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

[Fra]

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.

Btw, this would be related to "interactions" or transitions between backgrounds, which is something that is still the subject of future research. I see this also at the heart of the matter in string theory as well, there the physics around "selection" of the background (includingng the compactified ones) are still a difficult aread.
So rejecting such ideas on the basis that it "contradicts" special relativity, seems somewhat simplistic and misses out that there is something much deeper to possible be gained, if the ideas work out. So I prefer to at least give all those ideas the benefit of doubt.

/Fredrik

 

[vanhees71]

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

Already in the abstract you admit, it's not Lorentz covariant!

 

[gentzen]

Quite generally, the book "QFT for the gifted amateur" is excellent for developing conceptual intuitive understanding of the main ideas, but not very reliable as a reference for technical mathematical aspects of QFT. The authors themselves say in the preface that they are experimentalists.

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

Philosophers of physics who find standard QFT textbooks technically formidable may learn a lot of QFT from [11].
[11] P. Teller, An Interpretive Introduction to Quantum Field Theory (Princeton University Press, Princeton, 1995).

Most of my conceptual and technical understanding of QFT originates from these two books. Of course I knew that I have only very limited technical knowledge of QFT. But getting confirmation of that knowledge like that feels quite humbling nevertheless. A bit opposite to the experience of "having learned nothing new" after reading a reference given in a B level thread, but apparently targeted towards I level:

This thread is marked as B level - its can't really be explained at that level - you need at least an I level, and even then an A level thread would be better - but you can to a large extent get a 'feel' for what's going on at the I level.

In that vein, and in the hope the OP and others reading this thread, can glean something from reading it see the following:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

It is a somewhat similarly humbling experience to reading in the preface of a book on theoretical solid state physics:

Im Umfang von Band 1 sollte auch jeder experimentell arbeitende Festkörperphysiker Kenntnisse in theoretischer Festkörperphysik haben. Zusammen mit einem Buch oder Skript über experimentelle Festkörperphysik kann der Inhalt daher auch Grundlage für ein Wahlfach „Festkörperphysik“ im Master-Studiengang sein und zusammen mit dem Inhalt von Band 2 Grundlage für ein Wahlfach „Theoretische (Festkörper-)Physik“ im Master-Studiengang. Für eine Master-Arbeit über theoretische Festkörperphysik braucht man allerdings noch über den Inhalt von Band 1 und 2 hinausgehende Kenntnisse über spezielle Methoden der Vielteilchen-Theorie.

OK, the solid state physics textbook experience was a bit more humbling, because it happened before I started to dig into those two daunting books, which I still have not fully mastered today.

 

[gentzen]

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

Already in the abstract you admit, it's not Lorentz covariant!

This might be related to the second mentioned "opportunity" in my initial question:

• 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.

Why does BM breaks invariance under ... transformations? How does it break that invariance? A Bell like strategy could be to isolate some positive properties of BM, and show that any theory (or "interpretation") sharing those positive properties with BM would be forced to also break invariance under ...

 

[Demystifier]

Why does BM breaks invariance under ... transformations? How does it break that invariance? A Bell like strategy could be to isolate some positive properties of BM, and show that any theory (or "interpretation") sharing those positive properties with BM would be forced to also break invariance under ...

In the paper I explain it through the analogy with gauge potential. The gauge potential in a Coulomb gauge breaks the Lorentz invariance, yet all measurable predictions are Lorentz invariant. Hidden variables a'la Bohm/Bell are like inventing gauge potential for the electric and magnetic field and saying that the potential is "real". It would be interesting to find a general theorem that implies invariance breaking, but such is not known yet.

 

[Demystifier]

Already in the abstract you admit, it's not Lorentz covariant!

And in the same abstract, I point out that the measurable predictions are Lorentz invariant. What's the problem? Are you a mathematical Platonist (who insists that the formalism should be Lorentz invariant), or a natural scientist (who insists that the measurable predictions should be Lorentz invariant)?

When I think of it, it seems to me that all our circular discussions about quantum interpretations stem from the fact that you cannot decide whether you are a mathematical Platonist or a natural scientist. If you could decide, and stick to it consistently, all our interpretational discussions would be settled in a minute.

Natural scientist? No problem, Bohmian mechanics makes right predictions and hence it's right, even for relativistic QFT.

Mathematical Platonist? Then there is the measurement problem because the minimal interpretation does not define measurement mathematically. You need some non-minimal interpretation. There are many non-minimal interpretations on the market, but if you would need to choose one, I have a feeling that you would choose the Bohmian one.

Conclusion: You are in the superposition of a mathematical Platonist and a natural scientist. But in your case, this is really a superposition of two versions of a Bohmian. So you are really a Bohmian, but you don't know it because your wave function cannot collapse. You are like a cat who does not know that it is a cat because it is in a superposition of white cat and black cat.

 

[AndreasC]

It would be interesting to find a general theorem that implies invariance breaking, but such is not known yet.

Invariance breaking under what conditions?

 

[Demystifier]

Invariance breaking under what conditions?

Existence of Bell-like $\lambda$ variables compatible with quantum theory.

 

[Fra]

Existence of Bell-like $\lambda$ variables compatible with quantum theory.

I might add, existence of inside observers(agents), that we take seriously and these physical systems infer and encode a theory. Ie. their perspectives receive an "ontic status". Then observer equivalence is genereally broken; but we still have what i tend to label observer democracy.

If we are allowed to associate the inside observers "encoded information" with $\lambda$, then alot of Demystifiers reasoning makes good sense to me, even as someone representing a very different interpretation.

As we know in QM and QFT, observers are by construction NOT inside, this is a blessing as it keeps things simple, but it is also problematic! Those who keep deny it, still runs into trouble when we want to mix it with GR and cosmology. Who keeps insisting there are no inside observers?

/Fredrik

 

[gentzen]

Invariance breaking under what conditions?

(I largely agree with Fra's answer to this just above.) Probably if your theory/"interpretation" allows you to represent truly closed systems together with a measurement theory that doesn't implicitly break that "closedness".

See this discussion about violation of conservation laws and closed systems that I "somehow provoked" (in the end this goes back to my study of Heisenberg's writings for "general audience and philosophers"):

Indeed, I don't expect this. The violation of conservation laws event by event (in such a situation) is much less surprising than ...

To be clear, I don't think there is any actual violation of conservation laws--it's just that if you only look at the measured system, you aren't taking into account all the relevant conserved quantities.

...

In general this is true, but it doesn't mean conservation laws are violated. It just means the system is not a closed system--it interacts with the measuring apparatus during measurement. If a system is not closed, you should not expect it to obey conservation laws in isolation.

Of course, event-by-event conservation means that you must have a state, for which the conserved quantity takes a definite value.

You will if you include everything that interacts, which means including the measuring apparatus. As @Demystifier points out, we don't currently have a formulation of QM that does that and also explains (instead of just postulating) single outcomes; that means we don't currently have a formulation of QM that allows us to test conservation laws during measurements.

(I did study Heisenberg's writtings on the one hand in the hope of learning about the practical and pragmatic aspects of the "elusive" Copenhagen interpretation, and on the other hand in the hope of learning how to interpret statements like "quantum mechanics is a complete theory," whose literal interpretation seemed to make little sense to me. Both hopes were fulfilled, but ... new questions arose, more related to the involved persons themselves, persons like Sommerfeld, Bohr, Born, Schrödinger, Pauli, Dirac, von Weizsäcker, Teller, ..., and our perception of them.)

 

[Ken G]

I see a convergence of two seemingly different lines of thought that is happening here. On the one hand we have the important difference between requiring that all observables are Lorentz covariant, versus requiring that all ontic pictures required to correctly predict those observables be comprised strictly of Lorentz invariants. On the other hand we have whether we imagine that closed systems can have "states" of their own, even before they are coupled to any observing apparatus, versus whether the very concept of a "state" must necessarily always include an observing apparatus or it is an angel on the head of a pin.

The convergence of these seemingly disparate dichotomies is that they both encounter a similar incompleteness: the inspiration for Lorentz covariance is that different observers must in some sense cohabit the same reality (i.e., the key role of objectivity in science), but that immediately imposes a gulf between the nature of that reality and the character of ontic elements of any theory (the longstanding contrast between "theory" and "experimentation" in science). Moreover, the inspiration for the concept of the state of a system is that we wish that state to correspond to reality, but as an objective version of reality we must include something capable of making objective statements, i.e., an observing apparatus.

I believe this gulf is the same as what gets called the "Heisenberg gap," which unfortunately normally gets associated with micro and macro realms, when it is not so much a matter of scale as it is a matter of deciding what physics is. Until we stop pretending there is a seamless functionality between the moving parts of scientific ontology and epistemology, then Einstein will ultimately be correct, that quantum mechanics is still incomplete. What Einstein perhaps did not recognize is that this incompleteness is not a fundamental trait of QM, that is merely the place we are forced to come to terms with it. There is a difference between resolving a problem and simply getting away with leaving it unresolved.

 

[gentzen]

I believe this gulf is the same as what gets called the "Heisenberg gap," which unfortunately normally gets associated with micro and macro realms, when it is not so much a matter of scale as it is a matter of deciding what physics is. Until we stop pretending there is a seamless functionality between the moving parts of scientific ontology and epistemology, then Einstein will ultimately be correct, that quantum mechanics is still incomplete.

I like what you wrote above this quote passage, but I don't get what you want to say here. I never heard of a Heisenberg gap, do you mean the Heisenberg cut? Heisenberg's attutide towards it was "just put it sufficiently far away," Bohr attitude was that there is a "correct" place for the cut, which is somewhat harder to swallow, and grants classical concepts more importance. No idea what you mean by "functionality," or why you predict that quantum mechanics is still "incomplete".

 

[Ken G]

I like what you wrote above this quote passage, but I don't get what you want to say here. I never heard of a Heisenberg gap, do you mean the Heisenberg cut? Heisenberg's attutide towards it was "just put it sufficiently far away," Bohr attitude was that there is a "correct" place for the cut, which is somewhat harder to swallow, and grants classical concepts more importance. No idea what you mean by "functionality," or why you predict that quantum mechanics is still "incomplete".

Yes, "cut" might be a more standard term for it, but the point is that it is normally framed as a physical difference between behaviors on micro and macro scales. I think Bohr had a better way to frame it, that our modes of thought are conditioned on our experience, so to say we "understand" reality, it requires that we bring all our physics ontologies into contact with the realm of our experience. Heisenberg in a sense "punted" on that requirement, by taking essentially the opposite perspective that it will be impossible to bring the quantum realm into contact with our experience, so we should not even try. I'm saying that the problem cannot be resolved that way, because it is not so much a gulf between length scales, it is the fundamental difference between knowing something because it is the result of a repeatable objective experiment (like the track of a particle in a cloud chamber), and knowing something because it is well described by ontological structures (like electric field lines). We teach that science involves iteration between these elements until a successful unification is achieved, but this might be somewhat disingenuous to the potential incompatibilities between these separate elements of the process.

Perhaps we should instead recognize the fundamental instability encountered when asking these somewhat opposing, and potentially incompatible, approaches to work together. Of course we must get them to work together as best we can, but the "peace" between them might be a bit like the "cheating between the wars" as it was characterized above. But we don't need to adopt such confrontational language if we simply accept the subjective component of doing science, where the objective world in which all scientsts must intersect to make progress can be distinguished from the subjective insights each takes advantage of. Hence the process of scientific progress mirrors the same questions as does its theories, about how broadly should we apply the requirement for objectivity.

 

[PeterDonis]

existence of inside observers(agents)

What does this mean? Where are you getting it from?

 

[Fra]

What does this mean? Where are you getting it from?

To give a mathematical theory of the "inside observer" and it's interactions, is of course an open issue, i have no answer.

But conceptually en external observer is external to the system of study, where it can without principal limits prepare, control and monitor the system of study and make repeats to get statistics. The systems back-reaction onto the observing context, is limited to updating counters or state revisions. No need to worry about the observer beeing saturated with information, or dominated by the system. This is like the normal observer in QM, where essentially the whole classical environment is the observer.

An internal observer is one that is rather existing "inside" the system. So the internal observer essentially observes all of it's own environment. So the usual "preparations" and acquisiton of confident statistics etc isnt possible the same way. In this case hte backreaction from the system onto the observing context cant be ignored. But there is not quantum theory for this, but this doesn't mean one can entertain it's conceptually.

It's like an extension of the tradition of gedanken observers of Einstein, where he essential pondered about what observer in various states of motion would observer, taking it further seems unavoidable when pondering about howto unify QM with gravity, as the inside observer is the natural thing.

Especially in a computational perspective, the difference between external and internal observers become important as an inside observer is conceptually constantly overflowed with information, and has to simplifly, compress and decide what to discard. An external observer, such as a big lab, studying atoms, don't have the same problem, here only time limits the inferences.

Towards Physics of Internal Observers: Exploring the Roles of External and Internal Observers
"Following Einstein's thought experiments, one could ask: What would it look like to sit inside a photon or to be a photon? And what type of observer could represent this more global perspective of the photon's interior? To address these questions, we introduce the concepts of internal and external observers with a focus on their relationship in quantum theory and relativity theory"
-- https://arxiv.org/abs/2304.01677

The concept of inside or intrinsic observers in different context are older than Einstein though, even Riemann was seeking the "intrinsic measures" of geometry by considering what can be measured by inside observers. But the concept can be generalized to the inferred theories. As we know, Einstein mainly worried about states of motion, but if one considers also the encoded information, we get the well known weird information paradoxes and other things. How can one understand the invariance of the laws of physics during these transformations? And the point of my post was really that, perhaps transient violation of some observer equivalence relations are unavoidable in order to understand this. Ie. to what extent CAN we understanda "equivalence" between two observers can simply can't hold comparable amounts of information? Exemplified by the extreme of the external and inside observer?

/Fredrik

 

[PeterDonis]

To give a mathematical theory of the "inside observer" and it's interactions, is of course an open issue, i have no answer.

Then you are verging on personal speculation, which is off limits here. You do give a reference, which is good, but please stay within the bounds of what is in the literature.

 

[Fra]

Then you are verging on personal speculation, which is off limits here. You do give a reference, which is good, but please stay within the bounds of what is in the literature.

(I am aware of this by now, so even if I had some answers, I would not put it on here, at least not until it's published elsewhere.)

The role I rather take on here, is to try to broaden the perspectives on how we see and understand theories in general. Quite often, different stances or interpretations tend to fail to see the logic in the other perspective, so discussions rarely lead anywhere. Sometimes it stops by agreeing to disagree on a definition of a word. I have been fascinated by seeing similarities rather than differences. Different stances have different primary notions (or ontics that Demysitifer calls it), and with it comes also correspondingly different guiding principles or constraints. I am thinking that it may exist dualities here, so that the different approaches are simply different, but they aim to understnad the same world, so we might benefit from understanding the relations between perspectives.

Constraints vs Emergence is one such thing, which seems to have a flipside, which is finetuning vs evolution, which makes a difference to some when it comes to explanatory value. I think these questions appear in different disguises in all the different research programs.

In string theory we have the fine tuning among all the backgrounds that one arries at by a constraintn based approach. Does it have to be manually "tuned" or is there a better way?

In Bohmian mechanis, the primary picuture superficially violates the observer equivalence of SR, but perhaps it is instead to be understood not as a constraint, but as emergent, or are there constraints to arrive a similar situations as in string theory?

and the list of comparastions go on, but what is a common denominator here? can we associate elements of different apparoches to each other and gain insight? Probably each approach has it's advantages and disadvantages.

/Fredrik

 

[Demystifier]

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.

Finished:
https://arxiv.org/abs/2308.10500

 

[Demystifier]

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.

You don't need to claim that it's needed for everybody. You can claim that you understand it better when you imagine that this fantasy stuff is real. And maybe some (not all) other guys will also like your fantasy and conclude that they also better understand it when they imagine that the fantasy stuff is real. In this way, the fantasy may become a useful thinking tool, a mental trick, that transforms an abstract entity into something that some humans can grasp more intuitively. So who cares that this fantasy is invented, if the fantasy serves a practical purpose?

Mathematics is full of useful invented fantasies, like infinity, complex numbers, real numbers, perhaps even integers. Some mathematicians believe that these things exist on their own and that mathematicians discover them, rather than invent them. Other mathematicians disagree. But at the end of the day that's irrelevant, what matters is that these things are useful as thinking tools.

The same is the case with quantum interpretations. If, for instance, someone likes to think that paths in Feynman path integrals are "real", because such a way of thinking makes path integrals more intuitive to him, nobody forces you to think that way. At the end of the day, people with different styles of thinking need to agree on measurable predictions. But how they arrived to them, did they use a minimal style of thinking which you prefer, or a style dressed with additional fantasy stuff, who cares? Why it bothers you that some people like to think in a less minimal style, if they all eventually arrive to the same results?

 

[Ken G]

And even those who say "shut up and calculate," aren't. When I'm asked "which quantum interpretation do you think is the right one," I say, "I think you have a mistaken idea about what an interpretation is for."

 

[gentzen]

Mathematics is full of useful invented fantasies, like infinity, complex numbers, real numbers, perhaps even integers. Some mathematicians believe that these things exist on their own and that mathematicians discover them, rather than invent them. Other mathematicians disagree. But at the end of the day that's irrelevant, what matters is that these things are useful as thinking tools.

Are fantasies and fictions the same thing? Not sure whether infinities per se are a fantasy, or whether the fantasy are just the inexhaustibly many different types of infinity.

Let me link to my old comment and my old FOM post on Mathematical fictionalism vs. physical fictionalism:

Like many other mathematicians, I believe in a principle of 'conservation of difficulty'. This allows me to believe that mathematics stays useful, even if it would be fictional. I believe that often the main difficulties of a real world problem will still be present in a fictional mathematical model.
...
From my experience with physicists (...), their trust in 'conservation of difficulty' is often less pronounced. As a consequence, physical fictionalism has a hard time

 

[WernerQH]

In this way, the fantasy may become a useful thinking tool, a mental trick, that transforms an abstract entity into something that some humans can grasp more intuitively.

One of the most fruitful "fantasies" is of course the field concept, or originally Faradays "lines of force" that @vanhees71 still finds hard to grapple with.

 

[vanhees71]

I've no problem with the field concept but only with the depiction as field lines. For me they are no more than the lines pointing in direction of the field to be depicted. How dense the field lines are depends on my choice of how dense I plot them to get an overview about how the field is directed. It's no clear measure for the field strength so.

 

[Ken G]

I think the most useful element of a field line comes in the form of effective stresses. Electromagnetic field lines act as though they had a tension to them, producing a restoring force when they bend. This allows a nice picture for the electromagnetic oscillations of light, as well as the propagation of Alfven waves in magnetohydrodynamics. Imagining that the field is threaded with lines is thus actually pretty useful, because the mathematics of Maxwell can often appear quite similar to the mathematics of strings under tension. That is in a sense similar to the concept of a quantum mechanical interpretation, we are looking for a kind of conceptual analog where the mathematics can be framed similarly, so we can borrow from insights we have developed in other contexts.

 

[Demystifier]

Are fantasies and fictions the same thing?

Fiction, of course, in this context is a better word, but @vanhees71 used the word "fantasy" to emphasize the negative connotations associated with it, so I used the same word in a reply.

 

[Demystifier]

I've no problem with the field concept but only with the depiction as field lines. For me they are no more than the lines pointing in direction of the field to be depicted. How dense the field lines are depends on my choice of how dense I plot them to get an overview about how the field is directed. It's no clear measure for the field strength so.

I guess you are just not a visual type, for you visualizations of abstract ideas do more harm than good. If I'm right, you probably don't like all these pictures of spacetime in special and general relativity, because they are all misleading if taken too literally.

 

[vanhees71]

Minkowski diagrams and their relatives in GR are indeed more complicated than thought. Already for reading a Minkowski diagram you have to abandon your well-trained thinking in terms of the Euclidean plane and substitute it with the Minkowski pseudo-metric. E.g., you have to construct the right "tic marks" for the axes of inertial frames with hyperbolae. Sometimes such spacetime diagrams may give an intuitive picture about some things like the relativity of simultaneity etc. As you say, one should be very careful in taking them too literally.

 

[martinbn]

I guess you are just not a visual type, for you visualizations of abstract ideas do more harm than good. If I'm right, you probably don't like all these pictures of spacetime in special and general relativity, because they are all misleading if taken too literally.

That is a bad example. The spacetime diagrams are not fantasies or a thinking tool, they are an accurate discription of spacetime.

 

[Demystifier]

That is a bad example. The spacetime diagrams are not fantasies or a thinking tool, they are an accurate discription of spacetime.

I didn't say they are fantasies. I conjectured that @vanhees71 is not a visual type, and proposed a test of my conjecture. If my conjecture is true, he should dislike these diagrams even though they are not fantasies.

 

[martinbn]

I didn't say they are fantasies. I conjectured that @vanhees71 is not a visual type, and proposed a test of my conjecture. If my conjecture is true, he should dislike these diagrams even though they are not fantasies.

And how is this related to the thread?!

 

[Demystifier]

And how is this related to the thread?!

If he is not a visual type, while Bohmian interpretation is intuitive precisely because it's visual, it explains why he doesn't find the Bohmian interpretation intuitive.

 

[martinbn]

If he is not a visual type, while Bohmian interpretation is intuitive precisely because it's visual, it explains why he doesn't find the Bohmian interpretation intuitive.

No, it doesn't, that's why I said it was a bad example. I like space-time diagrams, and I find them intuitive and usefull. But I don't feel the same way about BM.

 

[Demystifier]

No, it doesn't, that's why I said it was a bad example. I like space-time diagrams, and I find them intuitive and usefull. But I don't feel the same way about BM.

I think you dislike BM for different reasons than him. All likers of BM are alike, each disliker of BM dislikes it in his own way.

 

[vanhees71]

Spacetime diagrams, when properly read, provide a picture of observable things ("events"). Bohmian trajectories are illusions. They are not depicting anything observable and may lead to false intuitions.

 

[Demystifier]

Bohmian trajectories ... may lead to false intuitions.

Of course they can. But any intuitive idea may lead to false intuitions, if you don't understand it properly.