

Bohmian mechanics, a ludicrous caricature of Nature




A constraint that defines Bohmian mechanics is simple: it should be a classical theory that emulates quantum mechanics as well as it can. The champions of the Bohmian theory know that getting the same predictions as quantum mechanics is the maximum goal they may dream about – they can never beat quantum mechanics – and they sort of realize that even this tie is too much to ask in general. Most of the Bohmian advocates seem to know that their theory can't be accurate, especially because of its fundamental conflict with relativity – but they don't seem to care. The fact that the Bohmian mechanics agrees with their fully discredited preconception that Nature is fundamentally classical is more important for them than the (in)accuracy of the predictions extracted from their pet theory.

It's straightforward to explain why it's possible to design a classical theory that parrots quantum mechanics when it comes to certain questions.

Bohmian mechanics is at least vaguely defensible in the non-relativistic quantum mechanical models only; in more general theories, it collapses completely. How does it rebuild non-relativistic quantum mechanics for one particle, for example?

Proper quantum mechanics of this system may be written down in Schrödinger's picture that dictates the following time evolution to the wave function:\[


\] The way how this wave is evolved in agreement with the equation above contains all the "mathematical beef" of quantum mechanics for the given system and to get the right numbers, any classical caricature of quantum mechanics simply has to contain some objects that are pretty much equivalent to \(\psi(q,t)\). These objects are then assigned totally different, wrong interpretations in the caricatures but they must be there and they must evolve according to the same Schrödinger's equation.

Bohmian mechanics buys \(\psi(q,t)\) and incorrectly interprets it as a classical wave – a field that has objective values and is in principle measurable. Of course, we know from quantum mechanics as well as experiments that the value of the wave function simply shouldn't be and isn't measurable in a single repetition of an experiment. So the Bohmian apologists must also invent convoluted mechanisms to make the wave unmeasurable – because it is unmeasurable according to the experiments – despite the fact that the wave function is fundamentally measurable in their theory.

Bohmian Rhapsody, via Dilaton.

Is this the real life? Is this just fantasy?
Caught by the guiding wave. No escape from reality.
Open your eyes. Look up to the skies and see:
I'm just [a] state vector, I need no images.
Because I'm easy come, easy go.
A little high, little low.
Anyway the [pilot] wave blows, doesn't really matter to me, to me.

The pilot-wave theory adopts \(\psi(q,t)\) as an objective classical wave – which it gives a new name, the "guiding wave" or "pilot wave" – but in order to agree with the fact that particles may be observed at sharp locations despite the fuzziness of the wave functions associated with them, they must add some additional degrees of freedom: the actual classical position of the particle. The defining philosophy of Bohmian mechanics is that the actual, classical position of the particle is "guided" by a function of the classical field emulating the wave function so that the probability distribution for the particle's positions remains what it should be according to quantum mechanics. For example, the laws that guide the actual classical particle must be such that they repel the particle from the interference minima in a double-slit experiment:

The right end of the picture (the photographic plate) shows denser and less dense regions, the interference maxima and minima.

Can you find the appropriate rules for one non-relativistic spinless quantum particle that is able to do it in a way that imitates quantum mechanics? You bet. All the tools are available in conventional quantum mechanics for this system. Recall that in quantum mechanics, \(\rho=|\psi(q,t)|^2\) is the probability density that the particle is sitting near location \(q\) at time \(t\). But quantum mechanics also allows you to define the probability current\[

\bold j = \frac{1}{m} \mathrm{Re}\left ( \psi^*\bold{\hat{p}}\psi \right )

\] Note that it is again sesquilinear (bilinear with one star) in the wave function. We act on the wave function by the momentum operator \(\bold{\hat{p}}=-i\hbar\nabla\), multiply the result by \(\Psi^*\) just like when we calculated the probability density, take the real part, and divide it by the mass \(m\). You see that it only differs from the formula for the probability density by the extra operator \(\bold{\hat{p}}/m\), the operator of the velocity \(\bold{\hat v}\), inserted in the middle. The real part could have been added to the probability density as well because it was real to start with.

At any rate, if you define the probability density and the probability current correctly, they obey the continuity equation\[

\frac{\partial \rho}{\partial t} + \bold \nabla \cdot \bold j = 0.

\] The divergence of the probability current exactly agrees with the decrease of the probability density in the given region. It means that the probability current measures how the probability has to flow into/from a given infinitesimal volume if you want the probability density to change just like it should according to Schrödinger's equation.

Now it's easy to realize that if you define a classical "velocity field"\[

\bold{\hat v} = \frac{\bold{\hat j}}{\rho},

\] it will be very useful for emulating quantum mechanics. It's not hard to prove that if you define Bohmian mechanics as the "classicalized" wave function together with a classical position \(\bold{\hat q}(t)\) that evolves according to the "guiding equation"\[

\ddfrac{\bold{\hat q}}{t} = \bold{\hat v} (\bold{\hat q}(t)),

\] the trajectories of the classical particles will be repelled from the interference minima, attracted to the interference maxima, and will obey a more specific rule: If you imagine that the particles in the initial state are distributed according to the probability distribution given by \(\rho(\bold{\hat q},t)\), it will be true for the final state, too.

This trick may be generalized to the case of \(N\) non-relativistic particles. In this case, the wave function \(\psi\) becomes a classical wave that is a function of the \(3N\)-dimensional configuration space. This configuration space is larger than the ordinary space and is "multi-local" and because we have this "multi-local" old-fashioned classical field, the theory becomes explicitly non-local and a violation of the Lorentz symmetry, at least in principle, is inevitable.

I would like to emphasize that it's no surprise at all that it's possible to find the equation that evolves the probability distribution in the right way. Imagine that you start with a wave function \(\psi(\bold{\hat q})\) at some time \(t_0\). Throw a trillion of dots – particles – to the space that are distributed according to \(\rho = |\psi|^2\). Do the same thing for the final moment \(t_1\) when the wave function is different. You will have two configurations of trillions of particles. It's not shocking that you may "connect the dots" from the initial state to the final state in some way.

A way that is simple enough, one based on the probability current and described above, gives you one of the solutions. But it's not the only solution. In reality, the "initial dots" could be connected with the "final dots" in infinitely many ways (well, a "mere" trillion factorial if you only have a trillion of dots). In the continuous language, you could e.g. make the particles move along spirals inside the cylinders that surround the interference maxima. Is one way to connect the dots better than others?

Of course, it's not. All of them are equally good. Quantum mechanics commands you to learn something about the initial state – some wave function or density matrix that encode the initial probability distribution – and it allows you to predict the probabilities for the final state. But it doesn't tell you which of the initial particles is connected with which final particle, i.e. how to connect the dots. It doesn't inform you about any preferred classical trajectory that connects them (and Feynman's approach orders you to sum over all trajectories). If you could actually "measure" this permutation that determines how the dots are connected, quantum mechanics would be shown incomplete.

However, it's totally obvious that there's no way to measure the trajectories or permutations inside. The particles just don't have well-defined, in principle measurable trajectories between the measurements for the usual Heisenberg uncertainty principle-based reasons. If you tried to measure the trajectory before the final measurement, you would change the experiment and destroy or damage the final interference pattern. So all the precise lines on the "caricature of the double-slit experiment"

are pure fantasy. They're just crutches for the people who need some specific picture of the intermediate states to be drawn. But the specific picture we drew is in no way better than infinitely many other pictures we could draw that would predict the same interference pattern, the same probability distributions for the final state. Everything we added because we wanted the physical system to have objective properties prior to the measurement – because we're bigots who can't accept the fact that classical physics has died – is unphysical. The added value is purely negative. Everything we added to get from proper quantum mechanics to Bohmian mechanics is rubbish. And many things we're forced to lose when we switch from quantum mechanics to Bohmian mechanics are essential.

Because the wave function has a probabilistic interpretation in proper quantum mechanics (it is a ready-to-cook meal from which one may quickly prepare various probability distributions by a calculation), it doesn't matter that it spreads. The spreading of the wave function doesn't make the world more fuzzy. It only makes our knowledge about the world more uncertain. But once we learn the answer to a question – e.g. about the position of a particle – the world fully regains its sharp character it boasted at the beginning. If you only know that the probability of 1,2,3,4,5,6 are 1/6 for some dice in Las Vegas, it doesn't mean that the dice became structureless balls or that the digits written on their sides have become fuzzy or mixed or smeared. It just means that we have one equally sharp cubic die but we just don't know its orientation in space. The uncertainty coming from quantum wave functions are analogous – they only differ from the "classical uncertainty" by their inevitability.

That's not the case of Bohmian mechanics. The wave function is interpreted as a classical field of a sort and it is objectively spreading. So something objective is being diluted all over the Universe. That's terrible because this objectively makes the Universe increasingly more fuzzy and bizarre. The useless parts of the guiding wave – the "classicalized" wave function – should be killed in some way because they became useless. But Bohmian mechanics doesn't imply anything of the sort. If you want to clean the garbage of the no-longer-needed branches of the wave function, you will have to add another independent contrived mechanism. Such a mechanism will be a new source of a violation of the Lorentz invariance.

(You also need a special mechanism that prepares the guiding wave in a certain initial state and one more mechanism that distributes the "actual particle" inside the appropriate distribution with the right odds because these two things don't follow from Bohmian mechanics as we have defined it above, either. Most of these things are ignored by the Bohmists. Note that with the right probabilistic interpretation – quantum mechanics directly connects the knowledge about the past with the knowledge about the future, without any new crutches in between – we don't need to invent any new mechanisms.)

I think that a sane, critically thinking person must be able to realize what he is doing if he is doing such things. He is drawing a ludicrous caricature of Nature – a physical system that is actually governed by the laws of proper quantum mechanics – that reproduces some properties of the correct, quantum theory. The project of drawing the caricature is motivated by the desire to defend a philosophical dogma that the world is fundamentally classical even though it is clearly not. If he has at least some conscience, he must feel analogously as if he were counterfeiting a $100 banknote. He must know that what he is producing isn't the "real thing"; it is just a forgery that can bring him greater personal benefits than the actual banknotes but that's where the advantages stop.

But every change from the proper quantum mechanics to the pilot-wave theory is clearly wrong – the "added value" is unquestionably negative. Because the Bohmists don't like the probabilistic character of the wave function, they turn it into a classical wave – the guiding wave. But a classical wave that spreads objectively makes the world ever more fuzzy. So one has to introduce new tricks to have a chance that this increasing fuzziness doesn't spoil the world. All these tricks – tricks that can't really ever be defined in such a way to imitate quantum mechanics completely accurately – have to be considered and added just in order to mask the fact that the wave function is simply not a classical field.

It's fair to say that the claim by quantum mechanics that the wave function is not an objectively real wave or field that can be in principle measured is something that we have proven by direct experiments. Attempts to pretend that the wave function is a classical wave are just attempts to mask the truth. I am confident that every Bohmist must ultimately realize it is so and he must be dishonest if he claims that his efforts are more justifiable than the efforts of creationists who are trying to obscure the explicit evidence in favor of evolution: they are exactly equally unjustifiable.

Moreover, it's sometimes being said or thought that the perfect emulation of quantum mechanics can be done. Because the invalidated dogma that Nature is fundamentally classical is holy for these bigots, they think that it should be done, too. But the truth is that it can't be done for a general physical system and for a general choice of observables we may measure in actual experiments described by general enough quantum theories.

Try to add the spin to a particle. If the logic of Bohmian mechanics – the wave function "is" a classical field and we should also add some classical values of a maximum set of commuting observables – were universally valid, it's clear that aside from the spinor-valued wave function \((c_{\rm up},c_{\rm down})\), we should also assume that Nature "objectively knows" about the classical bit of information that tells you whether the spin is "actually" up or down.

However, even the Bohmists realize that if every electron "objectively knew" whether its spin is up or down with respect to the \(z\)-axis, then the laws of physics would break the rotational symmetry because the \(z\)-axis would play a privileged role. Roughly speaking, the ferromagnets would always be oriented vertically, to mention an example. If the \(z\)-component of the classical angular momentum is quantized, it's totally obvious that the other components can't be quantized. A nonzero vector can't have integer (or half-integer) coordinates in each (rotated) coordinate system.

Because they sort of realize that the rotational symmetry holds exactly and the hypothesis that the classical value exists with respect to one axis would break the symmetry kind of maximally, they decide that the Bohmian rules must be "skipped" in the case of the spin – they just manually omit some degrees of freedom that should be there according to the general prescription of Bohmian mechanics and hope that the spin measurements are ultimately reduced to position measurements so that it doesn't hurt if some degrees of freedom are not doubled in the usual Bohmian way.

The reason why the case of the spin is obvious even to them is the fact that different components of the spin are non-commuting observables none of which is more "natural" than others. After all, they are exactly equally natural because they are related by the rotational symmetry.

While the spin is an obvious problem, the pathological character of Bohmian mechanics is much more general. Every (qubit-like) discrete information in quantum mechanics – information labeling a finite-dimensional Hilbert space – is incompatible with the Bohmian philosophy. Recall that Bohmian mechanics added "classical trajectories" \(\bold{\hat q}(t)\) and these coordinates were functions of time that evolved according to some differential equations. But that was only possible because the spectrum of the coordinates was continuous. If you think about observables with a discrete spectrum, it just doesn't work because they would have to "jump to a different, sharply separated discrete eigenvalue" at some points and there can't be any deterministic laws that would govern such jumps.

Quantum mechanics tells you that a quantum computer composed of a very large number of qubits may perfectly emulate any quantum system. But that's not the case in Bohmian mechanics. An arbitrarily large quantum computer is composed of qubits, e.g. many electron spins, and because the spin isn't accompanied by a classical bit, Bohmian mechanics is forced to say that an arbitrarily large quantum computer only contains the "classicalized" wave function but no additional classical information analogous to the classical trajectories. So for a quantum computer, the whole "redundant superstructure" (which is how Albert Einstein called these extra coordinates – he was a foe of the pilot-wave theory, despite his being a disbeliever in quantum mechanics) has to be omitted. This is quite an inconsistency in the Bohmian treatment of different quantum systems. The actual reason behind the inconsistency is clear, of course: some physical systems may be caricatured by the pilot-wave trick, others can't. But in Nature, there actually isn't any qualitative difference (in principle observable difference) between these two classes of situations.

I said that Bohmian mechanics doesn't allow you to consistently treat the particles' spin or any other discrete degrees of freedom, for that matter. But the inadequacy of Bohmian mechanics is much worse than that. It really doesn't allow you to correctly deal with most observables in general quantum systems, not even with observables with a continuous spectrum. I have discussed similar problems in Bohmists and the segregation of primitive and contextual observables four years ago.

The problem is that Bohmian mechanics forces you to choose some observables that "really exist" – are encoded in the objective extra coordinates that are supplemented to the "classicalized" wave function. However, quantum mechanics implies that other observables just can't have a well-defined value at the same moment – because they don't commute with the first ones, stupid. That also means that Bohmian mechanics can't have any answers to questions about the value of these observables.

The Bohmian trajectories in the picture above pretend that a particle has an objective position and an objective velocity. But what about the orbital angular momentum \(\bold{\hat L} = \bold{\hat q}\times \bold{\hat p}\)? A basic result of quantum mechanics is that the spectrum of \(\bold{\hat L}_z\) is discrete; the eigenvalues are integer multiples of \(\hbar\). Already this elementary fact in quantum mechanics – even non-relativistic quantum mechanics – is completely inaccessible to Bohmian mechanics. The cross product of the classical position and the classical momentum of the "added Bohmian trajectories" isn't quantized at all. It has really nothing to do with the angular momentum that can be measured.

And be sure that the measurement of the angular momentum is often – e.g. for electrons in atoms – much more natural and "fundamental" than the measurement of the particles' positions or momenta. It's because its eigenstates are much closer to the energy eigenstates and those are the most natural basis of a Hilbert space because they describe stationary – and therefore lasting – states. But such a direct measurement of the discrete orbital angular momentum can't be done in Bohmian mechanics. Instead, Bohmian mechanics tells you that you have to continue the evolution of the wave function according to the laws stolen from proper quantum mechanics up to the moment when you can actually convert the original measurement to a measurement of a location, and hope that Bohmian mechanics knows how to emulate the measurements of positions. It isn't quite the case, either, but even if it were the case, Bohmian mechanics is just bringing an amazing degree of inconsistency into the way how different observables – different functions of the phase space – are treated. A sensible theory should treat all functions of the coordinates and momenta i.e. all functions in the phase space equally, following unified rules. Quantum mechanics obeys this criterion, Bohmian mechanics doesn't. We could say that just like the solipsists say that their own mind is the only physical system that may be claimed to be self-aware, Bohmian mechanics remains silent and reproducing the (accurately emulated) quantum evolution up to the moment when macroscopic positions are apparently being measured (those are the "conscious events" that are supposed to replace quantum mechanics with something else). But in the real world, there's nothing special about the minds of the solipsists (except that they belong to the set of crazy people) and there's also nothing special about the positions of macroscopic objects in comparison with many other observables we may define.

In quantum mechanics, you may directly construct operators for the angular momenta and ask about their possible values, eigenvalues, and about the predicted probabilities that the measured value will be one or the other. It doesn't matter whether the angular momenta belong to large or small or conscious or unconscious objects. Quantum mechanics allows you to deal with all observables equally. In Bohmian mechanics, those things matter. Effectively, any measurement has to be continued up to the moment when it imprints itself into a position of a macroscopic object which Bohmian mechanics claims to reproduce correctly.

A totally new minefield for Bohmian mechanics is relativity. The minimum consistent relativistic theories of quantum particles are quantum field theories (QFTs). They include the spin; I have already discussed the Bohmian problems with the spin. But there are infinitely many similar problems. For example, you may choose many different bases of the QFT Hilbert space. They may be eigenstates of the occupation number operators; eigenstates of field operator distributions \(\hat \phi(\bold{x})\), and so on. It is not clear at all which of these observables are added as the "extra classical trajectories" to Bohmian mechanics. In fact, it is totally obvious that none of the choices will behave correctly in all the experiments that may test a quantum field theory. Also, you can't add many of them or all of them (e.g. both positions and particles and classical values of the fields) because it would be clearly undetermined which of these "added", mutually conflicting classical degrees of freedom defines the "actual reality" that decides about a measurement.

Sometimes, the value of the field at a given point may be measured, especially when the frequencies are low. So it would seem like you need to add a "preferred classical field configuration" to the Bohmian version of a QFT. However, especially for high frequencies, the quantum field manifests itself as a collection of particles so you may want to add the trajectories of the particles instead. Moreover, even if you represent a QFT as a system describing many particles, your Bohmian theory won't be able to deal with the basic and most universal processes that must exist in a QFT or any other relativistic quantum theory such as the pair creation of a particle and an antiparticle and their destruction.

If individual particles evolve according to the "guiding wave" equations we discussed at the beginning, it's simply infinitely unlikely (the probability refers to the selection of the initial positions from the distribution) that they will ever collide with one another. Two random lines in a 3D space simply don't intersect one another. But if they don't directly collide, it means that they can't annihilate! To allow the particles to annihilate (and be pair-created) with the (experimentally proven) nonzero probability, you would need to introduce a totally non-local extra dynamics that sometimes allows the particles to jump to a completely different place; or you would have to allow the annihilation of particle pairs that don't coincide in space. Any such an extra mechanism would force you to change the original laws of physics in a way that would almost certainly contradict some other experiments because the unmodified quantum laws simply work and it was a healthy strategy for you to emulate them "perfectly" at the very beginning. Such modifications would especially contradict some experimental tests of relativity because these modifications are so horribly nonlocal.

So you have no chance to construct an operational Bohmian caricature of a quantum field theory. Needless to say, the problems become even more extreme once you switch to quantum gravity i.e. string theory because many more observables have a discrete spectrum, there are many more ways to choose the bases, the nonzero commutators of various observables are more important than ever before, and Bohmian mechanics just can't prosper in such general quantum situations. On one hand, quantum gravity i.e. string theory is just another quantum theory. On the other hand, it is "more quantum" than all the previous quantum theories simply because the quantum phenomena affect many more questions that could have been thought of in the classical way if you worked with simpler quantum mechanical theories (for example, the spacetime topology – especially the number of Einstein-Rosen bridges in the spacetime – can't even be assigned a linear operator in a quantum gravity theory, as Maldacena and Susskind argued).

The non-local fields, collapses, non-local jumps needed for particle annihilations, and other things represent an inevitable source of non-locality that can, in principle, send superluminal signals and that consequently contradicts the Lorentz symmetry of the special theory of relativity. There's no way out here. If you attempt to emulate a quantum field theory in this Bohmian way, you introduce lots of ludicrous gears and wheels – much like in the case of the luminiferous aether, they are gears and wheels that don't exist according to pretty much direct observations – and they must be finely adjusted to reproduce what quantum mechanics predicts (sometimes) without any adjustments whatsoever. Every new Bohmian gear or wheel you encounter generally breaks the Lorentz symmetry and makes the (wrong) prediction of a Lorentz violation and you will need to fine-tune infinitely many properties of these gears and wheels to restore the Lorentz invariance and other desirable properties of a physical theory (even a simple and fundamental thing such as the linearity of Schrödinger's equation is really totally unexplained in Bohmian mechanics and requires infinitely many adjustments to hold – while it may be derived from logical consistency in quantum mechanics). It's infinitely unlikely that they take the right values "naturally" so the theory is at least infinitely contrived. More likely, there's no way to adjust the gears and wheels to obtain relativistically invariant predictions at all.

I would say that we pretty much directly experimentally observe the fact that the observations obey the Lorentz symmetry; the wave function isn't an observable wave; and lots of other, totally universal and fundamental facts about the symmetries and the interpretation of the basic objects we use in physics. Bohmian mechanics is really trying to deny all these basic principles – it is trying to deny facts that may be pretty much directly extracted from experiments. It is in conflict with the most universal empirical data about the reality collected in the 20th and 21st century. It wants to rape Nature.

A pilot-wave-like theory has to be extracted from a very large class of similar classical theories but infinitely many adjustments have to be made – a very special subclass has to be chosen – for the Bohmian theory to reproduce at least some predictions of quantum mechanics (to produce predictions that are at least approximately local, relativistic, rotationally invariant, unitary, linear etc.). But even if one succeeds and the Bohmian theory does reproduce the quantum predictions, we can't really say that it has made the correct predictions because it was sometimes infinitely fudged or adjusted to produce the predetermined goal. On the other hand, quantum mechanics in general and specific quantum mechanical theories in particular genuinely do predict certain facts, including some very general facts about Nature. If you search for theories within the rigid quantum mechanical framework, while obeying the general postulates, you may make many correct predictions or conclusions pretty much without any additional assumptions.

If you ask any of the hundreds of questions (Is the wave function in principle observable? Are observables with discrete spectra fundamentally less than real than those with continuous spectra? Is there a way to send superluminal signals, at least in principle? And so on) in which proper quantum mechanics differs from Bohmian mechanics, the empirical evidence heavily favors quantum mechanics and Bohmian mechanics can only survive if you adjust tons of parameters to unnatural values (from the viewpoint of Bohmian-like theories) and hope that it's enough (which it's usually not).

In 2013, even more so than in 1927, the pilot-wave theory is as indefensible as a flat Earth theory, geocentrism, the phlogiston, the luminiferous aether, or creationism. In all these cases, people are led to defend such a thing because some irrational dogmas are more important for them than any amount of evidence. That's what we usually refer to as bigotry.

And that's the memo.

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reader Dilaton said...

I dont know why this is, but I just cant prevent my mind from thinking Bohemian Rhapsody whenever I see the words Bohmian mechanics ... :-D

Going to read this later, from scrolling througy I see that it obviously contains a lot of nice physics I like.

reader Luboš Motl said...

LOL, I live in Bohemia so I would be distracted all the time if I shared the distractions with you. ;-)

reader Peter F. said...

Freakishly good song, that one. Thanks Dilaton for associating and Lumo for linking! :-)

reader lucretius said...

I agree with almost everything (modulo the epithets). I have always been allergic to Bohm not so much because he was, as you say “media savvy commie”, but because of all the “Eastern mystical gibberish” that his ideas are associated with and which made them so cool with the hippie crowd. In fact last year during a trip to Canta Cruz, California we visited a (actually quite nice) “natural food” restaurant, where the walls and the menu were covered with “quantum mystical” deep thoughts that sounded like stuff out of “Wholeness and the Implicate Order”.

Having lived for over 20 years in Japan I am quite familiar with Buddhist thought and it is indeed true that one can find some curious parallels with modern physics but not really more so than one can find in “De Rerum Natura” authored by my namesake. I would say that the similarities are about 90% coincidence and 10% due to some basic structure of human thought and logic, and, of course, that the both ancient Indian (and Greek) thought and high energy physics are concerned with the same basic issue: the origin and nature of everything.

But Bohm’s contribution to the confusion does not endear him to my heart or mind.

Niether of course, does his being a commie - but if you really view this as a serious charge there will be few of his contemporaries among physicists left unscathed. I am not quite sure if this has any relation to his views of physics and metaphysics. I note however that the strongest supporter of Bohm’s view that I have met, Jean Bricmont, is a leftist raving lunatic and an associate of Chomsky (although he has to be given some credit for co-authoring Fashionable Nonsense (

I am glad that Bohm lived in Israel for only 2 years - otherwise I would have felt compelled to like him more.

I have never quite understood why physicists, at least in the early post-war years, were so much more left-wing than mathematicians. I can name quite a few strongly anti-communist mathematicians (above all John von Neumann and my Stanislaw Ulam - my favourite of that generation, and many others) but among physicists Teller is perhaps the only one who comes to my mind, and the situation does not seem to be very different today.

Finally, it seems to me that, apart from the mysticism, the main thing that attracts people to ideas like Bohm’s is the psychological difficulty many face with accepting probability as something that is part of physical reality rather than a human device invented to cope with ignorance. This is true even of mathematicians who work in probability. I have collaborated with “pure” probabilists and have got the impression that only a minority believe in randomness as a feature of the “real world” although everyone has heard that most quantum physicists claim otherwise. In fact, I find myself frequently hesitating about this issue,depending on my mood. For a mathematician probability theory is just a branch of measure theory and all its interesting results involve limit theorems - whose relation to the physical world appears dubious. It seems to me that many people still feel queasy about randomness in physical laws (the way Einstein felt) and this suggests that attempts to find non-probabilistic interpretations of quantum phenomena will continue to find supporters.

reader Mephisto said...

I must admit that religious mysticism is something of a hobby for me. I studied quite a lot (zen buddhism - Hui Hai, Huang Po, Tibetan buddhism, taoism, christian mysticim - Meister Eckhart, Ramana Maharishi, Jiddu Krishnamurti). Jiddu Krishnamurti was a personal friend of David Bohm and I believe he influenced his views a lot. It is fair to say that Krisnamurti was never interested in physics, he was interested in human consciousness, so the holomovement is the sole creation of Bohm himself
Although I would describe myself as a mystic, I am against mixing mysticism with physics. I read the book by Fritjof Capra (Tao of Physics) and disliked it. Modern variants are various kinds of Akashic fields and stuff like that
It is impossible and unwise to mix religion with science. For mystics and pantheists like me, sciece is just a part of devine reality

reader Justin Glick said...

You seem to think that a particle has a precise position at all times, but we just don't know what it is. QM does not say this.

reader serene deputy said...

I think Lubos just wanted to say that you are still describing the same system, say, one structureless point-like particle, not a field or a ghost (otherwise your starting Hamiltonian and Schrödinger equation would have changed), but whose position becomes fundamentally undetermined to some extent.

reader NumCracker said...

Dear Lubos, excuses for this off-topic comment: would there be a way to experimentaly test other interpretations, not formulations, of QM and QFT as the Many-World one? Have this ever being done? Thanks

reader Dilaton said...

Yeah it would be fun, if Lumo could adapt the whole songtext to this TRF article ... :-D

reader Stephen Paul King said...

Qm, IMHO, demands that Nature does not have a preffered observable.

reader Diana Z. said...

Yay, finally a good explanation without too much technical stuff.
I also have an OT request. Can you explain, in this same understandable style, why time goes slower for objects closer to the source of gravity. I looked, and I couldn't find a proper explanation. I hate it when something starts promising and then you see several pages of formulas that will give anyone a headache. With an added "it all stems from relativity, go read it" at the end. Ugh! It almost makes me believe, the authors themselves don't have a clue.

reader Luboš Motl said...

Right, lucretius. I remember the story from Feynman's book that said, among other things, that some promoters of paranormal phenomena convinced a professor David Bohm that they had supernatural abilities...

reader Luboš Motl said...

Dear Numcracker, there doesn't exist any specific enough formulation of MWI that would give some predictions differing from proper QM (at least in principle) - except for versions that are immediately ruled out even by the simplest experiments.

Just like I said about Bohmian mechanics, the best thing that MWI proponents are hoping - and it's just a hope, and an unjustified one - is that they reproduce the predictions of QM exactly. And they're extremely far from it. But everyone knows that QM with a proper interpretation gives predictions for pretty much everything and pretty much every physicist knows that they're correct so to "emulate them exactly" is the ultimate dream of any other "interpretation". An unachievable dream.

So MWI isn't a real theory that would be used to really do active physics. It's a philosophical declaration that some physicists sometimes endorse at the level of words even though they don't exactly know what this theory is supposed to say.

reader Luboš Motl said...

One doesn't need to "demand" it. Nature obliged well before quantum mechanics - and humans - were born. The chronology is exactly the opposite than you suggest. Nature created a world with many observables none of which is "preferred" and people constructed theories that were selected by the demand that they agree with Nature.

All modern, post-1925 fundamental theories of Nature are demanded to agree at the level of the atomic details, i.e. respect the general rules of quantum mechanics, which also means that they have to agree with the fact about Nature that it doesn't have preferred observables.

reader lucretius said...

This thread made me try to think of any Western physicist of whom I knew that he was definitely not left-wing and then I remembered the following.

The first time I learned about the violations of Bell’s inequalities and its implications was in 1981 by reading an article by Bernard D’Espagnat in “Encounter”. I just searched the web and and found it here:

I have not read it since it first appeared, that is, for over 30 years (it will be interesting to see how current it sounds today) but I always remembered its main point, namely, that the results of experiments showed that concept of “independent reality” had to be abandoned. Trying to understand this induced me to learn some fairly technical physics, which I had not been interested in before.

I am not sure how many people reading this are old enough to grasp the significance of such an article appearing in “Encounter”. "Encounter "was then Europe’s leading intellectual publication whose raison d'être was anti-communism. In fact, it was founded by the Paris based Congress for Culutral Freedom, a center-left organization dedicated to opposing communist influence in the West. It’s founder’s were the poet Stephen Spender and the “father” of American neo-conservatism Irving Kristol. Among its leading contributors were major cultural figures such as Raymond Aron, Ignazio Silone, Arthur Koestler and lots of others. There is a good account of all of it on the Wikipedia.

(I used to be a subscriber and still have all my old copies).

I don’t know anything about D’Espagnat’s politics but the fact that he chose to publish that article in "Encounter" means that at least he was definitely not a communist or a “fellow traveller”. In 1967 it had been discovered that the CIA had been secretly funding the magazine, which of course made it a taboo for anyone on the left. I suspect that publising in "Encounter" must have ruined D’Espagnat’s reputation among leftist physicists.

This article was, if I remember correctly, the only article on physics ever to appear in "Encounter" - which shows how much importance was attached to this matter then. It was followed by a polemic between D’Espagnat’s and the well known conservative philosopher Antony Flew ( Flew was a clever many but like many layman, refused to accept that the idea of “non-existence of independent reality” made any sense.

reader Florin Moldoveanu said...

All known QM interpretations are faulty and the only correct interpretation can come from the project to reconstruct QM from natural principles (see QM also goes beyond the usual C* algebraic formulation into the non-commutative geometry formulation of the SM.

QM and classical mechanics are distinct "fixed points" in a category theory formulation and any attempt to derive one from the other is a fool's errand. Any non-unitary time evolution of QM (e.g. the collapse postulate) is incompatible with QM's framework, but MWI is not the answer. The answer is much more subtle and mathematical sophisticated but for all practical purposes the collapse postulate does the job (using the collapse postulate is like using ict in relativity and ignoring additional mathematical structures - see and for the beginning of the answer).

The wavefunction is neither ontological nor epistemological in the usual sense.

reader Dimension10 said...

Great post...

I am quite confused about why Bohmian mechanics is often listed as an "interpretation" of QM, such as here: (That too, for that document, the authors are like Becker, Styer, etc.).

As you say in the post, Bohmian mechanics can't describe all the QM phenomena exactly, so I don't see how it can be listed as an "interpretation of Quantum Mechanics?

In my opinion, it should be listed as... an "alternative" non-mainstream theory to QM, like how MOND is a non-mainstream alternative to NG.

Also, finally, an off-topic question: "How do you get inline MathJax on your post? The MathJax CDN doesn't seem to allow $...$ and ##...## but only $$...$$ which results in display math. Do you use [itex] ... [/itex] or something like that? .

reader Luboš Motl said...

Dear Dimension10, exactly, Bohmian mechanics is an alternative theory - or a wishful thinking about the existence of an alternative theory, if we want to go beyond the known toy examples - so it's demagogic to sell it as an "interpretation" of QM.

The sequences to write TeX via Mathjax are \(E=mc^2\) and\[

E = mc^2

\] but they don't work in DISQUS. Mathjax allows you to define other sequences that start the displayed and inline math modes, including $...$ and $$....$$. The latter actually does work here as well but I didn't allow the single dollar because I sometimes is the character as a unit of money.

reader Dimension10 said...

I just realised you have the "listen" feaure enabled. It pronounces the equations very nicely : ) .

reader Lisa Korf said...

Hi Luboš, I am curious to know how you would reconcile weak measurement trajectories, as in (illustration of measured average trajectories from the article here: ) with your suggestion that "If you could actually 'measure' this permutation that determines how the dots are connected, quantum mechanics would be shown incomplete. " since these, although averaged and still interpolated, are not arbitrary either, and an interference pattern can still be observed. Thanks. LK

reader Luboš Motl said...

Dear Dr Korf, thanks for your question which however shows that you are confused about the status of various claims and patterns here.

The picture you included is pretty much the very same picture that I included in this very blog post and it wasn't measured. The trajectory of a quantum particle can't be measured without affecting it.

The copy of the picture in the Science Magazine is a result of a "weak measurement" but a "weak measurement" isn't a measurement. What is critical is that a weak measurement doesn't measure a property of the measured object/system only. Instead, it determines some function of the properties of the system and numerous conventions and choices that were used to define a particular weak measurement procedure. See e.g.

So the weak measurement isn't unique in any way and the trajectories on the picture were obtained with one particular prescription for a weak measurement protocol. One could get pretty much any other permutation of the dots - any other picture like that with the same density of lines in each region - if we were drawing these pictures using other weak-measurement protocols. There is nothing physical about the randomly drawn trajectories - any choice is just a convention and all conventions are equally physical at the end.

reader lucretius said...

These sort of things can be produced "ad infinitum" so debunking them one by one is no more productive a way to spend time than trying to work out precisely what is wrong with this:

reader Scott Lahti said...

I thank you for your kind words regarding my 20x expansion, from late 2012, of the Wikipedia entry for Encounter magazine, one of whose seeds and two of whose results appear below:

reader bustemup said...