# How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics

Many people here know that I am a “Bohmian”, i.e. an adherent of a very non-orthodox interpretation of quantum mechanics (QM). Indeed, in the past, I have published a lot of papers on Bohmian mechanics in peer-reviewed journals from 2004 to 2012. So how can I not worry and love orthodox QM? As a “Bohmian”, shouldn’t I be strictly against orthodox QM?

No. If by orthodox QM, one means instrumental QM (which is well explained in the book “Quantum Theory: Concepts and Methods” by A. Peres), then orthodox QM is fully compatible with Bohmian QM. I am not saying that they are equivalent; indeed Bohmian QM offers answers to some questions on which instrumental QM has nothing to say. But I am saying that they are compatible, in the sense that no claim of instrumental QM contradicts any claim of Bohmian QM.

But still, if instrumental QM has nothing to say about certain questions, then why am I not worried? As a “Bohmian”, I certainly do not consider those questions irrelevant. So how can I not worry about it when it says nothing about questions that I find relevant?

The answer is that I stopped worrying and learned to love orthodox QM precisely because I know about Bohmian QM. But let me explain it from the beginning.

I always wanted to study the most fundamental aspects of physics. Consequently, as a student of physics, I was much more fascinated by topics such as particle physics and general relativity than about topics such as condensed-matter physics. Therefore, my graduate study in physics and my Ph.D. were in high-energy physics. Nevertheless, all the knowledge about quantum field theory (QFT) that I acquired as a high-energy physicist did not help me much to resolve one deep puzzle that really bothered me about QM. The thing that bothered me was how could Nature work like that? How could that possibly be? What could be a possible physical mechanism behind the abstract rules of QM? Should one conclude that there is no mechanism at all and that standard QM (including QFT) is the end of the story?

But then I learned about Bohmian QM, and that was a true revelation. It finally told me a possible story of how could that be. It didn’t definitely tell how it *is* (there is no direct evidence that Bohmian mechanics is how Nature actually works), but it did tell how it *might* be. It is comforting to know that behind the abstract and seemingly paradoxical formalism of QM may lie a simple intuitive mechanism as provided by Bohmian QM. Even if this mechanism is not exactly how Nature really works, the simple fact that such a mechanism is possible is sufficient to stop worrying and start to love instrumental QM as a useful tool that somehow emerges from a more fundamental mechanism, even if all the details of this mechanism are not (yet) known.

However, something important was still missing. Bohmian QM looks nice and simple for non-relativistic QM, but how about relativistic QFT? In principle, Bohmian ideas of that time worked also for relativistic QFT, but they did not look so nice and simple. My question was, can Bohmian ideas be modified such that it looks nice, simple and natural even for relativistic QFT? That question motivated my professional research on Bohmian QM and I published a lot of papers on that.

Nevertheless, I was not completely satisfied with my results. Even though I made several interesting modifications of Bohmian QM to incorporate relativistic QFT, neither of those modifications looked sufficiently simple and natural. Moreover, in arXiv:1309.0400, the last specialized paper on Bohmian mechanics I have written, a referee found a deep conceptual error that I was not able to fix. After that, I was no longer trying to modify Bohmian QM in that way.

Nevertheless, partial satisfaction came from a slightly different angle. In an attempt to make sense of local non-reality interpretation of QM, I developed a theory of solipsistic hidden variables which is a sort of a hybrid between Bohmian and Copenhagen QM. In this theory, an observer does play an important role, in the sense that Bohmian-like trajectories exist only for degrees of freedom of the observer and not for the observed objects. That theory helped me to learn that, in order to understand why do we observe what we observe, it is not necessary to know what exactly happens with observed objects. Instead, as solipsistic hidden variables demonstrate, in principle it can be understood even if the observed objects don’t exist! It was a big conceptual revelation for me that shaped my further thinking about the subject.

But it does not mean that I became a solipsist. I don’t believe that observed objects don’t exist. The important message is not that observed objects might not exist. The important message is that the exact nature of their existence is not really so important to explain their observation. That idea helped me a lot to stop worrying and learn to love orthodox QM.

But that was not the end. As I said, in my younger days, my way of thinking was largely shaped by high-energy physics and not by condensed-matter physics. I thought that condensed-matter physics cannot teach me much about the most fundamental problems in physics. But it started to change in 2010, when, by accident, I saw in Feynman Lectures on Physics that Bohmian mechanics is related to superconductivity (see here) That suddenly made me interested in superconductivity. But superconductivity cannot be understood without understanding other more basic aspects of condensed-matter physics, so gradually I became interested in condensed-matter physics as a field. One very interesting thing about condensed-matter physics is that it uses QFT formalism which is almost identical to QFT formalism in high-energy physics, but the underlying philosophy of QFT is very different. Condensed-matter physics taught me to think about QFT in a different way than I was used to as a high-energy physicist.

One of the main conceptual differences between the two schools of thought on QFT is the interpretation of particle-like excitations resulting from canonical quantization of fields. In high-energy physics, such excitations are typically interpreted as elementary particles. In condensed-matter physics, they are usually interpreted as quasiparticles, such as phonons. Since I was also a Bohmian, that led me to a natural question: Does it make sense to introduce a Bohmian trajectory of a phonon? An obvious (but somewhat superficial) answer is that it doesn’t make sense because only true particles, and not quasiparticles, are supposed to have Bohmian trajectories. But what is a “true” particle? What exactly does it mean that a photon is a “true” particle and a phonon isn’t?

It was this last question that led me to my last fundamental insight about Bohmian mechanics. As I explained in Sec. 4.3 of arXiv:1703.08341 (accepted for publication in Int. J. Quantum Inf.), the analogy with condensed-matter quasiparticles such as phonons suggests a very natural resolution of the problem of Bohmian interpretation of relativistic QFT. According to this resolution, the so-called “elementary” particles such as photons and electrons described by relativistic QFT are not elementary at all. Instead, they are merely quasiparticles, just as phonons. Consequently, those relativistic particles do not have Bohmian trajectories at all. What does have Bohmian trajectories are some more fundamental particles described by non-relativistic QM. Non-relativistic QM (together with Bohmian interpretation) is fundamental, while relativistic QFT is emergent. In this way, the problem of the Bohmian interpretation of relativistic QFT is circumvented in a very elegant way.

There is only one “little” problem with that idea. There is no experimental evidence that such more fundamental non-relativistic particles actually exist in Nature. Perhaps they will be discovered one day in the future, but at the moment it is only a theory. In fact, it is not even a proper theory, because it cannot tell anything more specific about the exact nature of those hypothetical non-relativistic particles.

Nevertheless, there are at least two good things about that. First, unlike most other versions of Bohmian mechanics, this version makes a testable prediction. It predicts that, at very small distances not yet accessible to experimental technology, Nature is made of non-relativistic particles. Second, at distances visible by current experimental technology, this version of Bohmian QM says that Bohmian trajectories are irrelevant. This means that, as far as relativistic QFT is concerned, I do not need to worry about Bohmian trajectories and can love orthodox QFT, without rejecting “common sense” in the form of non-relativistic Bohmian mechanics on some more fundamental scale. That’s how I finally I stopped worrying and learned to love orthodox QM.

Theoretical physicist from Croatia

To elaborate my concern. I was hoping that making the wave function as simply calculation tool would make all classical.. without needing any quantum cut.. but in the double slit experiment, treating the wave function as simply calculation tool means we only deal with the output or the detector screen.. we ignore what happens between emission and detection.. is this what you mean or a good example.. and the reason we still need the cut is because we need to know what happens inbetween.. or how reality comes from non-reality?

It's really a headache to treat the wave function as objective.. I have headaches for many days lol.. so treating it as calculational tool can give us relief.. but the cost is unable to determine the reality/non-reality cut in the sense we don't know what happens between emission and detection? Is this the exact reason so I know.. thanks..Yes, you can try to make everything classical, eg. Bohmian mechanics or MWI are famous approaches to making quantum mechanics classical. But if you only make everything notionally classical, without equations (ie. without Bohmian Mechanics or MWI), you have no way to interact with quantum mechanics and pull quantitative predictsion about reality (or the "classical" or "macroscopic" world). Basically, quantum mechanics does not tell us when a measurement occurs, and we need that input to pull a quantitative prediction out.

but the cost is being unable to determine the reality/non-reality cut in the sense we don't know what happens between emission and detection?Yes, you're pretty much there. Now, if you could just manage to be happy about paying that cost….

If the wave function is not real, but the measurement apparatus and the results are real, why do quantum mechanics still need a reality/non-reality cut.. (by reality you mean classical and nonreality quantum? why didn't you use the word classica/quantum and instead use reality/non-reality?) Can you please give an example why the cut is still needed. We can treat all as classical, and the quantum result only a tool to produce probability…To elaborate my concern. I was hoping that making the wave function as simply calculation tool would make all classical.. without needing any quantum cut.. but in the double slit experiment, treating the wave function as simply calculation tool means we only deal with the output or the detector screen.. we ignore what happens between emission and detection.. is this what you mean or a good example.. and the reason we still need the cut is because we need to know what happens inbetween.. or how reality comes from non-reality?

It's really a headache to treat the wave function as objective.. I have headaches for many days lol.. so treating it as calculational tool can give us relief.. but the cost is unable to determine the reality/non-reality cut in the sense we don't know what happens between emission and detection? Is this the exact reason so I know.. thanks..

In all versions of Copenhagen, the classical/quantum cut does exists whether the wave function is real or calculational. If the wave function is not real, but the measurement apparatus and the results are real, quantum mechanics needs a reality/non-reality cut. The unitary evolution of the non-real wave function does not say what is measured, nor when a measurement occurs – it does not say when reality pops out of non-reality. There is a cut somewhere – different people call it by different names.If the wave function is not real, but the measurement apparatus and the results are real, why do quantum mechanics still need a reality/non-reality cut.. (by reality you mean classical and nonreality quantum? why didn't you use the word classica/quantum and instead use reality/non-reality?) Can you please give an example why the cut is still needed. We can treat all as classical, and the quantum result only a tool to produce probability…

When we treat the wave function as objective.. we have problems with the consequence of real collapse (a varient of Copenhagen) or all the terms existing (MWI) or all terms existing but they are not real and only one particle being pushed around (Bohmian).. all of these are greatly disturbing. So why don't we just treat the wave function as just for calculation purposes and all of us happy.. I mean.. does this eliminate the classical-quantum cut by making all classical.. how does treating the wave function as calculational tool only affect the need or requirement of the classical-quantum cut?In all versions of Copenhagen, the classical/quantum cut does exists whether the wave function is real or calculational. If the wave function is not real, but the measurement apparatus and the results are real, quantum mechanics needs a reality/non-reality cut. The unitary evolution of the non-real wave function does not say what is measured, nor when a measurement occurs – it does not say when reality pops out of non-reality. There is a cut somewhere – different people call it by different names.

vanhees71 does not accept the classical-quantum cut, which even Peres does.

Peres is an excellent book, but it is not quantum orthodoxy. Although he hides it very well, ultimately his flawed sympathy with Ballentine shows itself in his lack of a clear statement of the measurement problem, and statements about fuzzy Wigner functions that try to avoid the measurement problem. Basically, unless a book about foundations talks about the measurement problem, it is useless as a book about foundations. The measurement problem is the most important problem in the foundations of quantum mechanics.When we treat the wave function as objective.. we have problems with the consequence of real collapse (a varient of Copenhagen) or all the terms existing (MWI) or all terms existing but they are not real and only one particle being pushed around (Bohmian).. all of these are greatly disturbing. So why don't we just treat the wave function as just for calculation purposes and all of us happy.. I mean.. does this eliminate the classical-quantum cut by making all classical.. how does treating the wave function as calculational tool only affect the need or requirement of the classical-quantum cut?

The default hypothesis is that it persists, but a hypothesis that it doesn't is also legitimateIsn't it known to be possible for Lorentz invariance to emerge at large distance scales from a quantum field theory that is non-relativistic on small distance scales? IIRC (I think I first came across this in Zee's QFT textbook), the Lorentz invariant speed is something like a "sound speed" in an underlying medium that emerges from the non-relativistic QFT.

Interesting thoughts Demystifier, thanks!

I still don't understand what do you mean by "one particle". That the whole universe contains only one particle? That's excluded.

Concerning the number of particle types, I cannot exclude any possibility.If one type of fundamental particle were manifest as all various types of particles/quasi-particles,

what prevents associating one particle only of only one type to all the world lines in space time?

Yes, Ballentine himself is slightly sympathetic to Bohmian mechanics. But if the main point of Ballentine's book is correct, then Bohmian mechanics is pointless – vanhees71 has drawn the logical conclusion from Ballentine.

Thus in fact, it is Copenhagen – which Ballentine hates – that promotes Bohmian mechanics. As your Insights article explains, there is no reason for a Bohmian not to love Copenhagen.You really like to push your conclusions to the extreme. :biggrin:

Your style reminds me of the great philosopher of science, Feyerabend.

I strongly disagree, see Secs. 14.2 and 14.3. of his book. I would rather say that he is agnostic about Bohmian QM. He does not say that there is no measurement problem, but demonstrates that a lot can be understood without talking about it explicitly.Yes, Ballentine himself is slightly sympathetic to Bohmian mechanics. But if the main point of Ballentine's book is correct, then Bohmian mechanics is pointless – vanhees71 has drawn the logical conclusion from Ballentine.

Thus in fact, it is Copenhagen – which Ballentine hates – that promotes Bohmian mechanics. As your Insights article explains, there is no reason for a Bohmian not to love Copenhagen.

But in a way, Ballentine is anti-Bohmian. If Ballentine were correct, there is no measurement problem, and Bohmian mechanics is pointless.I strongly disagree, see Secs. 14.2 and 14.3. of his book. I would rather say that he is agnostic about Bohmian QM. He does not say that there is no measurement problem, but demonstrates that a lot can be understood without talking about it explicitly.

The problem is that the errors are fundamental, not incidental.You say errors, but I have the feeling that you mean opinions different than yours. Can you give examples?

However, I do love Peres's book, although I dislike Ballentine's. In other words, I forgive Peres because he is so charming, at least in writing :)Have you read the whole book of Ballentine? May be you only dislike some parts.

I find Ballentine charming too. :smile:But in a way, Ballentine is anti-Bohmian. If Ballentine were correct, there is no measurement problem, and Bohmian mechanics is pointless.

The problem is that the errors are fundamental, not incidental.Yes, but they are not visible after the blurring.

However, I do love Peres's book, although I dislike Ballentine's. In other words, I forgive Peres because he is so charming, at least in writing :)I find Ballentine charming too. :smile:

Well, Peres's and Ballentine's books have something in common. If you read the fine details of the books, you can find erroneous statements. But if you make an appropriate blurring of the books, the fine errors cancel out and the books as a whole become great. :biggrin:The problem is that the errors are fundamental, not incidental.

However, I do love Peres's book, although I dislike Ballentine's. In other words, I forgive Peres because he is so charming, at least in writing :)

The book is very good, because Peres for the most part accepts the classical quantum cut. But he cannot bring himself to articulate it explicitly. He accepts it implicitly when he talks about the need for a second classical measuring apparatus, if we treat one measuring apparatus as quantum. A book about foundations should be as explicit about axioms as possible, not hide the ones that he doesn't like in implicit statements. And because he dislikes the axiom, eventually he does make a misleading statement about blurring of the Wigner function. There may be a way to read it without being misled, but as you can see from vanhees71's post, Peres has managed to mislead an expert.Well, Peres's and Ballentine's books have something in common. If you read the fine details of the books, you can find erroneous statements. But if you make an appropriate blurring of the books, the fine errors become invisible and the books as a whole become great. :biggrin:

I wouldn't say that Peres accepts a classical-quantum cut. What he accepts is something more like (abstract formalism)-(laboratory phenomena) cut. He says that quantum phenomena do not occur in Hilbert space, but in a laboratory. It would be akin to a statement that classical phenomena do not occur in phase space, but in a laboratory.The book is very good, because Peres for the most part accepts the classical quantum cut. But he cannot bring himself to articulate it explicitly. He accepts it implicitly when he talks about the need for a second classical measuring apparatus, if we treat one measuring apparatus as quantum. A book about foundations should be as explicit about axioms as possible, not hide the ones that he doesn't like in implicit statements. And because he dislikes the axiom, eventually he does make a misleading statement about blurring of the Wigner function. There may be a way to read it without being misled, but as you can see from vanhees71's post #31, Peres has managed to mislead an expert.

The flaw of Peres is that he fails to state the classical-quantum cut clearly. I believe he also does not include state reduction in his axioms.Why would he talk about classical-quantum cut clearly if he doesn't think that there is such a cut?

Concerning the axioms, he is developing a practical instrumental approach, not an axiomatic approach. This is like complaining that a handbook of civil engineering does not state axioms of stable building construction.

In the last chapter he very clearly discusses measurements on the example of the Stern-Gerlach experiment (the "Drosophila" of quantum physicists ;-)), and it becomes very clear that his view on the "classicality of measurement apparati" to ensure an irreversible storage of the measurement result is seen in the sense of an emergent phenomenon through the usual coarse-graining argument of quantum statistics (he calls it "blurring").

As I said, for me this book has been a relief be cause it cleans up the QT-foundational discussion of all unnecessary philosophical complications.Yes, that blurring is exactly where Peres reveals his mistaken sympathies with Ballentine. It is simply wrong.

Not "collapse" – state reduction is fine – in fact state reduction is often synonymous with "collapse". Only some people misunderstand Copenhagen and believe that "collapse" is necessarily physical.

The flaw of Peres is that he fails to state the classical-quantum cut clearly. I believe he also does not include state reduction in his axioms.In the last chapter he very clearly discusses measurements on the example of the Stern-Gerlach experiment (the "Drosophila" of quantum physicists ;-)), and it becomes very clear that his view on the "classicality of measurement apparati" to ensure an irreversible storage of the measurement result is seen in the sense of an emergent phenomenon through the usual coarse-graining argument of quantum statistics (he calls it "blurring").

As I said, for me this book has been a relief be cause it cleans up the QT-foundational discussion of all unnecessary philosophical complications.

vanhees71 does not accept the classical-quantum cut, which even Peres does.I wouldn't say that Peres accepts a classical-quantum cut. What he accepts is something more like (abstract formalism)-(laboratory phenomena) cut. He says that quantum phenomena do not occur in Hilbert space, but in a laboratory. It would be akin to a statement that classical phenomena do not occur in phase space, but in a laboratory.

Why do you think that it is not orthodoxy? Just because it doesn't involve collapse? Why do you think that orthodoxy must involve collapse?Not "collapse" – state reduction is fine – in fact state reduction is often synonymous with "collapse". Only some people misunderstand Copenhagen and believe that "collapse" is necessarily physical.

The flaw of Peres is that he fails to state the classical-quantum cut clearly. I believe he also does not include state reduction in his axioms.

Peres is an excellent book, but it is not quantum orthodoxy.Why do you think that it is not orthodoxy? Just because it doesn't involve collapse? Why do you think that orthodoxy must involve collapse?

Well, what you don't like about Peres's book is precisely why I like it ;-)). As I said, it's a nice example for the "no-nonsense approach" to (quantum) physics.

In the article I defined orthodox QM as instrumental QM a la Peres (which does not involve collapse), and I think that @vanhees71 is OK with it.vanhees71 does not accept the classical-quantum cut, which even Peres does.

Peres is an excellent book, but it is not quantum orthodoxy. Although he hides it very well, ultimately his flawed sympathy with Ballentine shows itself in his lack of a clear statement of the measurement problem, and statements about fuzzy Wigner functions that try to avoid the measurement problem. Basically, unless a book about foundations talks about the measurement problem, it is useless as a book about foundations. The measurement problem is the most important problem in the foundations of quantum mechanics.

Peres is among the best books on interpretational issues ever! A clear no-nonsense approach, which seems to me at least very close to the minimal interpretation.

But you don't see the merit of orthodox QM either :PIn the article I defined orthodox QM as instrumental QM a la Peres (which does not involve collapse), and I think that @vanhees71 is OK with it.

No, orthodox QM includes the collapse, which is only making trouble without any other merit either. That's why I'm a minimal interpreter with great sympathies for it's simplified version called "shutup-and-calculate interpretation".

Well, I don't see any merit of Bohmian mechanics to begin with. It just assumes unobservable "trajectories" in non-relativistic QT and otherwise predicts the same thing as QT in its minimal quantization. So this argument doesn't convince me too much. I've to check out what Horava gravity might be.But you don't see the merit of orthodox QM either :P

Well, I don't see any merit of Bohmian mechanics to begin with.Of course. The insight article is about how

Istopped worrying and learned to love orthodox QM. It does not say that everyone should follow the same path. When all think alike, then nobody thinks much.Well, I don't see any merit of Bohmian mechanics to begin with. It just assumes unobservable "trajectories" in non-relativistic QT and otherwise predicts the same thing as QT in its minimal quantization. So this argument doesn't convince me too much. I've to check out what Horava gravity might be.

There seems to be really a limiting speed, c, and it seems to be universal no matter of which system is studied.It seems, but we don't know if this persists at even smaller distances than available by current experimental technology. The default hypothesis is that it persists, but a hypothesis that it doesn't is also legitimate and Bohmian mechanics is not the only motivation for such a "heretic" hypothesis. See e.g. Horava gravity.

What I find not so convincing about the final conclusion of the article is the fact that obviously nature is not Newtonian but relativistic, as is shown also in the domain of physics, where classical approximations are valid. There seems to be really a limiting speed, ##c##, and it seems to be universal no matter of which system is studied.

Of course, you have also in non-relativstic (condensed-matter) physics quasiparticles with relativistic dispersion relations and a lot of quite "exotic" features (Weyl fermions, magnetic monopoles, anyons ans what not has been discovered in the sense of quasiparticles but seem not to exist on a fundamental level), but these are only valid in the quasiparticle approximation and in fact describe collective low-energy excitations of the matter as a whole. At some point the non-relativistic approximation breaks down, and you have to use relativistic models.

Isn't that strings in a nutshell?No. For instance, a string can split into two strings.

That the whole universe contains only one particle? That's excluded.Isn't that strings in a nutshell?

Sorry, what I meant was have you excluded any of these possibilities for the more fundamental particle(s) ?

Multiple particles of multiple types?

Multiple particles of one type?

One particle each of multiple types?

One particle only of only one type?I still don't understand what do you mean by "one particle". That the whole universe contains only one particle? That's excluded.

Concerning the number of particle types, I cannot exclude any possibility.

I think a variant of (2) is that string theory is correct only as an effective theory, but when string theory fails, there is no more spacetime, so ##l_{rm nr}## does not exist, eg. gauge/gravity where the gauge theory is emergent from non-relativistic QM.Sure, 2) has an infinite number of versions, including this one.

Sorry, what I meant was have you excluded any of these possibilities for the more fundamental particle(s) ?

Multiple particles of multiple types?

Multiple particles of one type?

One particle each of multiple types?

One particle only of only one type?

There are 3 possibilities:

1) String theory is wrong. In this case the hypothetical fundamental distance ##l_{rm nr}## at which Nature starts to look non-relativistic is not related to the string scale ##l_{rm string}##.

2) String theory is correct, but only as an effective theory. In this case ##l_{rm nr}ll l_{rm string}##.

3) String theory is correct as the fundamental theory of everything. In this case my theory is wrong and there is no such thing as ##l_{rm nr}##.I think a variant of (2) is that string theory is correct only as an effective theory, but when string theory fails, there is no more spacetime, so ##l_{rm nr}## does not exist, eg. gauge/gravity where the gauge theory is emergent from non-relativistic QM.

It is interesting that possibility of relativity principle not being fundamental is generally not considered.It is considered (but perhaps not enough). One rather famous work in that direction is Horava gravity

https://inspirehep.net/search?p=find+eprint+0901.3775

cited about 1500 times. Indeed, this work also significantly influenced may way of thinking, as can be seen in

https://inspirehep.net/search?p=find+eprint+0904.3412

"What does have Bohmian trajectories are some more fundamental particles…"

Above, at, or below string level?There are 3 possibilities:

1) String theory is wrong. In this case the hypothetical fundamental distance ##l_{rm nr}## at which Nature starts to look non-relativistic is not related to the string scale ##l_{rm string}##.

2) String theory is correct, but only as an effective theory. In this case ##l_{rm nr}ll l_{rm string}##.

3) String theory is correct as the fundamental theory of everything. In this case my theory is wrong and there is no such thing as ##l_{rm nr}##.

Multiples of multiple types?

Multiples of one type?

One each of multiple types?

One only of only one type? It would have to really get around, but how elegant.Sorry, I don't understand the questions. Any hint?

You talk of

non-relativistic particles, but I'm not sure how such things could exist, since we know spacetime, even locally, is not Galilean. Wouldn't the fundamental theory, in your assumed view, have torelativisticQM rather than non-relativistic? To put it a different way, how could we have particles existing in the world which respect Galilean spacetime, but not Minkowskian spacetime, when the latter is the one we know to actually be the case (or at least to be closer to the truth than the former)?It is interesting that possibility of relativity principle not being fundamental is generally not considered.Even if this mechanism is not exactly how Nature really works, the simple fact that such a mechanism is possible is sufficient to stop worrying and start to love instrumental QM as a useful tool that somehow emerges from a more fundamental mechanism, even if all the details of this mechanism are not (yet) known.Well said.

"What does have Bohmian trajectories are some more fundamental particles…"

Above, at, or below string level?

Multiples of multiple types?

Multiples of one type?

One each of multiple types?

One only of only one type? It would have to really get around, but how elegant.

since we know spacetime, even locally, is not GalileanWhat we know is that spacetime does not

appearGalilean at "large" distances (e.g. distances much larger than the Planck distance). How does it appear at very small distances, we don't know that.Are you worried about the chiral fermion problem, which seems to me the remaining problem in realizing the standard model using non-relativistic QM?I consider it to be a technical problem, with some proposed solutions already existing. So I do not worry too much.

Are you worried about the chiral fermion problem, which seems to me the remaining problem in realizing the standard model using non-relativistic QM?

Thanks for the stimulating read. I too have come to the conclusion in recent years that anyone serious about the Foundations of Physics must thoroughly acquaint themselves with Bohmian Mechanics; not necessarily because it will turn out to be correct, but because it provides the most coherent and well fleshed-out alternative to the usual bare-bones view of QM.

I find your idea of taking QM as fundamental, while QFT as emergent, particularly interesting, except for one thing. You talk of

non-relativistic particles, but I'm not sure how such things could exist, since we know spacetime, even locally, is not Galilean. Wouldn't the fundamental theory, in your assumed view, have torelativisticQM rather than non-relativistic? To put it a different way, how could we have particles existing in the world which respect Galilean spacetime, but not Minkowskian spacetime, when the latter is the one we know to actually be the case (or at least to be closer to the truth than the former)?Nice article. Thanks!