# Why do people still talk about bohmian mechanics/hidden variables [closed]

I was reading the Feynman lectures in physics and after thinking about it for a while it seems particularly unreasonable to talk about hidden variables. Let us say that the electron has some internal variables as yet unknown which determine its trajectory given a set of initial conditions just like in classical mechanics. But since these hidden variables are unobserved, coupling it with a classical system should make their effect unchanged. This is what Feynman says, I think, in the last paragraph of Ch1 Vol 3, that if in the double slit experiment, if these inner variables dictate that the electron goes through the upper slit and land at a particular place on the opposite screen, and some other place for the lower screen, then the probability must neccesarily be the sum of two Gaussian like peaks, which does not agree with experiment.

So if I concluded that inner workings of an electron had some additional hidden variables, then it should yield, as they should be independent of the classical apparatus, mutually exclusive probabilities that do not quiet add up the way as observed. But then I do a hidden variables search on the archive and a lot of smart guys still write about it, as late as Feb 2011.

So the argument I have used might be somehow incomplete, can anyone explain how?

EDIT: Sorry for editing this question almost three years later. I tried to locate the exact reference from the Feynman lectures I was referring to and this is the updated source, Sec 7 Ch 1 Vol 3

We make now a few remarks on a suggestion that has sometimes been made to try to avoid the description we have given: “Perhaps the electron has some kind of internal works—some inner variables—that we do not yet know about. Perhaps that is why we cannot predict what will happen. If we could look more closely at the electron, we could be able to tell where it would end up.” So far as we know, that is impossible. We would still be in difficulty. Suppose we were to assume that inside the electron there is some kind of machinery that determines where it is going to end up. That machine must also determine which hole it is going to go through on its way. But we must not forget that what is inside the electron should not be dependent on what we do, and in particular upon whether we open or close one of the holes. So if an electron, before it starts, has already made up its mind (a) which hole it is going to use, and (b) where it is going to land, we should find P1 for those electrons that have chosen hole 1, P2 for those that have chosen hole 2, and necessarily the sum P1+P2 for those that arrive through the two holes. There seems to be no way around this. But we have verified experimentally that that is not the case. And no one has figured a way out of this puzzle. So at the present time we must limit ourselves to computing probabilities. We say “at the present time,” but we suspect very strongly that it is something that will be with us forever—that it is impossible to beat that puzzle—that this is the way nature really is.

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## closed as not constructive by mbqMar 19 '11 at 17:46

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

Sorry, but such questions are somehow not working on this site -- they collapse into an useless random argument. – mbq Mar 19 '11 at 17:54
@mbq if you close a question, with so many answers and so many votes, are you not disallowing those who have not yet answered the chance to do so in the future? The question could have been formulated in a less confrontational manner, but I think its a bit late to close it, IMHO. There are some very detailed and non-argumentative answers here. – user346 Mar 19 '11 at 19:53
@Deepak It is certainly my error to close it so late; I'll try to be more reactive. – mbq Mar 19 '11 at 20:02
To think about hidden variables is not necessarily unreasonable at all. One could take the opposite stance and ask "Why isn't every physicist a Bohmian?" as in this interesting paper arxiv.org/abs/quant-ph/0412119 . – jdm Aug 2 '11 at 19:15
Well, I will disagree with the great Feynman ,"But we must not forget that what is inside the electron should not be dependent on what we do, and in particular upon whether we open or close one of the holes. So if an electron, before it starts, has already made up its mind (a) which hole it is going to use, and (b) where it is going to land"a) he is anthropomorphising the electron b)ignoring that all wavefunctions are dependent on the boundary conditions.It is the boundary conditions that make the electron wavefunction "know" where it will go.Boundary conditions exist for complex systems too. – anna v Dec 14 '13 at 7:28

I agree with Luboš that this question has a lot to do with psychology.

I think the tic-tac-toe analogy is relevant. There are an infinite number of games that are precisely equivalent to tic-tac-toe, but humans are probably terrible at playing most of these games.

Chess is even worse. You can teach a child the rules of chess in a few minutes, but imagine doing so without the board! Consider one of the simplest games of chess:

1. e4 e5
2. Qh5?! Nc6
3. Bc4 Nf6??
4. Qxf7# 1–0

A child can grasp the game, but even a grandmaster probably pictures a board as he reads those symbols.

A chess computer does not picture a chess board. It uses a different representation that is more efficient for its calculations. I suspect this formulation of chess would not hold a child's attention for very long, and only a very exceptional child would attain any skill at the game.

Some representations of chess or tic-tac-toe suit the human mind. Others are efficient to simulate on a computer. Still other representations are utterly useless, despite being precisely equivalent. Surely the same is true of the rules of physics.

For this reason, I like Bohm's efforts to find an experimentally indistinguishable reformulation of QM, whether or not he succeeded. Imagine if we've been playing 'JAM' all this time, when we could have been playing 'tic-tac-toe'!

I think that's why people still talk about Bohm.

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great point, +1 – lurscher Mar 17 '11 at 22:42
• First point I want to address is a gross mischaracterization of people working on Bohmian mechanics or other hidden variable interpretations. I quote

Quantum mechanics remains unacceptable for many people, for quasi-religious reasons. [...] it's time for those people to seriously consider the hypothesis that quantum mechanics is really how the world works.

People for whom it is hard to swallow the hard reality of quantum mechanics, people who want to understand nature in terms of every day classical intuitions are the ones who often advocate Bohmian mechanics.

This is a straw man. Nobody I know working or having worked on hidden variable interpretations of quantum mechanics, be it Bell, Bohm, Goldstein, Bricmont, Maudlin, de Broglie or other, denies the reality of quantum mechanics. Quite the contrary, I would even say they are/were more aware of the implications than many people otherwise working with quantum mechanics. In particular they fully recognize the non-local nature of quantum mechanics. But I'll come back to that. I can of course not speak for ALL people dealing in hidden variable theories or other alternatives. I'm sure there will be a faire share of crackpots and other cranks. But there are many people who know their stuff.

• Second point is the Zeilinger article that @Luboš Motl mentions. I've only skimmed through the article, but it seems that the only non-local hidden variable theories that are disposed of are ones devised by Leggett. Moreover, on page 3 of the article, the authors recognize that while their work indeed rules out a vast class of non-local hidden variable theories, it does not rule out Bohmian mechanics. So it is disingeneous to use this article to discredit Bohmian mechanics. The work in the article is however very valuable since it puts more strict constraints on the type of non-local hidden variable theories that can reproduce the results of quantum mechanics. This is an interesting question that is also discussed in the excellent book Quantum Paradoxes by Yakir Aharonov and Daniel Rohrlich. In one of the later chapters, they discuss the very special nature of non-locality in quantum mechanics, pointing out that there are many varying degrees of non-locality which are either stronger or weaker than the non-locality of quantum mechanics. They say it is still an open problem to find a precise characterization of the nature of quantum non-locality which could be turned into a postulate from which quantum mechanics could be derived in a way analoguous to the way special relativity is derived from its basic postulates.

• Now, about Bell's theorem. I'll quote a piece of the following article which itself refers to a thought experiment proposed by Tim Maudlin. Of course, you'll recognize it is a variant of an EPR type experiment.

Here is a puzzle: two persons, call them $X$ and $Y$ , leave a room through opposite doors; at that point, each is asked a question. The precise nature of the questions does not matter, but there are three possible questions (say, $A$, $B$ and $C$). Each person must answer yes or no. This “experiment” is repeated many times, with sometimes the same question, sometimes diﬀerent questions being asked at the two doors. The two persons are allowed to decide, before leaving the room, to follow any strategy they want, but not to communicate with each other, after they have heard the questions. The statistics of answers have some strange properties. First of all, it turns out that when the two people are asked the same question, they always give the same answer. Is that mysterious? Of course not; they simply decide, before leaving the room, to follow a certain strategy: for example, to both say ‘yes’ if the question is $A$, ‘no’ if the question is $B$ and ‘no’ if the question is $C$. Altogether, there are $8 = 2^3$ different such strategies. Before proceeding further, the reader has to answer for himself or herself the following question: Is there any other way? Is there any way to account for the perfect correlations between the results at the two doors without assuming that the answers were predetermined (if we assume that the people cannot have any communication whatsoever with each other once the questions are asked)? I have never seen any suggestion of another possibility and I believe that if Bell’s theorem is arguably the most widely misunderstood result in the history of physics, it is precisely because this question is not answered before proceeding further.

So, let us consider, for the time being, the assumption that the answers are predetermined and let us call $v_i(\alpha) = \pm 1$, $i = X, Y$ , $\alpha = A, B, C$ those answers. These are “random variables”, namely they may take diﬀerent values when one repeats the “experiment”. However, if one looks at the statistics of answers when diﬀerent questions are asked at the two doors, one ﬁnds that the frequencies of the events in which the same answers are given is 1/4. And this, combined with the perfect correlations is strange. Indeed, a version of the no hidden variable theorems (similar to the one discussed in the previous section), known as Bell’s theorem.

I'll leave out the proof, you can read it for yourself in the article. It is just the usual Bell type inequality.

What is the conclusion of all this? We started from one crucial assumption: absence of “communication” between the two persons once they are asked the questions. I will from now on revert to a less anthropomorphic language and call this assumption “locality” – assume that there is no causal connection whatsoever between the two wings of the experiment. Then, we are led to a contradiction, so that this assumption has to be dropped. It is important to understand the logic of the argument: the perfect correlations plus the absence of communication (i.e. locality) between the two wings of the experiments, leads us to postulate the existence of the variables $v_i(\alpha)$ [...]. However, merely assuming that those variables exist leads to a contradiction with the experimental results obtained when different questions are asked. To put it simply: locality plus perfect (anti)correlation implies hidden variables; however, the latter plus statistics when different angles are measured implies a contradiction. Both the perfect correlations and the statistics for diﬀerent angles are empirical results; the theorem is a theorem, namely a logical deduction; the only assumption was the lack of “communication”, or locality. Hence, locality has to be given up, period.

So, I'll stress again the most important point of this text: hidden variables are postulated to explain the correlations in the absence of communication (i.e. locality assumption). But this leads to a contradiction with the predictions of quantum mechanics. Quantum mechanics is right, we have tested it experimentally, therefore locality isn't right. I think that's fairly limpid. Anybody claiming that quantum mechanics doesn't force us to conclude non-locality is the one who doesn't really accept quantum mechanics, contrary to what detractors claimed in point 1.

In his book Speakable and unspeakable in quantum mechanics, which is really a collection of Bell's papers, there are various presentations of the theorem, some of which are clearer than others. Another book which does a good job at explaining the interpretation and consequences of Bell's theorem is Tim Maudlin's Quantum Non-Locality and Relativity.

• And I've barely addressed Bohmian mechanics yet and the question of the OP. Why do people still work on Bohmian mechanics? Well, the original intent of EPR was to show that quantum mechanics is incomplete. EPR showed that assuming locality inevitably leads to hidden variables, which is the first part of the previous argument. But the second part of the argument, provided by Bell shows that this is inconsistent with quantum mechanics. Therefore locality can't be right. One might wonder, even if we have to drop locality, why insist on supplementing the theory with hidden variables?

It's important to understand that the only variables added in Bohm's theory are the positions of particles. There are no hidden variables for spin, momentum, angular momentum, etc... It does however explain how the measured values for spin, momentum, etc... arise from the specific experimental configurations. This is what is called contextuality and has already been mentioned by @Sina Salek. Non-locality is explained by the fact that the wave-function is a function on configuration space and not in physical space. Hence the possibility of entanglement. You can read more as well as find further references in the article I mentioned.

Beyond the fact that Bohmian mechanics makes the non-locality in quantum mechanics more explicit, it also provides a deterministic interpretation of quantum mechanics, showing that quantum mechanics does not force randomness upon us.

Now, wether one likes Bohmian mechanics or not, one can not deny that these are definitely strong points of the theory. However, it does have its weaknesses as well. As @sb1 mentioned, Einstein thought it was cheap and in a way, I do agree that the way the extra equation for the positions is added is rather cheap and even ugly. It does also have its fair share of problems, for instance in trying to generalize into a QFT.

Anyway, I leave this link containing a short exposition of Bohmian mechanics and further references.

• Finally, I want to address @Matt Reece about QFT and locality. I'm no expert in QFT, but I do remember that locality is imposed on the level of operators by requiring that two observables localized within distinct space-time regions should commute. I'm not entirely sure what this implies w.r.t. entangled states, but I suppose it doesn't rule them out otherwise QFT would be in contradiction with experiment. (I wonder though if there is a complete treatment of entangled states within the context of QFT?) But if entangled states are allowed, then violations of Bell type inequalities still are possible and thus non-locality is a fact. What this means is that whatever the status of the principle of locality in QFT, it's a weaker form of locality than the one required in setting up Bell's inequalities.
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This is just completely wrong. The theorem has more assumptions than just locality. The fact that its conclusion fails in reality doesn't mean locality has to be dropped. Rather, it means that one of the assumptions has to be dropped but it doesn't tell us which one. Why do you completely ignore this basic fact of logic? – Marek Mar 18 '11 at 21:57
See also the article at wikipedia: en.wikipedia.org/wiki/Bell%27s_theorem Not that I agree with everything they say over there but that article is pretty good, including the bottom line: "...as it implies that quantum theory must necessarily violate either the Principle of locality or counterfactual definiteness." Notice the or in this sentence ;) – Marek Mar 18 '11 at 22:00
Nope... you didn't read what I said. Locality is the most important assumption. Hidden variables follow from that assumption. This was already understood by EPR. Bell went one step further and showed that these hidden variables can not explain the correlations of quantum mechanics, therefore the assumption of locality from which they arose is wrong. Please, read the article and don't just say I'm wrong. – Raskolnikov Mar 18 '11 at 22:05
Quote from the article:"The reason for this misunderstanding is probably historical: the ﬁrst part of the argument (locality implies hidden variables) goes back essentially to Einstein, Podolsky and Rosen in 1935. But they did not put it this way and were certainly not interested in showing that the world is not local. On the contrary, they assumed (as if it was obvious) that the world is local and concluded that quantum mechanics is incomplete, namely that hidden variables must exist. As a logical reasoning, it was perfect. But Bell’s theorem was proven only in 1964, almost" – Raskolnikov Mar 18 '11 at 22:07
"...almost thirty years later. It showed that the hidden variables, whose existence was implied by the “obvious” assumption of locality made by EPR, led to a logical contradiction. However, between 1935 and 1964, the majority of the physics community became convinced that Bohr had satisfactorily answered Einstein [...] The upshot is that Bell, who of course knew and understood the EPR argument, took it as his starting point and proceeded to disprove the existence of those hidden variables, hence of locality." – Raskolnikov Mar 18 '11 at 22:09

When we talk about ruling out hidden variable theories, we basically mean non-contextual or local hidden variables, whereas Bohmian mechanics for instance is highly non-local and contextual.

For the details of contextuality see http://arxiv.org/abs/quant-ph/0406166

Or if you're particularly interested in Bohmian mechanics can watch these lectures: http://pirsa.org/C11001

I personally think Bohmian mechanics isn't the nicest formalism you can get, but as a physicist, I wouldn't reject a theory only on the aesthetics grounds!

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Dear Yayu, I am afraid that this question of yours, while excellent, could belong to a psychology forum.

Feynman's perspective was already totally sensible; however, since his death, an amazing sequence of ever more straightforward proofs that hidden variables can't exist has been found.

Let me mention the GHZM state, Hardy's "paradox",

and various experimentally realized thought experiments disproving various theories of "nonlocal realism" as well, see e.g.

http://arxiv.org/abs/0704.2529

The idea that the probabilistic nature of quantum mechanics is due to the hidden variables was indefensible when Feynman was writing his lectures in the 1960s, and maybe even in the late 1920s when quantum mechanics became settled. But it is much more indefensible today.

I am not sure whether I fully understand your proof but it is possible to describe the experimentally validated proof in similarly simple terms. Quantum mechanics remains unacceptable for many people, for quasi-religious reasons. But as Sidney Coleman said at the end of his excellent lecture,

http://motls.blogspot.com/2010/11/sidney-coleman-quantum-mechanics-in.html

in which he described the conceptual issues of QM very clearly, it's time for those people to seriously consider the hypothesis that quantum mechanics is really how the world works. Well, the lecture is 17 years old by now, too, indicating that the opposition to quantum mechanics will never disappear.

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Unfortunately, just reading the abstract of the paper you mention, the authors already fail at understanding Bell's theorem. Bell's theorem does not discard realism. It only discards locality. Bell had to reiterate that point many times over during his lifetime. Most misunderstood physicist ever. – Raskolnikov Mar 17 '11 at 18:31
You still haven't answered his question on why people still talk about non-local hidden variables such Bohmian model! So are you saying even contextual hidden variable theories are impossible? And based on what? – iii Mar 17 '11 at 18:31
@Raskolnikov, what Bell's theorem discards is "local realism." This doesn't mean giving up locality, if you are willing to give up realism. Of course, this is what quantum mechanics (especially quantum field theory) tell you that you should do. (Also: given that Zeilinger is among the authors of the paper Lubos linked, it seems a bit rash to accuse the authors of not understanding quantum mechanics on the basis of their abstract alone....) – Matt Reece Mar 18 '11 at 2:08
@Raskolnikov: what the hell are you talking about? Bell theorem doesn't discard anything. It just tells you that locality and hidden parameters are incompatible. Whether you choose to discard realism and retain locality (which is most sensible and what most people do) or discard locality and retain realism is totally up to you. – Marek Mar 18 '11 at 16:12
@Raskolnikov: I have read many (but not all) of Bell's articles in that book. While his inequality is important, I disagree strongly with his interpretations of it and of quantum mechanics in general. He seems to view everything through the lens of wanting hidden variables to work (and of a strong affection for Bohmian mechanics). At times he even wrote that Bell's inequalities imply an incompatibility of QM with relativity! This shows that he failed to really understand the lessons of quantum field theory (despite making important contributions to it himself). QFT is very much about locality. – Matt Reece Mar 18 '11 at 16:16

Bohmian mechanics is a non-local hidden variable theory. It can reproduce the results of ordinary quantum mechanics. Since Bell's theorem and the subsequent experimental verdict ruled out only local hidden variable theory, Bohmian mechanics can still survive in principle.

In reality however it survives due to a different reason as pointed out by Lubos. The reason is essentially regressive. People for whom it is hard to swallow the hard reality of quantum mechanics, people who want to understand nature in terms of every day classical intuitions are the ones who often advocate Bohmian mechanics. IMHO it is extremely difficult for a physicist to support this approach. Why? The reasons are as follows.

1. It violates Occam's razor by introducing extra equation in addition to the Schrödinger's equation.
2. It is explicitly nonlocal and inconsistent with special relativity.
3. It can not be extended to produce a quantum field theory.
4. It is an unnecessary superstructure over ordinary quantum mechanics.
5. The quantum mechanical spin becomes terribly messed up in this approach.

In short it is a cheap alternative to ordinary sane quantum mechanics.

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That "no real physicists can support this approach" is a little bit extreme, don't you think? Is Bohm a real physicist? – MBN Mar 18 '11 at 4:18
Oh, this is a common misconception that people think Bohmian mechanics contradicts relativity and cannot be made relativistic! Bohmian mechanics preserves no-signalling theorem. This is one example, although there are many of these arxiv.org/pdf/quant-ph/0303156v2 – iii Mar 18 '11 at 8:22
@Sina: Advocates regularly make such wrong claims. It is not new. If it were true then we should have seen a complete formulation of Bohmian quantum field thoery by now. The fact is that it is undeniable that Bohmian mechanics is explicitly nonlocal. What you do here can affect some thing there. Nothing can hide this nonlocality. – user1355 Mar 18 '11 at 8:38
Bell's theorem implies that nature and quantum mechanics are both non-local. Bohmian mechanics makes this explicit. This is a merit of the Bohmian picture. Remarks 1 and 4 are silly, like MWI is not violating Occam's razor? I do agree that it is troublesome to develop a QFT in Bohmian mechanics and that this is an important reason why progress has been slow in that venue. – Raskolnikov Mar 18 '11 at 12:34
@Raskolnikov: Nature is not non local, neither is quantum mechanics. This is just one of the many misconceptions people have about qm. Entanglement does not imply non-locality. It just implies, if the world were classical then the EPR effect would have been non-local. But we don't live in a classical world. We live in a quantum world and there is no non-locality. There is only quantum correlations. Also, I would advice you to study the links as given by @Luboš Motl – user1355 Mar 18 '11 at 12:45

There's a seemingly 'unknown' argument in this discussion to my eyes, for it seems to always be left out in these discussions about Hidden Variables Theories. I wrote about it (in pt_BR, but Google Translate is your friend ;-) some time ago: it's the Kochen-Specker theorem and the The Free Will Theorem (together with its stronger form, The Strong Free Will Theorem).

Essentially, here's the punchline: Hidden Variables Theories hinge on two hypothesis, (1) all hidden variables have a definite value at all times; & (2) these variables values are "intrinsic" and independent of the measuring device used to detect them (aka "observable"). The Kochen-Specker Theorem is a complement to Bell's Inequalities and it proves that there is a fundamental contradiction between the two hypothesis above: in QM, observables do not need to be commutative (by hypothesis, a commutative algebra underlies hidden variables theories). In this fashion, as the Free Will Theorem is a based on the Kochen-Specker one, it invalidates (under very reasonable physical assumptions) all hidden variable theories.

Given that i haven't slept in quite some time, it's possible that i haven't been all that clear above. In any case, i'm leaving a list of references that should hopefully patch this. :-)

### References

This list of references is by no means comprehensive, but it's extensive enough to give a glimpse into this discussion: the tip of the iceberg, if you will. Also, the 'level' of the refs varies a bit, some links are to Wikipedia and some are to published articles: i tried to use more rigorous refs for the trickier topics (whether or not i succeeded at this is anyone's guess ;-).

Hopefully, even if my answer did not connect all the dots, following these breadcrumbs can shed some light in this issue.

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Nice and informative, but what is you opinion about the question itself? Why do people still talk about Bohmina mechanics? – MBN Mar 19 '11 at 14:37
If the answer is informative, hopefully there's something to be learned from it — in which case my opinion is unnecessary: as the Marines say, "everybody has one and they all stink". People do stuff for all sorts of reasons… but, with some luck, after some time these things get sorted out in sciences… – Daniel Mar 19 '11 at 14:44
So it is an unnecessary temporary distraction, which hopefully will fade away with time? – MBN Mar 19 '11 at 14:49
@MBN: It's good to have a diversity of views and opinions… but Science is not exactly 'democracy', in the sense that there's a clear direction which is preferred: you can't choose to not "believe" or to have a "diverse opinion" about $2+2$; you can't have a "loud vocal minority" that doesn't endorse nor subscribe to basic arithmetic. On the other hand, it does take time to establish some facts across a large community, and all one can do is keep on teaching. – Daniel Mar 19 '11 at 14:59

For the same reasons as why people still talk about other theories which have been demonstrated to be flawed at some level. Classical mechanics is still useful and gives correct answers in it's regime, even though it's basic assumptions are totally flawed. It's relationship to the 'correct' theory can still be insightful and interesting.

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