QFT made Bohmian mechanics a non-starter: missed opportunities?

[gentzen]

At least for Bohmian mechanics

Which is not QFT. It is either an interpretation of non-relativistic QM, or (in its more ambitious formulations) an attempt to extend that interpretation into an actual competing theory, which, however, is still non-relativistic, and is therefore considered a non-starter by most physicists (though not all--at least one PF regular, @Demystifier, has published papers defending the view that Lorentz invariance is only an emergent symmetry and that we will end up finding that there is an underlying theory that works more like non-relativistic Bohmian mechanics).

I once conjectured that Bohmian mechanics arrived at an unfortunate point in time, when interest in QFT overshadowed potential opportunities offered by Bohmian mechanics:

When David Bohm proposed his new interpretation in 1952, the term "Copenhagen interpretation" didn't exist yet, he had to talk of the "usual physical interpretation of quantum theory" instead.
...
So the historical context is that the divergence problems of the quantum electrodynamics theory from Dirac, Pauli, and Heisenberg had been solved by Schwinger, Feynman and others in 1949 by renormalization. The predictive power was excellent, but interpretation remained elusive. And suddenly modifications, reformulations and reinterpretations of normal quantum mechanics started to proliferate, attacking normal quantum mechanics while remaining silent about quantum field theories.

• One of those opportunities was the analysis of non-locality, later done by Bell, and the reason why I brought up Bohmian mechanics in the other thread.
• Another "opportunity" from my point of view would have been an analysis of "how and why" Bohmian mechanics breaks invariance under (linear) canonical transformations. I still hope to learn more about this from Peter Holland's "Hamiltonian theory of wave and particle in quantum mechanics I. Liouville’s theorem and the interpretation of the de Broglie-Bohm theory" and "Hamiltonian theory of wave and particle in quantum mechanics II: Hamilton-Jacobi theory and particle back-reaction" (2001). I somehow blame Wolfgang Pauli for missing that analysis, because he was an expert for such invariances, shoot down de Broglie's initial proposal, and ignored (and ridiculed) Bohm's requests for feedback.
• In a certain sense, non-locality was Einstein's topic, and invariance was Pauli's topic. So I wonder whether Bohmian mechanics also contains "missed opportunities for analysis" of topics close to Heisenberg or Bohr. For Heisenberg, I have an idea for one such topic: Heisenberg justified the need for interaction between classical mechanics and (non-relativistic) quantum mechanics via measurement as some sort of boundary condition for open systems. His interpretation seems to allow ("classical") reactions or control based on measurement outcomes, while for Bohmian mechanics it is at least unclear whether such "classical" interaction based control is possible too, in case where Bohmian mechanics is only used to provide boundary conditions (i.e. not used in the MWI sense as a closed model of the entire universe).

What can be said about the opportunities I "believe" to have indentified above? Do you see other "missed opportunities for analysis" (not necessarily specific to Bohr or any other father of Quantum mechanics like Schrödinger, Born or Dirac, or similar in other ways to my examples)?

 

[Demystifier]

I don't understand, are you talking about opportunities that were missed in the 1950's, or are you talking about opportunities that were missed up to the present time? I would say that many opportunities that were missed in the 1950's were realized later. Right now I am working on an opportunity that was missed so far to better understand foundations of quantum statistical mechanics (mixed states, thermal mixed states, etc.) from a Bohmian perspective.

 

[gentzen]

I don't understand, are you talking about opportunities that were missed in the 1950's, or are you talking opportunities that were missed up to the present time?

Opportunities that were missed in the 1950s. Whether for example Peter Holland's work from 2001 or any other currently existing work manages to fully exploit such an opportunity is less important to me. If it is something that interests you, and where you try to better understand it, for example by studying existing works, and maybe simultaneously trying your own synthesis, then it is still an opportunity that interests me. And opportunities that have already fully materialized (like Bell's work on non-locality) interest me even more.

 

[gentzen]

What would be nice would be "ideas" how to argue against criticisms like

The problem with de Broglie-Bohm reinterpretations of the quantum formalism indeed is its non-local nature, which is at odds with the very foundations of local relativistic QFTs although there are some attempts in the literature that try do remedy this difficulty.

In my opinion, there's no need for such reinterpretations, because the probabilistic interpretation of the quantum state in the sense of the minimal statistical interpretation (Einstein, Ballentine,...) describes all observations very well, avoiding any confusing, unnecessary philosophical ballast which is just introduce to prevent people to admit that the classical, deterministic worldview suggested by our experience with macroscopic objects, simply is not the way Nature can be adequately described on a fundamental level. It's rather an emergent phenomenon, which is pretty well understood in terms of quantum many-body theory.

not by denying specific criticisms of Bohmian mechanics like "its non-local nature" or Pauli's criticism that "Bohm's language destroys the symmetry between position and velocity," but by embracing them instead as "opportunities for analysis".

 

[Demystifier]

What would be nice would be "ideas" how to argue against criticisms like

not by denying specific criticisms of Bohmian mechanics like "its non-local nature" or Pauli's criticism that "Bohm's language destroys the symmetry between position and velocity," but by embracing them instead as "opportunities for analysis".

What I don't understand about such criticisms is that they usually come from instrumentalists who otherwise argue that it only matters what are the measurable predictions of a theory, but in the Bohmian context they suddenly completely change their philosophy of physics and now the fact that Bohmian mechanics makes the same measurable predictions as the standard quantum theory is no longer enough for them.

 

[vanhees71]

My critizism against Bohmian mechanics is that it introduces unobservable elements, which do not contribute anything to the prediction about observable facts and that it's not really convincingly formulated for relativistic quantum fields. The only merit of Bohmian mechanics in first-quantized non-relativistic QM is that it provides a non-local "realistic" reinterpretation of the quantum formalism. From a physics point of view nothing is gained from the additional complications introduced by it.

 

[PeroK]

What would be nice would be "ideas" how to argue against criticisms like

By producing something that goes beyond what conventional QFT can do. If the additional substructure of BM does no more than replicate the results of QM/QFT, then it's really only of philosophical value.

It needs to prove itself.

 

[Demystifier]

My critizism against Bohmian mechanics is that it introduces unobservable elements, which do not contribute anything to the prediction about observable facts

What if I told you that Bohmian trajectories are somewhat like electric field lines, integral curves (of a certain vector field that appears naturally in the theory) that some people find useful for visualization and intuition? Would it then make more sense to you?

and that it's not really convincingly formulated for relativistic quantum fields.

This objection itself is not convincing.

 

[Demystifier]

By producing something that goes beyond what conventional QFT can do. If the additional substructure of BM does no more than replicate the results of QM/QFT, then it's really only of philosophical value.

If nothing else, BM offers an intuition that at least some physicists find useful in thinking. Bell, for instance, used BM intuition to discover his famous Bell theorem. A physicist does not need to be interested in philosophy to appreciate the value of intuition in physical insight.

 

[Demystifier]

The only question about BM that you should ask yourself is this: "Do I find it intuitive? If Bohmian trajectories were real, would QM look more comprehensible to me?" If your answer is no, then BM is not for you, so please ignore it! If the answer is yes, or at least a partial yes, then use it, whenever you find convenient, as an auxiliary thinking tool!

 

[vanhees71]

What if I told you that Bohmian trajectories are somewhat like electric field lines, integral curves (of a certain vector field that appears naturally in the theory) that some people find useful for visualization and intuition? Would it then make more sense to you?

No, to the contrary. These Bohmian trajectories simply don't exist. In contradistinction to electric-field lines in classical electrodynamics, they don't give a valid intuition about quantum systems.

This objection itself is not convincing.

:-)

 

[gentzen]

What would be nice would be "ideas" how to argue against criticisms like

By producing something that goes beyond what conventional QFT can do.

You quoted me a bit out-of-context. My sentence continued as follows:

not by denying specific criticisms of Bohmian mechanics like "its non-local nature" or Pauli's criticism that "Bohm's language destroys the symmetry between position and velocity," but by embracing them instead as "opportunities for analysis".

I brought up Bohmian mechanics in the other thread, because it has serious trouble coming up with particle trajectories for photons, as opposed to "field configuration trajectories for the electromagnetic field". So I embraced a limitation of (an extension of) BM to argue against interpreting photons as particles. And its further trouble with "field configuration trajectories" for fermions give this argument even more intuitive weight, in a certain sense. But overall, I just tried to find arguments for my experience and intuition that the particle picture does not work well for the electromagnetic field. If QFT offers better arguments for that intuition, I certainly won't object.

(The mentioned extension of BM needs "irreducible randomness" for creation and annihilation of fermions, and thereby loses one of the selling point of non-relativistic BM, i.e. that it mitigates the role of randomness in QM.)

If the additional substructure of BM does no more than replicate the results of QM/QFT, then it's really only of philosophical value.

It needs to prove itself.

Not sure whether BM "needs to prove itself". At least non-relativistic BM simply exists. Copenhagen non-relativistic QM too has an additional substructure (its interaction with classical mechanic), it is just less obvious. For QFT, both substructures seem to cause trouble, but the minimal statistical interpretation indeed seems to be an elegant way to avoid the need for such substructures. However, that interpretation was not yet established in the 1950s, it only became popular much later.

 

[Demystifier]

These Bohmian trajectories simply don't exist. In contradistinction to electric-field lines in classical electrodynamics, they don't give a valid intuition about quantum systems.

I don't understand. Are you saying that electric-field lines exist? In what sense? And how do you decide, in general, whether an intuition in physics is valid?

 

[vanhees71]

The electromagnetic field exists in an operational sense, i.e., it can be observed by observing the motion of charged matter, and the corresponding field lines give a picture of these fields, while there are no trajectories of particles in QM and thus these Bohmian trajectories don't give any physically interpretible picture about their behavior.

 

[gentzen]

The electromagnetic field exists in an operational sense, i.e., it can be observed by observing the motion of charged matter, and the corresponding field lines give a picture of these fields, while there are no trajectories of particles in QM and thus these Bohmian trajectories don't give any physically interpretible picture about their behavior.

Well, you are probably right that in their entirety, the Bohmian trajectories don't exist in an operational sense. And if one starts to use the trajectories to define things which actually exist in an operational sense, then BM risks to lose its simplicity. So it seems more fruitful to ask in which sense the Bohmian trajectories do exist. Here are some options:

Let mathematical existence mean no more than consistency of an otherwise arbitrary definition. Let physical existence be based on observations and experience. (Remember those arguments evoking the number of atoms in the universe?) Let philosophical existence mean that you either explicitly define what you mean by that word ...

I guess the existence of Bohmian trajectories is closely related to consistency and mathematical existence, but not in the sense of arbitrary definition. The sense is rather that their existence in its entirety is neither logically contradictory, nor would their observability lead to predictions that contradict non-relativistic QM (if they are distributed according to the Born rule, whatever that means).

 

[vanhees71]

I don't think that Bohmian mechanics is in any way mathematically inconsistent, but it's physically superfluous. Everything observable can be calculated with standard QT and using the minimal statistical interpretation. There's no need for Bohmian trajectories at all. In guess in some vague sense these trajectories are "hidden variables", and Bohmian mechanics is a "non-local realistic hidden-variable theory", which is consistent in its observable (proabilistic!) predictions with standard QT.

 

[Ken G]

I don't think that Bohmian mechanics is in any way mathematically inconsistent, but it's physically superfluous. Everything observable can be calculated with standard QT and using the minimal statistical interpretation. There's no need for Bohmian trajectories at all.

I believe this is the issue right here. In my opinion, @vanhees71 is in a sense talking past @Demystifier, rather than directly refuting them, because of a different scientific priority that is essentially philosophical in nature. That is the fundamental irony here, that the primary "dig" against BM is that it involves extraneous philosophical baggage that is not "required" to do QM (and here I restrict to everyday nonrelativistic QM, to avoid those stickier issues involving relativity and QFT, because I believe that same "unnecessary philosophical baggage" objection still holds in that context). I would point out that this position is itself fundamentally philosophical in nature. If one would say that all that matters is one can make correct predictions with minimal philosophical commitments along the way, that is quite clearly already itself a philosophical commitment, the commitment that unnecessary philosophical add-ons are to be avoided as a matter of course.

The situation seems analogous to nonstandard features in a new car. If one person holds that the purpose of a car is simply to get from point A to point B, then racing stripes and alloy wheels are automatically not worth paying extra for. But another person may say that it is important to travel in style, in which case they might pay for those extras. There is not a disagreement there, and neither person will convince the other, but it cannot be stated that the stylistic extras are fundamentally wrong to include in a car by any overarching automotive principle.

For me, I think the entire problem with interpretations of quantum mechanics is their fundamental purpose is being misconstrued. Too often we see the situation as an argument about "what is really happening" as described in the different interpretations, but I think it is naive to imagine that any physics theory is ever capable of establishing such a thing objectively. The real purpose of a physics theory, beyond simply making good and useful predictions, is to give each individual physicist a way of thinking about what is really happening, with no requirement that this description be unique. (Ask ten particle physicists what a particle is, and expect ten different answers.) That admits the subjective aspect of why we love physics, and when one has admitted that, the purposes of interpretations of theories becomes more clear. They give us a personal relationship with each theory that allows us to reimagine that theory in a way that grants us insight, and this is a fundamentally subjection relationship. I believe that is also what @Demystifer is saying, but they are welcome to speak for themself.

 

[vanhees71]

But QT in the usual minimal interpretation provides all what you say, namely "to give us a way of thinking about what is really happening", where "what is really happening" can only mean "what can be observed". Otherwise I can invent any kind of phantasy stuff, I like for some personal reasons, and claim it's needed to understand "what's really happening", but which cannot be observed. It's the same as with "many worlds", where they invent some "splitting of the universe" at any moment anything reads off a measurement result, but that's obviously not what we observe, and thus the many parallel worlds are simply declared as unobservable. So what's the point to introduce them in the same place? In BM it's the unobservable trajectories.

 

[Ken G]

But QT in the usual minimal interpretation provides all what you say, namely "to give us a way of thinking about what is really happening", where "what is really happening" can only mean "what can be observed".

But can it really only mean that? I certainly agree that your minimalistic position is the only way to restrict to what is objective, and science is intended to be objective. But that doesn't remove all subjective elements from science, it just means that when we test the theories and write the papers, we must restrict to a common domain of objectivity. I would thus argue that the entire concept of "what is really happening" has already left that common domain, it is not what can be observed but rather, something else entirely, something that science never actually needs or uses, but we all function in that mindset in our own subjective realms. We are scientists for a reason, and that reason is fundamentally personal, but as scientists, we all come together in that objectively testable common realm, and that's why our theories must only be tested in that objective realm.

Otherwise I can invent any kind of phantasy stuff, I like for some personal reasons, and claim it's needed to understand "what's really happening", but which cannot be observed. It's the same as with "many worlds", where they invent some "splitting of the universe" at any moment anything reads off a measurement result, but that's obviously not what we observe, and thus the many parallel worlds are simply declared as unobservable. So what's the point to introduce them in the same place?

That I would say is indeed the question. But can we not extend that question to its logical conclusion, why do anything beyond making and testing quantitative predictions? You said that electric field lines are real because they successfully describe the behavior of charged particles, and that behavior is objectively testable. But I can say that if all that is real is the objective behavior, why have a "picture" of any kind? We know the equations, we can make the predictions, and we know how to set up the apparatus that tests those predictions. Hence we never needed to mention field lines, or charges, or particles, as if they were anything but terms in the necessary equations and items on a shopping list for buying the necessary laboratory gear. We should really say "here is the equation we use and here is the way we like to picture what the equation means because it helps insure we apply the equation correctly. But all we ever test is that we did the calculation right, we never test the picture at all and the picture is not in the objective common realm where the calculations and testing occur."

To that last I would add, in my opinion if we were ever contacted by an intellectually and technologically superior alien race, we might discover that they regard all of our physical pictures as almost humorously simplistic and naive, like stick figures in the artwork of a five year old. It is a perspective that helps keep the scientist humble as they imagine their own achievements. We are stuck with the fundamental limitation that "what is really happening" must be restricted to what we can demonstrate is happening (i.e., objective observations), yet we could never allow our thoughts to be so restricted. We must have our pictures, which for us seem incredibly sophisticated and beautiful, yet to someone else might seem naive, even cute!

 

[Demystifier]

The electromagnetic field exists in an operational sense, i.e., it can be observed by observing the motion of charged matter, and the corresponding field lines give a picture of these fields, while there are no trajectories of particles in QM and thus these Bohmian trajectories don't give any physically interpretible picture about their behavior.

The Bohmian trajectories give the picture of the probability current, in the same way the electric field lines give the picture of the electric field. The probability current itself is a part of standard QM.

 

[vanhees71]

But that's not what's calculated as "Bohmian trajectories", right?

 

[Demystifier]

But that's not what's calculated as "Bohmian trajectories", right?

Mathematically, the Bohmian trajectories ARE the integral curves of the probability current.

 

[Ken G]

What I don't see is why electric field lines should be regarded as fundamentally different from gravitational field lines. But even before Einstein, we knew that gravitational dynamics could be correctly handled using either Lagrangian or Hamiltonian approaches, involving actions and energies, with no need to take forces seriously as "beables" of these equivalent interpretations. Scalar fields have gradients, but if the gradients don't appear anywhere in the application of the interpretations, then how can threading those gradients with lines be considered part of a minimalistic approach to what is real? Then of course we tack on general relativity, and we see that all these Newtonian approaches can be replaced by geometrical effects that don't even use the same formalism so really have no need for the force concept. How do we know there is not some new theory of electromagnetism that similarly replaces the entire notion of an electromagnetic force, and sees field lines as approximate entities that are to be discarded in some more accurate theory? I don't dispute the extreme usefulness, even beauty, of the field line concept, but it still seems more like racing stripes than an inseparable element of the objectively observed behaviors.

 

[Ken G]

Mathematically, the Bohmian trajectories ARE the integral curves of the probability current.

Indeed I wish that was exactly what they were described as being. Then we'd escape the tendency to claim that particles really follow those trajectories, which to me misses the whole point of an interpretation (which is to provide a subjective scaffolding to theories that feel sterile if they are nothing more than objective prediction machines).

 

[vanhees71]

Mathematically, the Bohmian trajectories ARE the integral curves of the probability current.

Yes, but then you should interpret them as such and not claim they were particle trajectories.

 

[Demystifier]

Yes, but then you should interpret them as such and not claim they were particle trajectories.

But physicists do such things all the time.
1) The particle paths in a Feynman path integral are not real particle trajectories, yet even experts sometimes like to imagine that they are, because it helps intuition.
2) The lines in a Feynman diagram are even less particle trajectories, yet even experts sometimes like to imagine that they are, because it helps intuition.

 

[Ken G]

There are other examples of using classical thinking in quantum mechanical contexts. How often have we heard statements like, "the electron that was in the atom was ionized by a passing photon." Since the context is an atom, the process being described is inherently quantum mechanical, yet we know from quantum mechanics that there is no such thing as "the electron that was in the atom," since to obey the Pauli exclusion principle, all electrons must be indistinguishable particles. That means the only time we can correctly attribute an individual identity to an electron is when something happens in the apparatus that specifically identifies that electron (like "the electron that was recorded in our detector"). But a process that takes a neutral atom into an ionized one is not such a process, the electron involved is never identified and cannot be referred to as a particular particle, only that the atom ended up with one less electron in it (which is saying something different).

It would of course be laborious to follow rules like that, so we don't bother, and that is regarded as acceptable, even though talking about the identity of an electron is no less a break from minimalist language than talking about its trajectory. The point is, we should either be accepting of subjectively based language if it is understood that some shortcuts are being used in the language, or we should be sticklers for the minimalist approach. Instead, we tend to see uneven application of these two contrasting attitudes!

 

[Ken G]

Yes, but then you should interpret them as such and not claim they were particle trajectories.

Perhaps the resolution is to interpret claims like that as really saying "we are choosing to picture the integral curves of the probability currents as particle trajectories, as an optional manner of informing our subjective insight." It gets laborious to say this every time, so better still would be for everyone to accept this as tacitly true, as is already the case with so much of our physics language (like "it is the force of gravity that causes the weight measured on a scale", etc.).

 

[AndreasC]

But QT in the usual minimal interpretation provides all what you say, namely "to give us a way of thinking about what is really happening", where "what is really happening" can only mean "what can be observed". Otherwise I can invent any kind of phantasy stuff, I like for some personal reasons, and claim it's needed to understand "what's really happening", but which cannot be observed. It's the same as with "many worlds", where they invent some "splitting of the universe" at any moment anything reads off a measurement result, but that's obviously not what we observe, and thus the many parallel worlds are simply declared as unobservable. So what's the point to introduce them in the same place? In BM it's the unobservable trajectories.

What's so wrong with the trajectories being unobservable? I can't observe an electron either. There are many things I can't observe. I only know about them because I read about them, which in turn was inferred based on an immense tower of conjectures, approximations and assumptions connected to interpretations of device readings. In the end, it doesn't matter what can be observed or not. I can picture the trajectories in my mind regardless of whether or not they are observable, in principle or in practice. If the issue is that it "doesn't really exist", then this is really an ontological claim, and other interpretations don't fair better.

The more serious issues I see with my limited knowledge and understanding is that there is no good extension of the Bohmian programme for QFT so far, that the more I learn about QFT the less I see the particle picture as useful, and that it honestly falls kind of short of Bohm's original idea. What I mean is that I'm learning that what Bohm and others really wanted to do at the time was invent new concepts using which QM could be understood in its own right without resorting back to classical mechanics. I'm reading about how not just him but also various philosophers and other physicists were rather annoyed by Bohr's mantra that in the end, it is classical quantities that you can think about and observe. It was an optimistic and commendable view that new concepts could be developed so that physicists can move beyond thinking that way, and Bohm himself didn't think this was really fully achieved by his theory.

In the end of the day, observable or not, real or not, having many different ways to intuitively think about something is good. Read JS Bell's Speakable and Unspeakable in Quantum Mechanics, where he has a chapter in which he talks about how the old, pre-Einstein picture of ether can sometimes be used to intuitively think about some problems, in which the Einsteinian view encourages a certain mindset that can be confusing and misleading.

 

[Ken G]

In summary, "vive la difference." Can we know the next great theory won't be inspired by BM type thinking, even if that approach did not play out the way it was originally intended?

 

[Demystifier]

The more serious issues I see with my limited knowledge and understanding is that there is no good extension of the Bohmian programme for QFT so far, that the more I learn about QFT the less I see the particle picture as useful,

Have you seen my https://arxiv.org/abs/2205.05986 ? Bohmian QFT does not insist on the particle picture.

 

[AndreasC]

Have you seen my https://arxiv.org/abs/2205.05986 ? Bohmian QFT does not insist on the particle picture.

No, I have not seen it, I will check it out! Again I have to repeat my knowledge is rather limited.

 

[AndreasC]

In summary, "vive la difference." Can we know the next great theory won't be inspired by BM type thinking, even if that approach did not play out the way it was originally intended?

Interestingly, studying the history of QM was what lead Feyerabend to eventually advocate for "anarchism" in science. His path was however kind of backwards, he learned about Bohmian mechanics and advocated for it and against Copenhagen from a methodological point of view, but eventually he appreciated Bohr much more, after he saw there were good reasons why the mainstream interpretation was developed that way. His conclusion was not however that this was the only right way and that BM was wrong, but that pluralism is good. And, well, eventually he (notoriously) took it to the next level where he argued things such as that there is no difference between physics and astrology, etc. But we don't need to get to that level. Here is a paper I found talking about all that:

https://scholar.google.com/scholar?...=#d=gs_qabs&t=1689975757097&u=#p=95NloVRSosQJ

 

[Fra]

Perhaps the resolution is to interpret claims like that as really saying "we are choosing to picture the integral curves of the probability currents as particle trajectories, as an optional manner of informing our subjective insight."

Yes, or as I think Demystifier also put it well in one of this older papers

"the deterministic point-particle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV’s, nonlocality in solipsistic HV’s can be substantially reduced down to microscopic distances inside the observer."
-- https://arxiv.org/abs/1112.2034

In a sense this can be interpreted so that the HV is the agents MAP, and in relation to relativity, there is a difference between "non-local" operations on hte MAP itself (which is encoded in the local observer) and non-local "operations" in the territory.

I imagine that the manifestation of relativity in this case would require understanding the interaction of MAPs, which is something that I think also normal QM or QFT fails to do - it is rather assumed, when talking about "observables" that there exists a unique equivalence class, and this is used as a constraint. But if it turns out that these constraints are rather only emergent, then the above "starting point" may be potentially misleading.

/Fredrik

 

[Demystifier]

No, I have not seen it, I will check it out! Again I have to repeat my knowledge is rather limited.

The paper is written precisely for people with limited technical knowledge of QFT.