Would this experiment disprove Bohmian mechanics?

[Alex Torres]

What is Max Planck's matrix concept?

... sorry can't give more details about that in here... don't want this thread closed or me being banned...but you can look for it in wiki and make your own conclusions...

 

[Demystifier]

... sorry can't give more details about that in here... don't want this thread closed or me being banned...but you can look for it in wiki and make your own conclusions...

Ah, I thought that you defend some orthodox/Copenhagen interpretation of QM. Now I see that I was wrong.

 

[PeterDonis]

sorry can't give more details about that in here... don't want this thread closed or me being banned

If you can't provide a valid reference, then you shouldn't be mentioning it at all. Hinting at something and then refusing to provide a valid reference when asked is what will get you banned from this thread, which I have now done.

 

[richrf]

What is Max Planck's matrix concept?

Max Planck is cited as using this phrase in a speech that he made in Florence, Italy in 1944. The best citation that I found is here. As yet, I have not found a full English translation of the piece, but this citation places the phrase in context as well as the original German transcript.

https://todayinsci.com/P/Planck_Max/PlanckMax-Quotations.htm

Als Physiker, der sein ganzes Leben der nüchternen Wissenschaft, der Erforschung der Materie widmete, bin ich sicher von dem Verdacht frei, für einen Schwarmgeist gehalten zu werden. Und so sage ich nach meinen Erforschungen des Atoms dieses: Es gibt keine Materie an sich. Alle Materie entsteht und besteht nur durch eine Kraft, welche die Atomteilchen in Schwingung bringt und sie zum winzigsten Sonnensystem des Alls zusammenhält. Da es I am ganzen Weltall aber weder eine intelligente Kraft noch eine ewige Kraft gibt - es ist der Menschheit nicht gelungen, das heißersehnte Perpetuum mobile zu erfinden - so müssen wir hinter dieser Kraft einen bewußten intelligenten Geist annehmen. Dieser Geist ist der Urgrund aller Materie.

As a man who has devoted his whole life to the most clear headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.
— Max Planck
Lecture, 'Das Wesen der Materie' [The Essence/Nature/Character of Matter], Florence, Italy (1944). Archiv zur Geschichte der Max-Planck-Gesellschaft, Abt. Va, Rep. 11 Planck, Nr. 1797. Excerpt in Gregg Braden, The Spontaneous Healing of Belief: Shattering the Paradigm of False Limits (2009), 334-35. Note: a number of books showing this quote cite it as from Planck's Nobel Prize acceptance speech (1918), which the Webmaster has checked, and does not see this quote therein.

 

[PeterDonis]

Max Planck is cited as using this phrase in a speech that he made in Florence, Italy in 1944. The best citation that I found is here.

Based on this, the concept in question is indeed off topic and out of bounds for discussion here.

 

[Demystifier]

"We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter." - Max Planck

I wonder, is this how the Matrix movie got its title?

 

[Nugatory]

I wonder, is this how the Matrix movie got its title?

More likely they picked up this use of the word from William Gibson's novel "Neuromancer"...

 

[Sophrosyne]

Bohmian mechanics claims that although it is deterministic, randomness emerges from the fact that we cannot know the initial conditions of the particle due to Heisenberg's uncertainty principle. However this experiment can put that to the test and determine whether randomness in quantum mechanics is due Heisenberg's uncertainty principle(not being able to know the position and momentum of the particle at the same time).The experiment is a variation of the double slit experiment, except for before the particles pass through the slit they travel through a type of detector which detects it's position, as it continues traveling it travels to another detector, where again its position is detected. From the time it took to get from first detector to the second, it could then be deduced the momentum at which the particle was traveling when it went through detector number 1. Now at that instance both the position and momentum of the particle were known when it was traveling. This would be repeated as the particles travel through the double slit. Once the experiment has finished, one could calculate trajectories using bohmian mechanics of the particle and determine whether bohmian mechanics was able to predict accuratley where the particles would land on the detector screen. As this experiment gets repeated more and more one would be able to determine whether the retroactive calculations made from bohmian mechanics are more accurate than the already accurate quantum mechanics. It would also be best to perform this experiment in a vaccum, and calculations could be made before the particle lands by potentially a computer if it was fed the data and the particle was traveling at slow speeds. Would this experiment work conceptually?

If Bohmian mechanics was right, it would create huge problems with trying to understand the Higgs field. Let's say Higgs particles are actually bouncing around in a baseline static frame of reference. That would mean that the relativistic principle that all frames of reference should be equal would get violated. Some objects, moving in one direction, would have more mass than those moving in another. It would be sort of the equivalent of the ether. We know we don't have ether, so therefore Bohmian mechanics can't be right.

I am just conjecturing. Is this a good way to think about it?

 

[Demystifier]

If Bohmian mechanics was right, it would create huge problems with trying to understand the Higgs field. Let's say Higgs particles are actually bouncing around in a baseline static frame of reference. That would mean that the relativistic principle that all frames of reference should be equal would get violated. Some objects, moving in one direction, would have more mass than those moving in another. It would be sort of the equivalent of the ether. We know we don't have ether, so therefore Bohmian mechanics can't be right.

I am just conjecturing. Is this a good way to think about it?

Basically, you are saying that Bohmian mechanics (BM) is wrong because it's not relativistic covariant. That's an old and well known objection, and does not necessarily need to involve the Higgs field. (But you are probably the first who used the example of Higgs for that purpose.)

That's indeed a deep and nontrivial objection against BM. There is no simple way to make BM consistent with relativity. Nevertheless, people who work seriously on that topic (including me) found various ways to reformulate BM in a manner consistent with relativity. The problem is that neither of those ways looks sufficiently simple and natural. Perhaps the simplest approach (at least conceptually, if not technically) is the approach I proposed in https://lanl.arxiv.org/abs/1703.08341 (Sec. 4.3). Basically, it says that there is ether, but its manifestation can only be seen at very small distances that are not yet amenable to our current experimental technologies. This version of BM makes a new testable prediction - that at some very small distances we should, one day, see evidence for the existence of ether. That's different from e.g. string theory, which predicts that at some very small distances we should, one day, see evidence for supersymmetry and not ether.

 

[bolbteppa]

You can't disprove a 'theory' which makes no sense Simply go and actually read the first five pages of Bohm's paper to see how laughable his proposal is, it's actually shameful to call a theory which randomly steals equations from QM and calls them axioms after which it goes off and misinterprets them a 'theory'.

Perhaps the simplest approach (at least conceptually, if not technically) is the approach I proposed in https://lanl.arxiv.org/abs/1703.08341 (Sec. 4.3).

From Sec. 4.3:

"Lorentz invariance and QFT are emergent, i.e. derived from non-relativistic QM... In this sense, non-relativistic Bohmian mechanics is fundamental... If so,then non-relativistic Bohmian mechanics is a natural ToE... This raises optimism that even quantitative features of the Standard Model can be derived from some non-relativistic quantum theory"

This can't be serious?

Quantum field theory is hard enough without trying to deny the most basic claims of QM and then work backwards from all it's results to try to save determinism, but claiming it's all Galilean is beyond the pale...

 

[vanhees71]

Well, non-relativistic Bohmian mechanics indeed makes a lot of sense. It's able to give a quite convincing plausibility for the Born rule, and it's a viable non-local realistic interpretation of non-relativistic QM. For a very good introduction, see the marvelous textbook

https://www.amazon.com/dp/3642306896/?tag=pfamazon01-20

It turns out that for everything that's observable in real the probabilistic predictions of Bohmian mechanics are precisely the same as quantum theory. The Bohmian trajectories play only a conceptual role but are not necessary to describe everything observable. The point of Bohmian mechanics is to show that there is a viable non-local deterministic interpretation of non-relativistic QT.

Of course, as long as Bohmian theory cannot be formulated relativistic and as long as there is no "Bohmian interpreation" of local microcausal relativistic QFT, I also don't see it as a very convincing argument to provide a "solution" of apparent (philosophical) problems with QT.

 

[Demystifier]

For a very good introduction, see the marvelous textbook
https://www.amazon.com/dp/3642306896/?tag=pfamazon01-20

That's not really a textbook but a collection of research papers. But there is indeed a marvelous textbook by one of the authors of this collection.

 

[bolbteppa]

Some of the problems I have with it are for example that non-relativistic Bohmian mechanics either 'derives' the Schrodinger equation from some absolutely unjustifiable starting point like the de Broglie relation (is it not anti-scientific to say that all of classical physics is wrong but we can randomly use concepts from this theory like energy and momentum out of the blue) or else simply it postulates the Schrodinger equation as an axiom (as that book seems to do) an equation explicitly derived on the assumption of no paths (c.f. Landau volume 3), and then ends up with a 'theory' that allows one to assume paths exist, or takes some other unjustifable step (https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivations), this is actually ridiculous if you think about it. 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.

If you go back to the beginning of the Bohm paper, it makes sense why one would even risk trying to make a theory which so flagrantly contradicts QM - he wants to try to force QM to be analogous to statistical mechanics and to then invent reasons why the microscopic variables are hidden (then claims his theory should lead to way more precise predictions the more accurate we get and it's been a few decades) so that we can save the idea of paths, then goes off and uses equations derived explicitly on (or equivalent to) the assumption of no paths, I think it's shocking something like this could be taken seriously.

 

[vanhees71]

That's not really a textbook but a collection of research papers. But there is indeed a marvelous textbook by one of the authors of this collection.

Perhaps I quoted the wrong book, but even though it's a collection of research papers, it reads very well and is textbook-like. I only know of a very new German one by Duerr, which discusses Bohmian Mechanics, GRW, and many worlds.

 

[stevendaryl]

Some of the problems I have with it are for example that non-relativistic Bohmian mechanics either 'derives' the Schrodinger equation from some absolutely unjustifiable starting point like the de Broglie relation (is it not anti-scientific to say that all of classical physics is wrong but we can randomly use concepts from this theory like energy and momentum out of the blue) or else simply it postulates the Schrodinger equation as an axiom (as that book seems to do) an equation explicitly derived on the assumption of no paths (c.f. Landau volume 3), and then ends up with a 'theory' that allows one to assume paths exist, or takes some other unjustifable step (https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivations), this is actually ridiculous if you think about it.

Derivations of laws of physics are nice to have, but are not necessary. You can take the equations axiomatically and ask what follows from them. How does it matter whether the equations were derived in another context? What's derived in one theory may be postulated in another.

 

[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