The best place to find the answer to this question that I know of it David Z. Albert's excellent book, "Quantum Mechanics and Experience." But the short answer to your question is that Bohmian mechanics has two problems:
1. In order to account for the outcome of Bell-type experiments on entangled particles it has to assign a temporal ordering to space-like separated events. The technical term for this is that you have to choose a "preferred foliation of space-time". There has to be a preferred reference frame. But you can never actually know what the preferred reference frame actually is.
2. Yes, particles "have positions", but you can never actually know what those position are (which is why I put "have positions" in scare quotes). This is where all the quantum randomness hides in Bohmian mechanics. It's all "pre-computed" in the infinite precision of a particle's position, but that position is necessarily hidden from observation. I call this an IPU, an Invisible Pink Unicorn. It's exactly the same thing as universe-weights in MWI -- a set of numbers that are part of the theory but rendered immune from observation not by practical limitations on technology, but by the theory itself.
This is the fundamental problem with all attempts to make quantum mechanics look deterministic. The simple fact of the matter is that it's not deterministic, so any attempt to make it look deterministic that makes the same predictions as QM has to hide the randomness somewhere. Bohm hides it in particle positions, and MWI hides it in universe weights. But it doesn't matter what you call the place in the theory where you've hidden the randomness. What matters is that there is a place in the theory where you've hidden the randomness, where it must forever remain hidden from the prying eyes of experiment. So the claims that both Bohm and MWI make of being deterministic are misleading at best.
>but that position is necessarily hidden from observation. I call this an IPU, an Invisible Pink Unicorn.
But why expect that all state of the universe be open to observation? This seems counter-intuitive to me. It seems far more reasonable that there necessarily are facts about an implementation that no supervening system can determine from within that system. For example, there are facts about a physical computer that no software running on that computer could deduce. So the fact that a QM theory posits state that is in principle off-limits to observation doesn't seem like a reductio, but the expected case.
That's a good point, but remember, this is about rhetoric, not physics. The question is not whether hidden state exists (it clearly does) but what kind of story you want to tell about it. If you find it enlightening to think about hidden state as position, and you don't mind accepting all of the difficulties that entails (like having to choose a preferred foliation), then by all means go for it. But that is very different from saying that this story is actually true. The only reason to prefer Bohm over a similar story that ascribes the randomness to a literal invisible pink unicorn making decisions about experimental outcomes is aesthetics.
What EPR and Bell's arguments showed is that if you have definite results of experiments at the space-time locations where/when we think the results happened, then there has to be something non-local going on and a foliation is the simplest way to orchestrate that. So either give up a certain kind of definiteness (MW) or introduce a foliation (BM). A foliation is somewhat unpleasant, but there are ways to tease them out of the existing structures of relativity + wave function [0].
As for determinism, that is not the main point for many proponents of BM. Rather, it was about having a clear theory. Let's start at the beginning. We decide to have a theory about particles. What does that mean? Well, there is some stuff with positions and those positions change in time. And that's what BM gives. It explains, immediately, why a wave function is on a configuration space of particles. Having this leads to a variety of important notions. For example, having a position leads to clarity on identical particles, namely, use a space without labels on the particles and the wave functions just work out[1] (disclaimer: I am an author on that one and did part of my PhD thesis on that [4]; my thesis also derives spin as well as the Dirac equation from a Bohmian perspective).
Another example is QFT and divergences. From a Bohmian perspective, QFT is best thought of as about wave functions over a configuration space consisting of different disjoint sectors involving different number of particles. To do this, there is a random jump process created (not deterministic!). Thinking about wave functions that work with that, one is led to wave functions where the probability moves from one sector to another appropriately based on this jumping. And that solves, at least in some simple cases, the UV divergence of QFT.[2]
The randomness of BM is actually quite interesting. It is all about the Quantum Equilibrium Hypothesis, something which is justified in similar ways to thermodynamics kinds of arguments. In fact, it makes it clear that what is interesting is not why we can't know some things, but why we can know stuff at all. [3]
Also, in case you have not seen it, you might want to take a look at a version of MW by some of the Bohmians behind the papers.[4] As with most things, there is a lot of clarity in their perspective.
Finally, as for why BM is not more popular, well, let's just say it is rather hard to stay in academia as a Bohmian. I barely tried, largely because academia is unpleasant for a variety of other reasons, but it simply is very hard to get hired when working on unfashionable material. Grants and all that. This is on top of the problem of getting people to change some fundamentally long held beliefs. This goes hand in hand with the fact that standard QM is the thermodynamics version of BM and so QM agrees with BM empirically to the extent that QM makes predictions. That is to say, BM provides the rigorous foundation for the collapse rules.
I would say that's exactly where Bohm runs off the rails. The fact of the matter is that quantum systems are not particles. They are waves [1]. They can sometimes bunch up into very small spaces and behave to a very good approximation as if they were particles, but they aren't.
If you insist that your theory talk about particles, then Bohm is a not-entirely-unreasonable place to end up. But that's kind of like saying that if you insist that your theory tell you how many angels can dance on the head of a pin that 42 is a not-entirely-unreasonable answer.
Thanks for the references, those look interesting.
I read the article you cited. While enjoyable, it does not make its case for me. It very much feels like presuming the wrong ideas of what a particle theory is.
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First, double slit. Points on the screen, wave pattern built up. The natural conclusion is a wave guiding a particle. That's what BM gives. BM does not deny the existence of the wave function. Rather, it gives it a reason for being. The article talks about viewing the wave function collapse as a ballon hitting a needle and popping. But it doesn't really explain why a world full of waves should have anything point-like. It certainly doesn't come from the dynamics of the Schrodinger equation. It just is a statement that the wave should localize when it encounters something already localized. Now, this being the wave function, it is not multiple waves on real space, but rather waves on R^3N space where N is the number of particles which includes those of the detecting screen. But what particles, right? An electron does not have a wave function. There is only one universal wave function. This is not N waves rolling around in 3-space. It is one wave in 3N space and its relation directly to our experience in 3-space is rather obscure.
This does not mean you can't have waves. But I think your angel analogy applies to saying "everything is a wave" and MW is not an unreasonable place to end up in.
The article also says that particles are not logically consistent with the 2-slit experiment. That is simply false as BM demonstrates. That theory has been mathematically proven to exist and agree with the standard QM predictions. It works. The double slit is explained as particle AND wave, two separate entities.
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Another piece of the article was about a confined wave that instantly expands. It seems to get at the heart of the misconception. There is no notion in BM of having to confine waves to make them particle like. Rather, BM allows waves to expand as they do. They can be their own thing, doing whatever they like. The particle aspect is handled by the particles which can do what the wave tells them to do. In the Dirac version of BM, the velocity can never be greater than the speed of light for the particle, basically by construction. To the extent that a narrowly confined wave function leads to problems, this would say, those would not be the relevant wave functions. One can always replace such a sharp thing with a close enough in L2 approximation to not have that kind of sharp behavior. This gets into the domain of the Hamiltonian which can have some pretty important aspects to the evolution.
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The vacuum and movement. This is just me spitballing, but in the ground state, according to BM, particles will not move. They just sit there. So it is quite possible for the vacuum to look empty (nothing moving), but there is plenty of stuff out there in terms of particles. Then when someone moves, they see the particles moving. Not sure if this is reasonable or not, but it is my thoughts on how one can have a vacuum with "no particle" and then have particles present with a relative motion.
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The final part I will comment on is that of QFT. This would presumably be the strongest of the arguments. But here, the field of operators is fundamentally different than the wave function. As presented in the article, we have a field of operators based on EM. They operate on wave functions over Fock space, which is the union of R^3N spaces (removing collisions and replacing that with boundary conditions). Is the claim that the operator field's expectation values are the reality of our experience? I am guessing the claim is that if I want to verify my chair's placement then I am supposed to compute the expectation values of those operators at the space-time point and out pops a chair?
The Bohmian version of this is that we use the wave function, evolving according to a Hamiltonian which may contain an operator valued-field, to guide the particles, including controlling the creation and annihilation of the particles. We can then do an analysis of the theory and come up with predictions, generally in the form of operators as observables. These are deduced, not postulated. A chair is where it is because the chair's particles are where they are. It is a conceptually simple process to map my experience to what the theory is talking about. Having a simple map from my experience to some state of something in the theory is a really nice feature. It is not crucial, but verifiability is greatly helped by this.
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A very important part of BM is that operators as observables is not postulated, but deduced. This has major advantages in that it is practically trivial to write down a Bohmian theory on a manifold. The standard stuff has problems, such as what the momentum operator becomes. In BM, you write down the theory and then one can analyze to see what would emerge, if anything, to take the place of that observable.
An application of this is creating a quantum theory on shape space, namely, the space of relative configurations that Julian Barbour likes to work with. It is a very natural space to consider and Bohmian mecahnics can accommodate it easily: https://arxiv.org/pdf/1808.06844.pdf
> The natural conclusion is a wave guiding a particle.
Indeed. But the natural conclusion can be wrong. Case in point: hold an object in your hand and let it go. It falls. The natural conclusion is that there was a force pulling it down. But this is not actually true. (I gather I don't have to explain this to you. AFAICT, you know physics better than I do.)
In fact, if you think about it, "points on the screen" is the only reason we have to believe in particles, which is to say, in spatially-localized quanta. But this is not probative. It only shows that the spatial localization is of the same order as the size of an atom. But we already know that atoms aren't particles, so this is manifestly not slam-dunk evidence that whatever is tickling those atoms is a particle, nor than an atom's constituent parts are particles.
> So it is quite possible for the vacuum to look empty (nothing moving), but there is plenty of stuff out there in terms of particles.
That doesn't seem reasonable to me. Particles exert forces on each other via gravity and electromagentism. I don't see how you're going to get a stable static vacuum configuration out of that without special pleading.
> Is the claim that the operator field's expectation values are the reality of our experience? I am guessing the claim is that if I want to verify my chair's placement then I am supposed to compute the expectation values of those operators at the space-time point and out pops a chair?
That's a bit of a caricature, but yes, if you want a completely accurate answer, that is what you have to do. Just as if you want a completely accurate answer about what happens when you drop an apple you have to solve Einstein's field equations. F=Gm1m2/r^2 is a damned good approximation, but it's deeply wrong about the physics.
> "points on the screen" is the only reason we have to believe in particles
There are also the cloud chamber paths. But more generally, I would say most people's experiences correspond closer to stuff having well-defined localization which is more in the ballpark of particles than waves. Waves spread.
Also, this is not a matter of what is true, but rather what is plausible. A natural conclusion which works would be a good candidate to continue to pursue. My opposition to the paper cited was simply that it wants to argue that everything is a wave, something which seems to be an assumption not supported by evidence. That reality can be described that way is one thing, and a fine thing if it leads to interesting notions, but to say it must be a certain way is a completely different kind of claim.
> That doesn't seem reasonable to me. Particles exert forces on each other via gravity and electromagentism. I don't see how you're going to get a stable static vacuum configuration out of that without special pleading.
Particles in BM do not exert forces on each other. The wave function moves the particles about directly by specifying the velocity, not the acceleration. The forces are all in the wave function evolution (gravity is a bit of a mystery, but what else is new). Keep in mind there is a single wave function that represents the universe. It has a complicated dynamics which is where the forces are at work.
Maybe the short paper Are All Particles Identical [0] might help. It describes a version of BM in which all particles are identical and electron, quark, etc., are different states of a single particle type with the mass being incorporated into the wave function itself. Particles in that theory really are just points with nothing else intrinsic about them.
So the typical vacuum state might be just a small part of the story with a non-interacting sector. I don't know, but it certainly does not seem to rule out particles to me as being impossible.
> Just as if you want a completely accurate answer about what happens when you drop an apple you have to solve Einstein's field equations.
Yes, but if you present me with the solved system, I understand immediately what it is describing: a path through space-time of the apple. In a solved version is easy to see the correspondence.
This is not true of quantum wave stuff. It is true of BM. Relativity might mess with our intuition and be difficult to compute, but it is easy to understand how the elements correspond to our experience. That's the crucial difference.
Now, there is no reason to believe that the fundamental theory has to have that property. It might not. But it is extremely important than to be very clear about how the elements of the theory, the stuff it cares about saying what it state is, does correspond to our experience.
> Particles in BM do not exert forces on each other.
Right. That's part of the problem IMHO. Particles in BM don't really do anything except get pushed around by the wave function. So they don't really correspond to what most people intuitively think of when they think of particles: electrons and protons (and neutrons), which combine not only a spatial location but also mass and electric charge into a single unified package. BM particles only have the spatial location part.
> it is easy to understand how the elements correspond to our experience
I think it's not so hard to see how QM corresponds to our experience if you look at it the right way. Not quite as easy as relativity, but not nearly as hard as it's commonly made out to be.
Note that our experience is at odds with "reality" long before you get to QM. Even in a purely classical model of an atom, it's mostly empty space, and what we perceive as "solid" objects are really just electrons in outer shells trying to push each other out of the way.
1. In order to account for the outcome of Bell-type experiments on entangled particles it has to assign a temporal ordering to space-like separated events. The technical term for this is that you have to choose a "preferred foliation of space-time". There has to be a preferred reference frame. But you can never actually know what the preferred reference frame actually is.
2. Yes, particles "have positions", but you can never actually know what those position are (which is why I put "have positions" in scare quotes). This is where all the quantum randomness hides in Bohmian mechanics. It's all "pre-computed" in the infinite precision of a particle's position, but that position is necessarily hidden from observation. I call this an IPU, an Invisible Pink Unicorn. It's exactly the same thing as universe-weights in MWI -- a set of numbers that are part of the theory but rendered immune from observation not by practical limitations on technology, but by the theory itself.
This is the fundamental problem with all attempts to make quantum mechanics look deterministic. The simple fact of the matter is that it's not deterministic, so any attempt to make it look deterministic that makes the same predictions as QM has to hide the randomness somewhere. Bohm hides it in particle positions, and MWI hides it in universe weights. But it doesn't matter what you call the place in the theory where you've hidden the randomness. What matters is that there is a place in the theory where you've hidden the randomness, where it must forever remain hidden from the prying eyes of experiment. So the claims that both Bohm and MWI make of being deterministic are misleading at best.