(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.

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).

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.

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.

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).

After some chaotic processes, it arrives to a final state described by another quantity

In this situation, how can you meaningfully claim that "the first 5 measured decimals of

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".

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 "

- the problem of renormalization in quantum field theory
- Zeno's paradoxes
- the relativity of infinity in the face of non-standard
models of arithmetic and set theory, and how this
ambiguity of infinity clarifies the understanding of the incompleteness
theorem and the impossibility to solve the halting
problem.

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"

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.

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 :

- Classical deterministic chaos generates probabilities of
outcome in the long term. But the observation and understanding
of short-term deterministic laws comes first ; long term
probabilistic laws only come as very sophisticated abstract
deductions, and appear much more complicated than their
deterministic explanations.

- The determination of gender of embryos could finally be
understood; the gender of the baby can now be "predicted" by
tests on the embryo (that already had it) ; the latter can be
chosen in-vitro by selection technologies, but still not
predicted when it is still random; anyway there is a specific
"choosing process" whose analysis cannot provide better
forecasting tools.

- The weather for tomorrow has never been given a seriously precise probability; the improvements to weather forecasts were painful but straightforward by improving observations and means of computation, while predictions are anyway just less and less reliable as they are applied to longer time intervals.
- Some refinements of formulas used by insurance companies and traders
- The practice of insider trading
- Improvements in the prediction of earthquakes remain slow and gradual.
- The spreading of illnesses had not been given probability laws in the past, and is still not very predictable now.
- Pseudo-randomness. Pseudo-random generators, with the double
property of fitting a given simple probability law and being
classically determined, and, unlike the butterfly effect,
staying separated from any quantum source of randomness, were
man-made using well-designed algorithms for this explicit
purpose. No such randomness comes from nature. (Even the
decimals of pi, for example, while coming from the "nature" of
mathematics, require some design to be physically computed).

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

BomBox

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 MissionContact 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.

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

This switch does not leave any trace because

- Since the position is a hidden variable, assuming the wavefunction to be known, the precise position on the side of the second wavelet after the event that came from the first wavelet, is not a physically relevant or easily measurable data;
- The coexistence of both wavelets is not a physically
relevant data either: looking at things from the many-world
perspective, the different worlds do not interact, so that
when the particle is in one wavelet, the presence (in the full
wavefunction) of the other wavelet to which position can
switch (in the past or in the future) is not relevant to the
understanding of the physical behavior

Related remarks :

- Quantum mechanics offers a jump in computational complexity of processes compared to a classical kind of law for large scale systems over a grid of data in the role of a state of a system with some given resolution (such as one bit per atom), in other words, a quantum computer can be "much more powerful" than a classical computer for given sizes of memory and number of operations per second. However a hidden variables interpretation over a quantum computer requires a still higher jump in the computational power of the hidden process of evolution of the hidden variable underlying this quantum computation.
- Bohmian mechanics violates Occam's razor, by adding extra stuff that is not needed when working in QM, and cannot be tested. Which may also be seen as part of the next problem:

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)

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

Listing these extraordinary discrepancies of properties between effective and underlying behaviors in the same order they were listed above as "problems":

- 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.

- 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).

- 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"....).
- Specifications of the exact structure of the deep causality laws cannot be investigated by experiments.
- 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".

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 ?

Sites supporting Bohmian mechanics:

- Bohmian-mechanics.net (big site with many resources)
- Bohmian Mechanics in Stanford Encyclopedia of Philosophy
- (an incomplete site : bohmianmechanics.org)
- Series of courses by Robert Spekkens : lectures 12&13 on the deBroglie-Bohm interpretation (heavy pdf files of images - archive of lectures list with more explicit titles)
- Some links
- J. Bricmont, What is the meaning of the wave function?
- Michael Esfeld
- Antony Valentini (does not have a good web site...) - some lectures
- Mike Towler has his presentation of the debate
- L.E.
Szabó

A blog article with discussion : Quick Impressions of Bohmian Mechanics

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

On some early objections to Bohm’s theory

Bohmian mechanics listed among "lost causes in theoretical physics" by R. F. StreaterHow 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

Stochastic
interpretation

Solipsistic hidden
variables interpretation

Main page of arguments on quantum physics interpretations

The Many-Worlds interpretation

Mind Makes Collapse interpretation of quantum physics