wave" dictating the non-local deterministic particle dynamics, and the probabilistic meaning of the effective wave function of the observed systems is derived from it, and the "split" in measured ("microscopic") systems and the "macroscopic" measurement apparatus is consistently described within BM, as explained by Dürr.

So the main reason for changing my opinion was the derivation of the "quantum equilibrium conjecture" from BM. It's not ad hoc as it occurs in everything I've read so far about BM but it simply follows from the usual continuity equation of probabilities,
$$\dot{\rho} + \vec{\nabla} \cdot \vec{j}=0,$$
where
$$\rho=|\psi|^2, \quad \vec{j}=\frac{-\mathrm{i}}{2m} [\psi^* \vec{\nabla} \psi -(\vec{\nabla} \psi^*)\psi].$$
Given that the BM trajectories are defined through the stream lines of the velocity field $\vec{v}$ which obeys $\vec{j}=\rho \vec{v}$ makes this consistent.

It's also convincingly derived that Born's rule, i.e., the possibility to derive the probabilistic meaning of the wave function in the standard (minimal) interpretation can be derive from the pilot-wave concept by considering the measured system as partial object of the full wave function including the macroscopic measurement apparatus for me makes BM to a reall non-local deterministic reinterpretation letting you derive the probabilistic meaning for the "effective wave function" of the measured system from this deterministic theory as you derive the probabilistic meaning of phase-space distribution functions for partial systems from Liouville's theorem of Hamiltonian many-body dynamics. In a sense you can take the quantum-mechanical probability-continuity equation of the orthodox interpretation as the "Liouville equation" for Bohmian many-body dynamics, leading to statistical descriptions for partial systems, i.e., the orthodox interpretation is derived from the deterministic Bohmian dynamics.

As I said, the only problem with the Bohm-de Broglie ansatz is that there's no convincing relativistic interpretation. My feeling is that this should somehow be possible using Schwinger's and Tomonaga's multi-time formalism of QFT, and instead using "wave functions" as pilot waves for particle trajectories one has to establish some "wave functional" as "pilot wave" for field correlation functions (various N-point functions). I'm sure that this has been tried since it's an obvious ansatz. If you know a paper in this direction, I'd be glad to look at it.

 

[Demystifier]

The mathematical rigor is just at the right level in this book. I never though BM to lack mathematical rigor, but I didn't get what it adds to the solution of the apparent interpretational problems of QT since I had the impression they just put in what they want to find out and add Bohmian trajectories which are not observable anyway. That's wrong in the approach by Dürr at all. There the (many-body!) wave function is not a probability amplitude as in the standard minimal interpretation to begin with but a "pilot wave" dictating the non-local deterministic particle dynamics, and the probabilistic meaning of the effective wave function of the observed systems is derived from it, and the "split" in measured ("microscopic") systems and the "macroscopic" measurement apparatus is consistently described within BM, as explained by Dürr.

So the main reason for changing my opinion was the derivation of the "quantum equilibrium conjecture" from BM. It's not ad hoc as it occurs in everything I've read so far about BM but it simply follows from the usual continuity equation of probabilities,
$$\dot{\rho} + \vec{\nabla} \cdot \vec{j}=0,$$
where
$$\rho=|\psi|^2, \quad \vec{j}=\frac{-\mathrm{i}}{2m} [\psi^* \vec{\nabla} \psi -(\vec{\nabla} \psi^*)\psi].$$
Given that the BM trajectories are defined through the stream lines of the velocity field $\vec{v}$ which obeys $\vec{j}=\rho \vec{v}$ makes this consistent.

That, of course, is said in many other texts on BM. Either you didn't read many of them or, for some reason, it only now clicked to you. But better now than never. The book that created "click" in my head was the one by Holland, but it is slightly less mathematically rigorous so perhaps you would like it less than the Durr's one.

It's also convincingly derived that Born's rule, i.e., the possibility to derive the probabilistic meaning of the wave function in the standard (minimal) interpretation can be derive from the pilot-wave concept by considering the measured system as partial object of the full wave function including the macroscopic measurement apparatus for me makes BM to a reall non-local deterministic reinterpretation letting you derive the probabilistic meaning for the "effective wave function" of the measured system from this deterministic theory as you derive the probabilistic meaning of phase-space distribution functions for partial systems from Liouville's theorem of Hamiltonian many-body dynamics. In a sense you can take the quantum-mechanical probability-continuity equation of the orthodox interpretation as the "Liouville equation" for Bohmian many-body dynamics, leading to statistical descriptions for partial systems, i.e., the orthodox interpretation is derived from the deterministic Bohmian dynamics.

The analogy with classical statistical mechanics is also emphasized in many other texts, but perhaps other texts don't explicitly mention the analogy with the Liouville equation. Now I see that they should.

As I said, the only problem with the Bohm-de Broglie ansatz is that there's no convincing relativistic interpretation. My feeling is that this should somehow be possible using Schwinger's and Tomonaga's multi-time formalism of QFT, and instead using "wave functions" as pilot waves for particle trajectories one has to establish some "wave functional" as "pilot wave" for field correlation functions (various N-point functions). I'm sure that this has been tried since it's an obvious ansatz. If you know a paper in this direction, I'd be glad to look at it.

How about my own one? https://lanl.arxiv.org/abs/0904.2287
(I have written it in my younger days when I still thought that Lorentz invariance should be fundamental.)

 

[vanhees71]

I'll have a look at it.

 

[bolbteppa]

That argument is based on a misconception about what it means to say that a physical theory is correct.
https://www.physicsforums.com/insights/classical-physics-is-wrong-fallacy/
https://chem.tufts.edu/answersinscience/relativityofwrong.htm

My posts, which said things like "we know classical mechanics should exist in some sense", are in agreement with your links - I am in no way questioning the fact classical mechanics, to quote the first link, "appears as a “simplification” or “approximation” whereby it becomes more and more valid as various parameters approach the common, everyday, terrestrial values", I'm just explaining the theoretical reason QM claims for why classical mechanics is just an approximation (paths don't exist) as part of addressing why the theory (Bohmian mechanics) the OP is asking about doesn't make enough sense to be disproven wrong...

It is also a complete hijack of the original poster's question, so this thread is the wrong place to continue the discussion.

If it is a complete hijack of a thread asking if experiment X would disprove theory Y to say theory Y does not make enough sense to be disproven in the first place, I can leave it no problem...

 

[bolbteppa]

May I ask why do you think so?

I think it's a good attempt, I think his thinking in the first few pages is interesting, I think it's interesting to try to frame QM as analogous to statistical mechanics as a way to explain why experiments indicate paths do not exist as a way to save the idea of paths existing as though they were analogous to the microscopic variables underlying statistical mechanics - but then to go off and literally just steal equations and concepts like wave functions out of thin air and use them blindly (because he wants to recover normal QM theory) is actually so egregious it can't be taken seriously...

By the way, many misunderstandings of Bohmian mechanics (BM) stem from reading only the first and not the second Bohm's paper. The true essence of BM can only be found in the second paper, which explains what happens during the measurement and why BM makes the same measurable predictions as standard QM. About 99% of "disproofs" of BM arise from ignoring the Bohm's crucial insight about the measurement process in the second paper.

The second paper does even less to address the fundamental issues with paths not existing and his use of concepts derived explicitly on the assumption of no paths as a way to end up with a theory allowing paths to exist.

(I have written it in my younger days when I still thought that Lorentz invariance should be fundamental.)

I must say any claims that Galilean relativity rules the world and in any way underlies relativity let alone the standard model is probably even more egregious than the notion of paths existing, it's not only denying quantum theory (since we are only trying to fit the square peg of Galilean relativity into the round hole of relativistic quantum theory in order to try to save Bohmian mechanics) it's also denying Einsteinian relativity, I don't know how people take this seriously - quantum field theory is fascinating and hard enough without trying to recover this stuff from a starting point which denies the very thing (lack of determinism) leading to all this stuff in the first place, but to also deny relativity as being fundamental, this is actually unbelievable.

 

[bobob]

The problem with trying to falsify bohmian mechanics is that the folks who see bohmian mechanics as an explanation will never make use of its ontology to make a prediction that differs from standard quantum mechanics, even though there is physics in the difference between interpretations. Standard quantum mechanics is telling you that the amount of information that exists about something is lmited by the uncertainty relations and that since nature follows tyhe same laws of physics that everything else (including us) must follow, even nature has no more information about those quantities. On the other hand, bohmian mechanics is telling you that information is there and used by nature, but for whatever reason (the quantum equilibrium hypothesis), we cannot access it. That should lead to different ways of figuring entropies. However, the point of bohmian mechanics seems to be to make certain that it doesn't get different answers from quantum mechanics, so no matter what the ontology might imply, it will be disregarded if it actually implies anything physical.

 

[Mentz114]

[]
So the main reason for changing my opinion was the derivation of the "quantum equilibrium conjecture" from BM. It's not ad hoc as it occurs in everything I've read so far about BM but it simply follows from the usual continuity equation of probabilities,
$$\dot{\rho} + \vec{\nabla} \cdot \vec{j}=0,$$
where
$$\rho=|\psi|^2, \quad \vec{j}=\frac{-\mathrm{i}}{2m} [\psi^* \vec{\nabla} \psi -(\vec{\nabla} \psi^*)\psi].$$
Given that the BM trajectories are defined through the stream lines of the velocity field $\vec{v}$ which obeys $\vec{j}=\rho \vec{v}$ makes this consistent.
[]

I recently read ( and finally grasped) the derivations of the Schrodinger equation and a classical wave equation in Schleich et. al.
It is impressive that one can write a (non-linear) wave equation for classical mechanics that reproduces the evolution of density in standard statistical mechanics.
But the way one derives the linear Schrodinger equation from the same ancestor I found illuminating. It requires two assumptions different from the classical case namely a different continuity equation and that the quantum dynamics be governed by the BM quantum potential. The second assumption removes the non-linear term from the classical equation.

This suggests that the Schrodinger equation silently assumes the BM equation of motion. I think I might get Duerr and Teufel (2009).

 

[Boing3000]

The problem with trying to falsify bohmian mechanics is that the folks who see bohmian mechanics as an explanation will never make use of its ontology to make a prediction that differs from standard quantum mechanics, even though there is physics in the difference between interpretations.

My understanding is that depends entirely on the existence of "non-equilibrium" configuration. That may or may-not exist. The fact that it may, and that is a feature uniquely understandble through BM, makes it a very interesting topic.

Standard quantum mechanics is telling you that the amount of information that exists about something is lmited by the uncertainty relations and that since nature follows the same laws of physics that everything else (including us) must follow, even nature has no more information about those quantities.

Nature certainly has enough information to frustrate physicists about information availability. I don't think the converse is true.

On the other hand, bohmian mechanics is telling you that information is there and used by nature, but for whatever reason (the quantum equilibrium hypothesis), we cannot access it. That should lead to different ways of figuring entropies.

And that's what actually make me appreciate BM. The quantum equilibrium, and especially its connection with non locality (as explained in the last paragraph here)

However, the point of bohmian mechanics seems to be to make certain that it doesn't get different answers from quantum mechanics, so no matter what the ontology might imply, it will be disregarded if it actually implies anything physical.

Not quite. The point of BM if the same point as QM (and the converse is true). It's quite a tautology, as BM is QM. The only valid reason why it is disregarded, is that it is not as powerful as QFT.

 

[bolbteppa]

The problem with trying to falsify bohmian mechanics is that the folks who see bohmian mechanics as an explanation will never make use of its ontology to make a prediction that differs from standard quantum mechanics, even though there is physics in the difference between interpretations.

The start of Bohm's paper makes very clear one should not only find new results, one should actually improve on standard QM in the realms where (he claims/at the time) it had issues

"...our alternative interpretation permits modifications of the mathematical formulation which could not even be described in terms of the usual interpretation. Moreover, the modifications can quite easily be formulated in such a way that their effects are insignificant in the atomic domain, where the present quantum theory is in such good agreement with experiment, but of crucial importance in the domain of dimensions of the order of 10cm, where, as we have seen, the present theory is totally inadequate. It is thus entirely possible that some of the modifications describable in terms of our suggested alternative interpretation, but not in terms of the usual interpretation, may be needed for a more thorough understanding of phenomena associated with very small distances"
- A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I. P166-167

e.g. especially in the domain where relativity kicks in, but let's just ignore that Bohm's theory by his own most basic reasoning should actually explain quantum field theory/RQM even better than the usual theory (the reality as we have seen in this thread is that one is likely to end up questioning special, special!, relativity as being fundamental) for no reason. This is another reason why it is simply so galling for him to go off and use the non-relativistic Schrodinger equation 2-3 pages later.

I recently read ( and finally grasped) the derivations of the Schrodinger equation and a classical wave equation in Schleich et. al.

Another Bohmian mechanics-like paper that begins with strawmen ('The reason given is that “it works”') that illustrates a serious lack of knowledge of the authors of basic standard QM ("This approach is unfortunate. Many of us recall feeling dissatisfied with this recipe.") and that magically introduces quantum concepts for no justifiable reason and calls them classical ("It is interesting that ħ appears in the nonlinear wave equation despite the fact that it is of classical nature"), this is unfortunately typical - every introduction of spin I have seen so far is even more hilarious, e.g. using the relativistic Dirac equation or spinor wave functions out of thin air but never a word about group representation theory or simple connectivity or why those concepts should even arise...

This suggests that the Schrodinger equation silently assumes the BM equation of motion. I think I might get Duerr and Teufel (2009).

Yes, Bohm derived everything from the Schrodinger equation, of course one can take PDE's like the Schrodinger equation and end up calling things velocity fields or paths or whatever you want, one needs to justify why one can even do this.

 

[Demystifier]

but then to go off and literally just steal equations and concepts like wave functions out of thin air and use them blindly (because he wants to recover normal QM theory) is actually so egregious it can't be taken seriously...

I don't understand. What's wrong with stealing results from other theories that are known to work? The point of Bohmian mechanics is not to replace QM with another theory. The point is to improve or refine QM to make it even better.

 

[bolbteppa]

I don't understand. What's wrong with stealing results from other theories that are known to work? The point of Bohmian mechanics is not to replace QM with another theory. The point is to improve or refine QM to make it even better.

It's very simple - one can't just steal equations (especially extremely complicated equations, and even worse extremely complicated equations obeying one symmetry group [Galilean] but not another [Lorentz], this is how one spots plagiarism in any other context) that were derived on the assumption of no paths, call them axioms and then use them to claim paths exist (in any sense) and expect to be taken seriously.

Doubly worse is calling this an improvement, refinement or an equivalent when one has literally torn to shreds the basis (no paths) which led to the equation they stole and then used those equations to derive the complete opposite (paths exist) of the claims (no paths) on which the entire theory rests.

 

[Mentz114]

[]
Yes, Bohm derived everything from the Schrodinger equation, of course one can take PDE's like the Schrodinger equation and end up calling things velocity fields or paths or whatever you want, one needs to justify why one can even do this.

This is your answer to speculation I made, which you clearly misunderstand. Most of your objections to BM seem to based on personal taste and have no discursive value.

 

[vanhees71]

For a long time I couldn't accept BM for the very reasons you state, but that's just that I've read not the best expositions of the theory. The point is that BM does not give the usual probabilistic meaning to the wave function but takes it as a "pilot wave", and the theory is a non-local deterministic theory of particle trajectories in configuration space.

Using this concept the probabilistic interpretation (Born's rule) is derived for effective wave functions describing "microscopic" subsystems in interaction with "macroscopic" measurement devices in an analogous way as you derive the probabilistic description of phase-space distribution functions from the Liouville equation.

All the ballast with making BM look like classical Hamilton-Jacobi descriptions and the ominous "quantum potential" (which is not a potential as in classical physics at all but brings in the non-locality).

It's also a feature of the theory that it leads to the same probabilistic predictions for measurements of microscopic objects with macroscopic measurement devices as QM in the standard minimal representation since QM is the best empirically verified theory ever. Whether you need (or even can afford) deviations from this standard core of QM is of course not clear, as long as alternative theories with such ingredients like spontaneous-collapse theories a la GRW aren't empirically tested with the necessary accuracy. In this sense BM is the most conservative interpretative extension of standard QM and as such pretty attractive.

 

[Boing3000]

It's very simple - one can't just steal equations

So QFT did not "steal" the equation of SR by using Lorentz covariance ?

that were derived on the assumption of no paths,

Can you point to a reference when that assumption is made ? Because not being based on "path" is not the same as proving they don't exist...

and expect to be taken seriously.

Actually reality has already proven you wrong on that point. So how can such a sentence be taken seriously ?

Doubly worse is calling this an improvement, refinement or an equivalent when one has literally torn to shreds the basis (no paths)

Actually, BM improve QM noticeably by getting rid of the measurement postulate (also known as the "measurement problem"), by not "tearing it to shred" whatever you think that may means.

which led to the equation they stole

Equations do not sit a a vault so that nobody can "steal" them

 

[Demystifier]

one can't just steal equations ... this is how one spots plagiarism

It's not plagiarism if you don't say (as Bohm didn't) that you invented those equations.

that were derived on the assumption of no paths,

The Schrodinger equation is not derived from the assumption of no paths. It is guessed from the analogy with Hamilton-Jacobi equation, which does involve paths. Moreover, the first wave equation for quantum mechanics was proposed by de Broglie, who explicitly introduced trajectories. For that reason, Bohmian theory is also called de Broglie-Bohm theory.

call them axioms and then use them to claim paths exist (in any sense) and expect to be taken seriously.

As you can see, many have taken Bohm seriously. That proves that he was right in expecting to be taken seriously.

the claims (no paths) on which the entire theory rests.

As I already said, the theory does not rest on the claim of no paths. Read about history of quantum mechanics.

 

[bolbteppa]

The Schrodinger equation is not derived from the assumption of no paths. It is guessed from the analogy with Hamilton-Jacobi equation, which does involve paths. Moreover, the first wave equation for quantum mechanics was proposed by de Broglie, who explicitly introduced trajectories. For that reason, Bohmian theory is also called de Broglie-Bohm theory... As I already said, the theory does not rest on the claim of no paths. Read about history of quantum mechanics.

This is such a fundamental misunderstanding of the most basic claims of quantum mechanics - the Schrodinger equation is absolutely derived on the assumption of no paths, please carefully (it's a hard but cool book) read secton 1 (this alone for the basic claim of no paths, but to then get the general Schrodinger equation read), 2, 3, 6, 7, 8 and then 17 (to see how specialized the non-relativistic form of the Schrodinger equation is) of Landau vol. 3 and be ready to compare to ch. 1 of vol. 1.

I should not even need to point out the flaws with going by historical derivations or the first/early attempts at making sense of QM.

This is unfortunately very typical of all of the proponents of BM I have seen so far, for example the earlier paper quoted, or discussions of spin - start from a misunderstanding of QM and then end up contradicting literally the most basic claims of the theory without realizing it, even worse when it leads to questioning special, special!, relativity - again, how is this taken seriously.

 

[bolbteppa]

For a long time I couldn't accept BM for the very reasons you state, but that's just that I've read not the best expositions of the theory. The point is that BM does not give the usual probabilistic meaning to the wave function but takes it as a "pilot wave", and the theory is a non-local deterministic theory of particle trajectories in configuration space.

I would be very open to it if you could actually explain how it makes even a hint of theoretical sense to use things like wave functions let alone insanely complicated and specialized things like the non-relativistic (my god) Schrodinger equation without fundamentally contradicting either the most basic principles of either mathematics or classical mechanics, or without fundamentally contradicting the most basic claim of QM that paths don't exist.

I was really disappointed with the leaps Bohm made after his initial setup in his paper (which also has it's issues, but we could go with it for arguments sake), it's amazing that even recent books on BM take these things as postulates...

 

[Demystifier]

and then end up contradicting literally the most basic claims of the theory without realizing it

It's OK as long as one doesn't contradict any existing experiments. And Bohm's theory doesn't.

 

[vanhees71]

Well, for a very good reason one uses non-relativistic quantum theory where it is applicable. It's just simpler to solve certain problems, e.g., the bound-state problem. Also there is indeed tension between BM and relativistic QFT. I've not yet seen a convincing concept to extend the pilot-wave ideas to relativistic QFT, but I've also not read about a clear proof that such a formulation is not possible. With Bohm's original papers I've also never been happy, but with the exposition of the theory by Dürr et al in their papers and textbooks I got convinced that de Broglie and Bohm have had a point, but weren't able to explain it clearly enough to convince the Copenhagen believers, which formed the strongest group for decades concerning the interpretation of QT (and they are the main culprits to make QM as weird as some people think it is; even without BM there's nothing weird as soon as you accept the minimal interpretation, which is FAPP all you ever need to describe real-world observations).

Einstein has been convinced for a short time after Bohm's theory came out, but very quickly he realized the "non-locality" which he (and many other physicists) couldn't accept at the time. This non-locality, however is inherent in standard QT without BM. The point of course is that (a) there was the work by Bell who made this metaphysical quibbles of Einstein's a physically testable issue, and as has been proven by zillions of experiments since the 1980ies when Aspect pioneered the field, the "non-locality" of QT is precisely what's realized in Nature.

However, and even this is denied by some proponents of Copenhagen who follow the collapse hypothesis, there's no tension with Einstein causality, because relativistic QFT is by construction microcausal and thus the S-matrix obeys the linked-cluster principle. In other words, the interactions in realtivistic QFT are strictly local by construction, while the "non-local" correlations (I prefer to say "long-range correlations" between far-distantly observed parts of a single quantum system) described by entanglement are of course still there as it must be for any QT and in accordance with all the very precise Bell experiments.

The merit of BM is that, at least for non-relativistic QT, shows that there is a consistent non-local deterministic theory which let's you derive the probabilistic interpretation (Born's rule) for microscopic systems as measured by macroscopic systems (measurement devices). On top there's no quantum-classical cut to be assumed within BM. In my opinion, however, that's also not the case in conventionally minimally interpreted QT as soon as one uses the appropriate coarse-graining procedures of many-body quantum statistics to describe the macroscopic measurement devices necessary to make observations on the microscopic systems.

 

[bolbteppa]

It's OK as long as one doesn't contradict any existing experiments. And Bohm's theory doesn't.

This is why it is absolutely shocking BM is taken seriously - just ignore all the egregious issues and inherent contradictions (coupled with basic misunderstandings of QM in actual published literature for good measure) and claim it's all OK, we are a step away from justifying intelligent design by this logic...

 

[bolbteppa]

but with the exposition of the theory by Dürr et al in their papers and textbooks I got convinced that de Broglie and Bohm have had a point, but weren't able to explain it clearly enough to convince the Copenhagen believers,

https://arxiv.org/pdf/quant-ph/9503013.pdf

https://arxiv.org/pdf/quant-ph/9504010.pdf

https://arxiv.org/pdf/quant-ph/9512031.pdf

https://arxiv.org/pdf/0903.2601.pdfThere's a bunch of papers by Duerr that all blindly use wave functions and Schrodinger equations out of thin air, just as the Quantum Physics Without Philosophy book also does - how is this convincing in the slightest?

It's basically no different to Bohm's paper starting from wave functions and the Schrodinger equation (and the craziness of using concepts derived/needed explicitly on the assumption of no paths, otherwise it'd be crazy to even use these concepts, to end up with paths existing, [again Landau vol. 3 sec 1]).

 

[Demystifier]

This is why it is absolutely shocking BM is taken seriously - just ignore all the egregious issues and inherent contradictions (coupled with basic misunderstandings of QM in actual published literature for good measure) and claim it's all OK, we are a step away from justifying intelligent design by this logic...

It's actually good for BM to have opponents like you, because then the other former opponents of BM tend to turn into supporters.

 

[bolbteppa]

It's actually good for BM to have opponents like you, because then the other former opponents of BM tend to turn into supporters.

Thank you

I'm open to being convinced, indeed that's obviously why I read into this stuff, it really is just very very unlikely given how confused the basic claims are and how they have to hide behind stealing equations and calling them axioms, I was expecting better than this - I similarly encourage you to read the references I have mentioned and to think about how seriously BM conflicts with the most basic claims of QM.

 

[Demystifier]

This non-locality, however is inherent in standard QT without BM.

Are you now fine with calling it non-locality? Recently, before you turned into a BM sympathizer, you insisted that it should be called non-separability.

 

[Demystifier]

It's basically no different to Bohm's paper starting from wave functions and the Schrodinger equation (and the craziness of using concepts derived/needed explicitly on the assumption of no paths, otherwise it'd be crazy to even use these concepts, to end up with paths existing, [again Landau vol. 3 sec 1]).

Even from a strictly logical point of view, if there was a theorem saying

no paths $\Rightarrow$ Schrodinger equation

it would not logically follow that

Schrodinger equation $\Rightarrow$ no paths

 

[bolbteppa]

Even from a strictly logical point, if there was a theorem saying

no paths $\Rightarrow$ Schrodinger equation

it would not logically follow that

Schrodinger equation $\Rightarrow$ no paths

Indeed, I said the same thing a few posts ago:

Yes, Bohm derived everything from the Schrodinger equation, of course one can take PDE's like the Schrodinger equation and end up calling things velocity fields or paths or whatever you want, one needs to justify why one can even do this.

that's why it's so insane to take the Schrodinger equation as an axiom, and hilarious to take the special case of the non-relativistic one...

 

[Demystifier]

Indeed, I said the same thing a few posts ago:

So do you agree that Schrodinger equation is compatible with the possibility that paths might exist?

 

[bolbteppa]

So do you agree that Schrodinger equation is compatible with the possibility that paths might exist?

Just so we're clear - you're asking me if one can take a PDE and then end up calling some curve/characteristic on the surface satisfying this PDE a path? Absolutely, and this is exactly why one would expect the Hamilton-Jacobi formalism to be the most likely to end up approximately similar to QM in some cases...

 

[Demystifier]

Just so we're clear - you're asking me if one can take a PDE and then end up calling some curve/characteristic on the surface satisfying this PDE a path? Absolutely, and this is exactly why one would expect the Hamilton-Jacobi formalism to be the most likely to end up approximately similar to QM in some cases...

So let me try to explain your objection against BM in my own words. You like the idea that the theory is based on paths. You just don't like the idea that a theory that is based on paths takes the Schrodinger equation as one its postulates. You would be more happy if Schrodinger equation was somehow derived, perhaps as some kind of approximation resulting from a more fundamental theory based on paths. Would that be right?

If that's your objection, then I can agree with you that such theory would be much better than BM. And some people are trying to do something like that. Nevertheless, such attempts have not been very successful, so BM seems to be the best we can do at the moment. Perhaps we should not take BM too seriously as the final theory, but I believe that at least it can serve as an inspiration in a search for a better theory.

 

[vanhees71]

https://arxiv.org/pdf/quant-ph/9503013.pdf

https://arxiv.org/pdf/quant-ph/9504010.pdf

https://arxiv.org/pdf/quant-ph/9512031.pdf

https://arxiv.org/pdf/0903.2601.pdfThere's a bunch of papers by Duerr that all blindly use wave functions and Schrodinger equations out of thin air, just as the Quantum Physics Without Philosophy book also does - how is this convincing in the slightest?

It's basically no different to Bohm's paper starting from wave functions and the Schrodinger equation (and the craziness of using concepts derived/needed explicitly on the assumption of no paths, otherwise it'd be crazy to even use these concepts, to end up with paths existing, [again Landau vol. 3 sec 1]).

Why out of thin air? The Schrödinger equation is 92 years old. You cannot say it comes out of thin air at all. There is no "assumption of no path" anywhere. You cannot derive QT logically from anything else since it's the most fundamental theory we have today. It's always a creative act to get it somehow by intuition. In Schrödinger's case it was based on de Broglie's assumption of "wave-particle duality" also for particles from the idea of "wave-particle duality" for light. Then he used the analogy to go from wave optics to ray optics by using the eikonal approximation (singular perturbation theory) backwards to derive his equation as the wave equation whose eikonal approximation leads to the Hamilton-Jacobi partial differential equation. For Heisenberg it were transition probabilities as the "observable quantities" which he derived on the island Helgoland on the example of the harmonic oscillator, and for Dirac it was the idea of "q-numbers" obeying commutation relations as given through the Poisson brackets in classical Hamiltonian mechanics.

What de Broglie and later Bohm did was to use the Schrödinger equation and the resulting wave function but they reinterpreted the physical meaning of this wave function completely compared to the mainstream Copenhagen interpretation, which indeed has more problems than it pretends to solve, because it's merely philosophical with ad-hoc assumptions that are untenable like the naive collapse used in some flavors and the quantum-classical cut, which cannot be empirically verified at all (to the contrary the more refined our engineering gets the larger objects we can prepare in "non-classical" states), and then Bohr came around murmaring mystifyingly about "the principle of complementarity". Bohm just reinterpreted the wave function as pilot wave which guides the particles on their trajectories.

 

[vanhees71]

Are you now fine with calling it non-locality? Recently, before you turned into a BM sympathizer, you insisted that it should be called non-separability.

No, as I wrote, one should not use the same word for different things. E.g., relativistic local QFT is, as its name says, local in the sense that interactions are local, but as any QT it necessarily leads to entanglement of observables of far-distant parts of quantum systems (e.g., the polarization entangled state of photon pairs from parametric down-conversion). Also Einstein carefully called this inseparability rather than non-locality. Note that Einstein was not particularly happy with one of his most famous papers, i.e., the EPR paper, and he wrote a single-authored paper later in 1948 (however in German), where he makes this particular point very clear. I guess that's also the main reason for Einstein to dislike BM, because it didn't get rid with this unseparability. Nowadays we know of course that this is a feature rather than a bug for any theory, because as the empirical results concerning Bell's inequality and all that shows that this inseparability is as Nature really behaves, and thus it's a feature not a bug of QM or BM. I think Bell is a hero from bringing QM towards "physics without philosophy/Bohrian esoterics".

 

[vanhees71]

Just so we're clear - you're asking me if one can take a PDE and then end up calling some curve/characteristic on the surface satisfying this PDE a path? Absolutely, and this is exactly why one would expect the Hamilton-Jacobi formalism to be the most likely to end up approximately similar to QM in some cases...

Obviously you haven't read the very few pages needed to understand what BM is all about. So please check, e.g., the first few pages of the 2nd paper you quoted above yourself.

 

[Demystifier]

No, as I wrote, one should not use the same word for different things.

My question is this. If we accept the terminology according to which Bell theorem shows that QM is non-separable, and if we accept the QFT-textbook terminology according to which relativistic QFT interactions are local, then what is the correct word to describe BM? Is BM non-local, or is it just non-separable?

Another important point. To understand locality of interactions in quantum theory, you don't need to deal with QFT. Ordinary non-relativistic QM has local interactions if the potential in the $n$-body Schrodinger equation has the form
$$V({\bf x}_1,\ldots, {\bf x}_n)=V_1({\bf x}_1)+\cdots +V_n({\bf x}_n)$$
BM works perfectly for such local interactions in non-relativistic QM and again leads to characteristic Bohmian "non-locality" in entangled states. Again, would you call it non-locality of BM or non-separability of BM?

Or perhaps we need a third word to charactrize BM?

 

[Boing3000]

This is such a fundamental misunderstanding of the most basic claims of quantum mechanics - the Schrodinger equation is absolutely derived on the assumption of no paths, please carefully (it's a hard but cool book) read secton 1

Indeed you have a very fundamental misunderstanding of what Landau writes.

In quantum mechanics there is no such concept as the path of a particle. This forms the content of what is called the uncertainty principle, one of the fundamental principles of quantum mechanics, discovered by W. HEISENBERG in 1927.t In that it rejects the ordinary ideas of classical mechanics, the uncertainty principle might be said to be negative in content. Of course, this principle in itself does not suffice as a basis on which to construct a new mechanics of particles. Such a theory must naturally be founded on some positive assertions, which we shall discuss below (§2).

The emphasis is mine. I am under the impression that you cannot make the difference between those two propositions:
-QM is not based on path
-QM is based on no path.

It must also be said that the uncertainty principle is not something special within QM, and that it also apply to classical mechanics (which if I understood Landau correctly, is not refuted, contains path, and is a special case of QM.

I should not even need to point out the flaws with going by historical derivations or the first/early attempts at making sense of QM.

That's true, historian's fallacy will not help at all. That's why it is fine that "silly" QFT was kept alive in the 30th even though it was not mathematically sound, plaged with infinities, and I am quite sure many people name-call it "shameful laughable unjustifiable plagiarism".
Anyway, all those theories are confirmed by experiments (in their regime) and that's why they are called "scientific".

even worse when it leads to questioning special, special!, relativity - again, how is this taken seriously.

How can QFT can be taken seriously then ? It leads to question general, general!, relativity. It is unjustifiable shameful laughable to take seriously a theory that refute that apples fall

 

[bolbteppa]

There is no "assumption of no path" anywhere.

Even proponents of BM, such as slide 4 of http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf , are very clearly aware that all of standard QM can be based on the claim that there are no paths (after which you need to set up things to replace CM and this is the 'positive content' of QM as Landau calls it), it literally quotes the Landau reference I keep bringing up:

..an attitude which propagated into more or less every modern textbook:
“It is clear that [the results of the double slit experiment] can in no way be reconciled with the idea that electrons move in paths.
In quantum mechanics there is no such concept as the path of a particle.” [Landau and Lifshitz]
slide 4 - http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf

In BM the Schrodinger equation comes out of thin air, it's completely unjustified... In normal QM it absolutely does not come out of thin air, it is derived, either as e.g. Dirac does it, or as e.g. Landau does based on the HUP claiming no paths exist, Born, and the necessary existence of a quasi-classical limit, it's all in the Landau reference from first principles that even BM proponents reference...

The Schrodinger equation in BM is clearly just stolen from QM and at best (this is very common) hand-wavingly justified by the existence of these historical derivations as if that makes any theoretical sense or with ludicrous things like the de Broglie relation or probability conservation out of thin air - one can even understand why people would go along with BM: 'if you take X as axioms then Y happens', fine, but it's just a game unless one can face up to the immediate issues that normal QM answers so concisely in starting from 'no paths exist'... The Durr references are no basically different to all the other BM references in this respect.

Clearly if you steal an equation derived on the assumption of no paths and then end up with paths you've made such a gigantic error your 'theory' is immediately nonsense, it's so basic...

What de Broglie and later Bohm did was to use the Schrödinger equation and the resulting wave function but they reinterpreted the physical meaning of this wave function completely compared to the mainstream Copenhagen interpretation, which indeed has more problems than it pretends to solve

I am not even going after the many contradictions other people claim arise even when you take BM at face value, that's another huge discussion, my issues with BM are way more basic, the very tools it uses are completely illegitimate to even use if they do not begin by declaring that paths don't exist and this by itself immediately invalidates the whole thing.

 

[bolbteppa]

So let me try to explain your objection against BM in my own words. You like the idea that the theory is based on paths. You just don't like the idea that a theory that is based on paths takes the Schrodinger equation as one it's postulates. You would be more happy if Schrodinger equation was somehow derived, perhaps as some kind of approximation resulting from a more fundamental theory based on paths. Would that be right?

If that's your objection, then I can agree with you that such theory would be much better than BM. And some people are trying to do something like that. Nevertheless, such attempts have not been very successful, so BM seems to be the best we can do at the moment. Perhaps we should not take BM too seriously as the final theory, but I believe that at least it can serve as an inspiration in a search for a better theory.

Roughly that's correct yeah, I even would happily justify/defend BM if I thought it made sense - it would be so shocking and so revolutionary if the claims of BM were true since they would so directly refute the most fundamental issues in QM that one simply has to examine how BM was set up, test it's logic, and see what's going on - unfortunately it just falls apart and it just isn't serious if you question it, it would be shocking if BM proponents could genuinely set up a coherent theory, the field is wide open

 

[Demystifier]

Roughly that's correct yeah, I even would happily justify/defend BM if I thought it made sense - it would be so shocking and so revolutionary if the claims of BM were true since they would so directly refute the most fundamental issues in QM that one simply has to examine how BM was set up, test it's logic, and see what's going on - unfortunately it just falls apart and it just isn't serious if you question it, it would be shocking if BM proponents could genuinely set up a coherent theory, the field is wide open

So, what's your favored view of QM? The standard Landau/Lifshitz one? Or perhaps you prefer something radically different from QM and object that BM is not radically different enough?

 

[Lord Jestocost]

If we accept the terminology according to which Bell theorem shows that QM is non-separable, and...

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

 

[vanhees71]

My question is this. If we accept the terminology according to which Bell theorem shows that QM is non-separable, and if we accept the QFT-textbook terminology according to which relativistic QFT interactions are local, then what is the correct word to describe BM? Is BM non-local, or is it just non-separable?

Another important point. To understand locality of interactions in quantum theory, you don't need to deal with QFT. Ordinary non-relativistic QM has local interactions if the potential in the $n$-body Schrodinger equation has the form
$$V({\bf x}_1,\ldots, {\bf x}_n)=V_1({\bf x}_1)+\cdots +V_n({\bf x}_n)$$
BM works perfectly for such local interactions in non-relativistic QM and again leads to characteristic Bohmian "non-locality" in entangled states. Again, would you call it non-locality of BM or non-separability of BM?

Or perhaps we need a third word to charactrize BM?

Of course, you cannot discuss locality vs. non-locality in a Newtonian, i.e., non-relativistic context, since Newtonian mechanics is never non-loacal but a typical action-at-a-distance theory. What you call "non-local" in QM or BM should, however, be renamed somehow, but this will be impossible, because the unprecise language with this notion is too common.

"Locality" should be preserved for the notion in relativistic (Q)FTs, and then you should somehow name the "quantum correlations" described by entanglement differently. I think these correlations are what Einstein had in mind what he called it "inseparability" ("Inseperalität" in German). That's why my suggestion is to call it inseparability.

 

[vanhees71]

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

The word "realism" I'd completely abandon from any serious physics discussion. I have never understood what the philosophers precisely mean. In most of the cases they mean "deterministic". Bell's theorem is about what he called "local deterministic theories", and that's how we should label this class of models which are all ruled out by all "Bell tests" done today.

 

[Demystifier]

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

The first half of the Bell's theorem is indeed an inequality which only talks about local classical theories. But there is also the second half, which shows that quantum mechanics violates the inequality from the first half.

 

[Demystifier]

Of course, you cannot discuss locality vs. non-locality in a Newtonian, i.e., non-relativistic context, since Newtonian mechanics is never non-loacal but a typical action-at-a-distance theory.

That of course is wrong. Newtonian mechanics (which is more general concept than Newton gravity) can have both local and non-local forces. The Newton gravity is of course non-local, but potential of the form I have written in the post above is local, i.e. does not involve action at a distance.

 

[vanhees71]

Local forces are only if you have an external field, i.e., if $\vec{F}=\vec{F}(t,\vec{x}(t))$. Interactions must be instantaneous due to the Lex Tertia. That's the very point why the most simple way to realize causality in relativity is to use fields to describe interactions, i.e., you can obey momentum conservation without action at a distance since the fields are dynamical quantities carrying energy, momentum, etc.

 

[bolbteppa]

So, what's your favored view of QM? The standard Landau/Lifshitz one? Or perhaps you prefer something radically different from QM and object that BM is not radically different enough?

If I had to choose two books I would pick Landau and Dirac, of these two I would pick Landau - it's amazing that Bell translated it and becomes one of the main BM proponents

The whole Landau-Peierls Bohr-Rosenfeld relativistic quantum theory debacle is fascinating, c.f. volume 4 section 1 also, its this kind of craziness that made me look at BM properly, I can't imagine how BM could ever deal with these kinds of things (even if it made sense non-relativistically).