Problems with Bohmian mechanics

(also called the de Broglie-Bohm interpretation of quantum mechanics)

This is the most popular interpretation of quantum physics in terms of hidden variables, that are the "positions of particles". These hidden variables behave in a "deterministic" way that, in order to fit with the EPR paradox, must admit non-local (instantaneous, faster-than-light) interdependence between these positions throughout the universe, with respect to a supposed absolute time, i.e. simultaneity relation (partition of the universe into space-like 3D slices), that is hidden too.

There are several big problems with this interpretation.

Problem 1 : breaking relativistic invariance

Compatibility troubles with General Relativity

Bohmian mechanics breaks relativistic invariance by requiring the choice of absolute time, relatively to which its laws will be processed. This gap is well-known, but I did not read much about the full measure of how big is this gap. Since, just assuming an initial choice of an absolute frame at the beginning of time, as would fit a description in the framework of Special Relativity, does not suffice. Because the physical space-time does not (approximately) fit Special Relativity but General Relativity.

And in General Relativity, there is no natural way, even once chosen a space-like slice of space-time (that has no reason to possibly be a flat one) as a definition of the "initial time", to determine how space-time will have to be sliced into more "simultaneous" classes of events in the future. If we try the "simplest solution", that is taking the parameter of time defined as the age (the time spent since the Big Bang), so as to define simultaneity as equality of age, this cannot work because it will run into lots of singularities (especially at the centers of planets and stars).

On the other hand, quantum physics itself does not have any fundamental incompatibility with the symmetry principles of General Relativity, as explained by Carlo Rovelli, one of the founders of Loop Quantum Gravity, which is based on the care to fully keep both the founding principles of quantum physics and general relativity.
(They may reply that non-locality and the violation of the Lorentz invariance, is not just a problem with their interpretation, but a general problem with quantum physics, and more precisely of any interpretation that accepts actual randomness and the selection of an actual outcome of measurements, i.e. any interpretation that is not many-worlds).

It only interprets the Schrödinger equation (i.e. non-relativistic quantum mechanics), not Quantum Field Theory

The Stanford encyclopedia of philosophy article about Bohmian mechanics, tells in length what a wonderful interpretation it is of the (non-relativistic) Schrödinger wave equation. As if quantum mechanics and the Schrödinger equation were the same thing. I'm afraid they are not taking the full measure of the fact that the core of the argumentation is out of subject. As they only mention later, in a last section, the real big issue is where this interpretation fails :

The theory of quantum physics that is currently well-established as the proper description of physical reality, and that begs for an interpretation, is NOT the Schrödinger wave equation, but the full quantum theory, that is, Quantum Field Theory. Indeed without this extended framework it is not even possible to account for the possibility for an atom to absorb or emit a photon (while switching between energy levels), an event which occurs actually quite often ! Seriously, what a terrible subset of known physics is this little Schrodinger equation they are so proud of better explaining or visualizing in their way !
And adapting Bohmian mechanics to interpret quantum field theory is far from obvious. As replied to a question: De Broglie- Bohm Quantum Theory.

This article (Jul 2004), admits in the conclusion that "We leave open, however, three considerable gaps: the question of the process associated with the Klein–Gordon operator, the problem of removing cut-offs, and the issue of Lorentz invariance."
A detailed review of the situation can be found in Wallace's article The Quantum Measurement Problem: State of Play, section 7 (Relativistic quantum physics); there is a more recent article supporting Bohmian quantum field theory (2011).
Some works were done trying to fill this gap... a report I stumbled on
And even if a candidate Bohmian Quantum Field Theory is offered, it remains to check that it will avoid the trouble with the treatment of randomness that is explained below.

Problem 2 : the nonsense of deterministic randomness (like in classical deterministic chaos)

Of course the unfalsifiable character of this theory (the ineffectiveness of assuming deterministic causes from hidden variables that cannot be checked) is clearly on the table, in the sense that it is "only an interpretation" without any different prediction (it is the same prediction : pure randomness). However, I will comment here in details how deep I see this problem.

In short : Bohmian mechanics claims to be a deterministic theory, but I see no way in which this supposed quality of "determinism" can make any meaningful sense : even if true it would still just be an empty box that does not provide any effective answer about whether the world is deterministic, probabilistic, or even... divinely guided.
The same remark goes for the classical "deterministic chaos", which many philosophers assume to be a form of determinism (strangely still often referring to it when discussing determinism, though classical mechanics is outdated as a fundamental description of the universe).
Indeed, classical mechanics is essentially of the same kind as Bohmian mechanics, in the sense that their quality of "determinism" is illusory for the same reason, that is explained below.

Why the "determinism" of classical mechanics (as a purely theoretical concept disconnected from this world) is an empty concept

Even a hypothetical universe totally described by some "deterministic" classical physics, can be said to produce absolutely random phenomena too, though leaving an explanatory gap in the nature of this randomness.

Giving a real number between 0 and 1, is essentially the same as giving an infinity of binary digits, that constitute the binary expansion of that number.
The computation of a continuous function of a number, can be made in successive approximations as computations from the unlimited data of its binary digits (taken in finite amount, as many as needed for the required accuracy of the result).
This way, a reasoning about a continuous variable, can be equivalently expressed as if it were about a potential infinity of discrete variables.
The reality assumed by classical mechanics, as well as the hidden variables assumed by Bohmian mechanics, are continuous variables. Thus, they are equivalently expressible as an infinite series of discrete variables (to be progressively explored). 

Consider a physical system whose initial state is described by some quantity x=5.7843.....
After some chaotic processes, it arrives to a final state described by another quantity y that we can measure up to 5 decimals. The problem is that the determination of these 5 first decimals of y out of the exact value of x, must take account of, say, the first 1,000,010 decimals of x, as even a change in the millionth decimal of x may modify the value of y by several units.
In this situation, how can you meaningfully claim that "the first 5 measured decimals of y are not fundamentally random" ?

Indeed, even if a continuous variable is conceived as "well-determined", in practice, it only means that the first few digits are well-determined. For all practical purposes, beyond a certain scale of details, all the next digits down to infinity, have pretty well all the behavior of purely random data.
So, as an excellent physical approximation, we can "really" consider the first decimals of the final y as "absolutely random", in the sense that, if the first thousand decimals of x are [whatever], it will remain an excellent physical approximation to qualify its next thousands of decimals as "absolutely random".

Finally, a classical mechanistic chaotic system is quickly full of "absolute" randomness because the parameters of the initial state contain an infinity of digits of precision that, after the first few ones, necessarily turn out to be "absolutely random" for all practical purposes; and these random digits intervene in macroscopic behavior very quickly.

One might react by assuming that there is a fundamental difference between the "practical" and the "essential" versions of randomness. Indeed there are cases when this expression "for all practical purposes" can be used to refer to subjective human criteria that are relative, so that these "practical properties" can be dismissed as irrelevant when discussing what is essential. But there are other cases such as the one discussed here, where this distinction between the "essential" and the "emergent" or "practical" properties is effectively blurred - not just hidden but really broken. Such phenomena where essentialism is wrong, as the difference between what is "essential" and what is "practical", actually vanishes, can be found in other concepts, such as

A risk of trouble with Bohmian Quantum Field theories: the divergence of behavior in finite time

This problem with classical "deterministic" chaos might even be worsened by the possibility of a fractal process where the first decimal of a quantity depends on the 2nd decimal of its value 1 second before, which depends on the 3rd decimal 0.5 second before itself, which depends on the 4th decimal of its value 0.3 second before that, and so on, so that finally the number of decimals that it depends on, reaches infinity before a finite time interval.
And if I don't mistake, this is how things actually happen in fluids mechanics in the macroscopic formalization by partial differential equations (ignoring the behavior of individual molecules).

Now for Bohmian mechanics: even if such a divergence does not occur for the Schrödinger equation, how can we seriously expect to stay safe from such a divergence in any candidate Bohmian interpretation of quantum field theory, including compatibility with renormalization (that is also a sort of fractal process) ?
In addition to this question of the risk of divergence coming from the infinitely small with fractal structures of Feynman diagrams, comes the risk of divergence coming from the infinitely big: from the influence of the rest of the Universe, since according to Bohmian mechanics, the evolution of the "position" of a particle cannot be dissociated with what happens in the whole Universe - a form of "determinism" which does not start to make sense before you completely specify a cosmological model (is the Universe infinite, spherical, or something else ?).
A reference on the topic : Hall, M. J. W., Incompleteness of trajectorybased interpretations of quantum mechanics, J. Phys. A Math. Gen. 37 (2004) 9549 and quant-ph/0406054"

How quantum mechanics resolves the nonsense of classical deterministic randomness - a lesson of meaningfulness that Bohmian mechanics tries to reject, but why ?

One "scientific skeptic" from AFIS having no clue about physics pretended to incarnate modern scientific rationality by proclaiming this very stupid argument: "For all practical purposes, quantum effects can be neglected in macroscopic systems, so the world is classical, thus deterministic".
Yes, but classical (macroscopic) chaotic systems have the butterfly effect (sensitivity to very small differences of initial conditions). You can describe the butterfly effect as consequence of a classical physics which "is deterministic"; however, giving good approximate descriptions of general chaotic behaviors by mathematical models is one thing, but the issue of the "reality" of an underlying determinism in our universe, is another.
The physical fact in this universe, as shown by classical physics itself, is that the visible random results of such phenomena depend on smaller and smaller details of previous states when you trace back the causes to earlier and earlier states of the system. Finally, these details come from microscopic fluctuations, which are subject to quantum indeterminacy. Classical determinism is only an intermediate medium of communication across scales of processes, that displays macroscopic random effects coming from microscopic fluctuations of some earlier time, that come in fact from quantum randomness. No matter the possibility to theoretically deduce the properties of statistical mechanics from deterministic assumptions, the actual physical reality of our universe is that the macroscopic randomness displayed by classical deterministic chaos, as well as the particular thermic randomness with probabilities described by statistical mechanics (with its specific probability law of Boltzmann distribution), has a quantum origin, so that its randomness (and its obedience to the Boltzmann distribution in the thermic case), is exactly as pure and physically "absolute" as quantum randomness is. Indeed a careful examination of the macroscopic consequences of quantum mechanics (with its emergent process of entropy creation that goes on quite quickly) shows that the actually exact (not just the practically knowable or computable) probability law deduced from quantum theory on any possible measurement, quickly converges to the Boltzmann distribution at the given temperature.

Indeed : how can you even dream things to go otherwise in a continuous world ? How can you ever dream to conceive a mathematically well-defined causality law that describes an effect as depending on an infinity of details (an infinite amount of information) that the system contained at an earlier time ? How can you dream such a mathematical law to be an effective causality law at all, either in reality or as a meaningful mathematical prediction tool ?

The answer of quantum mechanics, to avoid the nonsense of a concept of a causality from an infinity of causes (such as the infinity of digits of continuous variables), is this one : there is an absolute limit to the amount of information that is physically present in a given local system, that can causally (physically) influence its future behavior. If you want to measure the details of the system beyond this amount of information that it physically contains, all you will get is newly created, purely random data that did not exist in the initial state of the system.
Still, while the amount of information in a quantum system is limited (finite), it is not a discrete pack of information but a continuous one (that fits with the continuous symmetries of geometry). This paradoxical combination is accomplished by the fact that this continuity is only a continuity in the values of probabilities of results when the system is measured, not a continuity of any "physically present quantity" that can be measured with unlimited accuracy. Thus a rejection of physical realism, as the continuity of the transition between the possibilities for 2 states to be identical or distinct, means that there is no physical reality of which state a system exactly is in. (As I once commented, a third option would be to break the continuous symmetries and opt for a digital universe, but this would leave us with no sense to make of the effective fundamental role of continuous symmetries in the formulation of theoretical physics)

Then, Bohmian mechanics reinterprets quantum randomness, as an unverifiable come-back of the previous concept of randomness, that is, as a classical deterministic chaos. Now, we come to a "deterministic" randomness that is both pure (with exact probabilities and with no means of prediction from any prior measurement) and with purely speculative and unobservable origin.
D. Wallace commented on the trouble with this in the 6.6 of his article ; I will comment it in my way.

The oddity of an intractable deterministic randomness : did you ever see it anywhere else ?

Do you know any other "random" process that once seemed so well random that a specific probability law was formulated, that seemed to be well confirmed by observations but without explanations, until deterministic causes were found that made the exact behavior effectively deterministic, i.e. predictable (or at least giving much better prediction tools than the former probability law) ? I cannot think of any.
Of course there are some obvious not-really-examples :

Anything more striking than this ?

Illustrating the problem by a tale

One day I saw an advertising panel for a new product, announced in this way :

The Perfect Random Generator
that Works in a
Completely Deterministic Manner
produced by BomBox, Inc.

Intrigued by such an amazing claim as the claim that perfectly random data can be produced deterministically, I went to a BomBox shop and asked the seller to explain about this new product.
He proudly explained to me why it was so valuable to have made this technological breakthrough, to guarantee that the numbers given by this random generator were indeed produced in a deterministic manner: the reason was, if the process generating these numbers was not deterministic, then we could not be exactly sure where this generated data came from, so that the guarantee of its perfectly unbiased random character would remain doubtful. The deterministic character of the process ensured that no uncontrolled bias could happen, and thus that the result indeed had the exact desired randomness property.
But I wanted to understand more, how such a seemingly paradoxical combination of qualities could indeed be implemented in a device. He refused to answer, as this was an industrial secret that could not be disclosed. In the face of my skepticism, he offered me the following guarantee : I would pay a regular monthly price to use it ; ifever I discovered any flaw in the working of this box, that it didn't have the advertised qualities, he would then soon come and fix it for free; or pay me back all what I paid from the start if he couldn't.
I accepted the deal and took the box with me. At home I started to test it, using a program designed to test randomness and look for patterns in series of digits. I discovered that the output indeed behaved randomly when I was there but started displaying patterns after some time I was absent. I noticed that the box had a little camera that took data from the room around, to be mixed with its internal computations so as to renew the randomness of its behavior. Indeed once this camera was completely hidden, the defects of its randomness came back.
I went back to the shop and reported that flaw. The seller offered to change the box, and as a compensation, he also offered me a solar panel to put on my roof to provide the needed electricity for the working of this box and even more uses if I need.

I accepted the deal, and the new box indeed appeared to offer a clearer and more systematic randomness than the previous one.
However I was still puzzled and undertook to examine the new system in more details. It turn out that the solar panel was hiding a little microphone recording the noise from the street and sending it to the BomBox as a means to reshuffle the internal data of its randomness computations.
Again I came back to the shop and complained that such a method was still an imperfect method of randomness generation, because the output from such a process could not be completely random as this box did not really produce its own randomness but only indirectly transmitted (after some reshuffling) the imperfect randomness of outside events that ultimately determined it, so that the detailed features of these events might still be a source of bias for the resulting so-called randomness.
Again he understood, and he offered to replace again the last BomBox with a new one that would also have the function of internet access.
It worked quite well, while I had disabled the flow of data from the solar panel, but I was still wondering how these random numbers could really be generated, so I decided to check the details of Internet connections it was making. I discovered that, while I was not supposed to be using the Internet connection, the BomBox was still making connections to the servers of the BomBox company, which answered in some visibly random manner. I understood that, once again, the BomBox was not really producing these random numbers from itself along, but only transmitting and reshuffling those provided by the Web servers of the BomBox company.
I went again to ask for explanations about this. The seller explained that this procedure did not jeopardize the quality of this randomness because the Web servers of the BomBox company were themselves perfectly reliable in producing random numbers in a deterministic manner, thanks to the full implementation of the real secret technology of the BomBox company, which the BomBox themselves did not contain, for fear that it might let its full secret technology to be leaked to competitors.

I replied that I still needed to check how the BomBox server was working, to verify both the deterministic and unbiased nature of its random behavior. I was invited to their servers room and could inspect the hardware of their servers. They indeed all used standard hardware known to behave deterministically. Still it wasn't clear if these servers were producing these random output all by their own or were only reshuffling any random data from somewhere else; and in the latter case I needed to check that other source too. They promised I could check all this in the next week.
The next week, I went back and noticed that these servers themselves received random data from another machine in another room, which I inspected too, and that itself was receiving random data from still another machine, which was also receiving data from somewhere else. I still wasn't satisfied, as I said I wanted to continue my inspection further, without any limit. But I had to wait one more week before continuing the inspections.
Meanwhile, they undertook to install a continuous assembly chain of electronic devices, each one connected by a wire to the next one being produced. The last machine I inspected last time was connected to the first produced device that was coming from a treadmill, which was connected to the next one behind, itself connected to a wire further in the treadmill whose end I could not see. Later as they approached, the last wire appeared connected to a next device, and, as they all approached, this all kept being repeated over and over again with more and more such devices each connected to the next one coming from the treadmill.

They told me : here you are ! You wanted the right to keep inspecting the devices producing the random data without limit. Now you see where the data comes from: it comes from a device, itself receiving its data from the next device, and so on. We are ready to let you inspect all these devices one after the other without any limit, as they arrive here in this chain from our production factory.
That sounded great, but I was still wondering : how can the last produced device in this chain provide its own random numbers, before receiving any further random data from the next device that will be added later to this chain ? I wanted to inspect the inside of the factory, to check how they were doing. But they refused to do so.

Instead, they gave up. They decided to cancel all transactions and give me back my previous payments.

But not only that, they were visibly fearful that other people might also inquire too much and eventually discover a loophole in their technology, and would come to complain in the same way. Indeed, as a last resort to prevent any such questions on the reliability of their technology from popping up again in the near future, they issued this bold job opening 

 Superman Wanted
for Super Mission
Contact BomBox, Inc

Then Superman came for this job, and was assigned the following task. He had to study the whole production chain of this series of devices each connected to the next one so as to generate a flow of random numbers towards the first one. Then his task would be to operate this production chain at a divergently increasing speed: he would produce the first copy of the device in one hour, the next one in half an hour, the third one in 15 minutes and so on, so as to finally get an infinity of them to be produced until the end of the second hour. Of course there was not enough place to collect that infinity of produced devices in this factory, but Superman would be able to complete his mission in outer space.

He accepted this mission, and started this production inside this factory until the last second of the second hour. At the last second, he completed his mission while skyrocketing up to the end of the Universe, leaving that seemingly infinite chain of devices hanging from the sky behind him.
Millions of people were amazed at that spectacular operation.
Then, as an effect of that demonstration of how an endless generation of perfectly random digits could indeed purely come out from that (infinite) chain of devices all behaving in a completely deterministic manner (without help from any other input), the profits of the BomBox Company started skyrocketing too. But I concluded to forget myself about this random generation service from then on, letting other people believe in this method if they liked.

Ten years later, I happened to see in the news that the BomBox Company had gone bankrupt. Intrigued by this news, I searched for further information, to understand how such a pitiful end could happen to this powerful company after the spectacular success it previously had. Here is what happened.

After Superman completed his mission, rumors started circulating on where he might have finally ended up at the very last moment, when reaching the end of the Universe. Some people simply assumed that the Universe was actually infinite, so that he could really complete the production of this chain of devices to an infinite length, while some other people speculated that, instead of this, he finally reached a border of the Universe very far away and met God there.
Based on the latter idea, a new cult emerged, claiming that, by performing some sorts of ceremonies, God might respond by carefully designing the data He would send to the very last link of this chain of devices, the one which was under His control, and this way finally influencing the supposedly random data of some BomBoxes around the world so as to serve some specified purposes.
Some time later, this cult claimed to have reached some success in their activities, pointing out, for example, that some of their members had won huge profits in lottery games. Though it was not exactly clear, after detailed examination, whether all these winners already belonged to that cult before their gain, or some of them were only enrolled there after this to get some fame (and also to benefit the cult leader's offer to let them meet a lot of female members of this cult) by pretending to have been a member before, the rumor could not be stopped : a wind of panic started blowing among BomBox users, afraid that, after all, the data generated by their BomBox might not be as reliably deterministic and unbiased as they were told, and decided to give it back and not use it any longer.

Problem 3 : Is it really worth saving Physical Reality at the expense of real physics ?

In short : the Bohmian picture does not fit with the proper, simple understanding of QM (especially the spin) and its link to classical physics.
Reference :
Guest post on Bohmian Mechanics, by Reinhard F. Werner (from which I copied the above title), with a long discussion.
Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems, Matzkin, A. and Nurock, V. (2007)
Bohmian mechanics, a ludicrous caricature of Nature by Luboš Motl

Metaphysically, a similarity with Last Thursdayism can be found. More precisely, the idea that the Universe can be suddenly destroyed and re-created... with a difference and no way to know that it was different from what the given memories suggest. Here is how : according to Bohmian mechanics, when 2 wavelets in a wavefunction meet, the "particle" can switch from a wavelet to the other. This may be technically not a likely risk to re-write memories since one can argue that memories are more likely stored as positions of particles rather than momenta, but... what if we imagine artificial intelligence systems with bits of memories temporarily stored as momenta ?
This switch does not leave any trace because After a little bit of analysis, if I deduce well, the situation turns out to be much more terrible than it might have seemed at first glance. Namely, let us consider a very ordinary kind of system: a gas in thermal equilibrium in a box. Whatever the initial state could exactly be, taking the ordinary phenomenon of stabilization of physical states of gases towards thermal equilibrium, then looking at the interpretation of this by Bohmian mechanics, it turns out that the wavefunction keeps continously meeting parts of itself with different momenta at the same positions, so that the stop-and-bounce of the hidden variable from a wavelet to another will keep happening all the time, thus letting the Bohmian position of each gas molecule follow a Brownian motion like molecules of gas but with much shorter elementary moves than the mean free path of the classical description of gases, thus almost standing still. If I deduce well (to be confirmed), the effective mean free path of the Bohmian motion even approaches zero, therefore making the positions of molecules standing still, as the number of gas molecules in the box increases.

Related remarks :

Problem 4 : Under-determinations of the theory

In short : there is not one Bohmian mechanics, but several possible versions, and no way to choose between them, except as a matter or taste.
See in D. Wallace's report "The Quantum Measurement Problem: State of Play", section 6.5 (p. 60)

Both last problems are also addressed in this preprint : The Bohmian interpretation of quantum mechanics : a pitfall for realism, Matzkin, A. and Nvrock, V (2004)

Problem 5 : a many-worlds interpretation in disguise - a terrible definition of "existence"

In the Artificial Intelligence theory of consciousness, the condition for an intelligent being to "really exist" as a conscious being, is the condition of "being effectively computed by physical processes". In Bohmian Mechanics, the introduction of a pointer to select which world is supposed to "exist", while other worlds remain "non-existing", does not change the fact that the continuing evolution of the wavefunction without collapse, still constitutes a real physical computation of the alternative worlds with all brains they may contain, and therefore, a way of still giving "real existence" to the minds they contain.

We can further expand this argument as follows :

How could a melody exist, not just as a succession of sounds but indeed as a melody, without somebody to hear it ?
In the same way, is the famous "hard problem of consciousness" : how can a thought exist, not just as a computation but as actually feeling something, in the absence of a non-physical soul inside the brain to actually feel what the brain is computing ?

By itself, the physical presence of a brain making some computations, is nothing else than a mathematical pointer that is "physically given" to that specific computation, that gives it the quality of being "physically computed" as opposed to other possible computations. But other possible computations, which do not receive this physical pointer, still mathematically exist, don't they ? How does the event of "physically" putting a pointer on a specific mathematical computation, give this computation a quality of "existing" more than any other possible computation ? You can arbitrarily decide to take this pointer as a definition of "conscious existence" for the whole computation (for this computation by a physically existing brain to constitute a mind), assuming it makes sense to speak about the "physical existence of a global computation" that is the event of having a long series elementary computations happening "together", while every elementary step of this computation is repeated lots of times here or there (but "not together") in the physical world.
But if this pointer is the definition of what "existence" means, then how can this name of "existence" still also mean what it was supposed to mean ?

In the same way, Bohmian mechanics introduces a assumption of presence of the arbitrary data of a mathematical pointer, that is, the hidden variables, to point to a specific world inside the many-worlds landscape. And then claims : this pointer is the definition of "physical existence" for a specific world inside the many-worlds landscape. But, if all what we have is an arbitrary mathematical pointer to a specific mathematical structure (world) inside a mathematical landscape of possible such structures (the many-worlds), then how can this pointer constitute the definition of "existence" for this specific world ? Because, the physical law governing this specific world (the formula of evolution of the hidden variables) is expressed as depending on the wavefunction, which is the many-worlds landscape, and thus requires this many-worlds landscape to already exist.

Reference : Solving the measurement problem: de Broglie-Bohm loses out to Everett

Synthesis of all the above : the Universe looks like a conspiracy

By which metaphysical accident could the laws of Nature happen to take, as Bohmian mechanics tells, the exact shape of that sort of incredible conspiracy, endorsing in a so exact manner some very specific effective properties that are a "miraculous" way of absolutely hiding some radically different kinds of underlying ontological causes ?

Listing these extraordinary discrepancies of properties between effective and underlying behaviors in the same order they were listed above as "problems":
  1. The world everywhere perfectly obeys relativistic invariance in all its many effective processes : no possible experiment can ever detect any fault in this invariance (measuring "which is the right frame") ; this invariance turns out to be one of the main pillars of the understanding of all physics, from gravitation to particle physics -- while no such invariance exists in the deep causes of all this.
  2. Despite the fundamental necessity for the Universe to be deterministic, there precisely appears one clearly best predictive theory (ordinary Quantum Mechanics) expressed in the form of a very elegant and convenient mathematical structure of probability law (better than that of underlying causes), that cannot be turned around by any means (the source of randomness is absolutely hidden from any possible investigation).
  3. The effectively relevant concepts to conveniently understand practical phenomena (the diverse observables of quantum physics and how concepts of classical physics come as their approximations) look very different from the shape of their real causes ("trajectories"....).
  4. Specifications of the exact structure of the deep causality laws cannot be investigated by experiments.
  5. The only thing that looks real for all practical purposes (the wavefunction, that has to be part of the equations to govern the evolution of "particle positions" but is not affected by them in return), is in fact a "totally unreal" thing (all the other worlds in the many-worlds picture it contains are "totally unreal"), while only the particle positions (which behave as mere hidden variables, totally unreal for all practical purposes), have the metaphysical quality of "real existence".
Would the Universe be schizophrenic or what ?
In several ways, Bohmian mechanics or its motivation are in conflict with a fundamental principle of modern science in general, and especially modern physics : logical positivism. Problem : if it can be okay for a scientist to dismiss idealism as antithetical to quantum mechanics in the name of the idea that idealism would be antithetical to the principles of logical positivism which are the very foundation of the proper understanding of quantum mechanics (and science in general), while, in fact, idealism is in perfect fit with logical positivism, then what should one think of those scientists who insist praising Bohmian mechanics for what they see as crucial or maybe required qualities of scientific meaningfulness, when these supposed "qualities" actually mean or imply the very antithesis of logical positivism ?

Links to other arguments and articles about Bohm's interpretation

Sites supporting Bohmian mechanics:

Bohmian Mechanics by Luke Bovard mentioning how cumbersome is Bohmian quantum field theory

A blog article with discussion : Quick Impressions of Bohmian Mechanics

Why isn't every physicist a Bohmian? reviewing some common objections

In Physics Stackexchange:
Why do people still talk about Bohmian mechanics/hidden variables
What is wrong with the De Broglie–Bohm theory a.k.a “Causal Interpretation” of quantum theory?
Quora: Why don't more physicists subscribe to pilot wave theory?

A former proponent's view : "Note that I spent myself a lot of time with the Bohmian interpretation before I rejected it as superficial, essentially for the reasons given by Werner. It didn't add any understanding but wasted a lot of my time"

On some early objections to Bohm’s theory

Bohmian mechanics listed among "lost causes in theoretical physics" by R. F. Streater
How is quantum wave collapse a more reasonable concept than pilot waves?
An article in Wired followed by a discussion

Bohm's Ontological Interpretation and Its Relations to Three Formulations of Quantum Mechanics

A discussion focusing on Bohmian mechanics (and secondarily, on many-worlds)

Paul Dirac's forgotten quantum wisdom. In this article, Luboš Motl speaks about "deluded pseudoscientists – from David Bohm to dozens of nameless crackpots".
It's been a tough week for hidden variable theories
Farewell to determinism
Reddit discussion

Other hidden variables interpretations

Stochastic interpretation
Solipsistic hidden variables interpretation

Related pages

Introduction to quantum physics, that provides a quick and clear initiation, useful for those not familiar with it yet

Main page of arguments on quantum physics interpretations

The Many-Worlds interpretation

Mind Makes Collapse interpretation of quantum physics