Talk:De Broglie–Bohm theory/Archive 1

These are the "Old Comments" I archived from the main talk page, to make way for further discussion. Deadly Nut (talk) 14:06, 29 October 2008 (UTC)

Old comments
Excised text:


 * Although for a long time considered a pariah among mainstream quantum physicists, Bohmian interpretation of quantum mechanics has recently gained ground due to the unequivocal experiment that has resolved the controversy Copenhagen vs. Bohm interpretation. Reactions from the physics community are yet to be seen. The paper on crucial experiment corroborating Bohmian interpretation (or, more correctly, shaking the Copenhagen orthodoxy) can be seen at Los Alamos site: http://xxx.lanl.gov/abs/quant-ph/0310096 (one could also consider http://xxx.lanl.gov/abs/hep-th/0304105 )

The quant-ph paper is hardly a description of a crucial experiment shaking the Copenhagen orthodoxy. It is a theoretical study comparing one model of the two slit experiment with another. There are slight differences between the results, but that could easily be due to differences between the inexact models used in each case. They do not claim that the differences are physical, and the experimental data fits both models. The main point of their paper was a demonstration of non-locality in the Bohmian interpretation. -- Tim Starling 23:53, Dec 4, 2003 (UTC) --

Hmm...I'm not sure whether we're talking about the same thing. As I've read in the quant-ph article, the point is that non-locality is present even in the classical physics limit, ie. decoherence alone is not sufficient for explanation of quantum-classical "transitions", or "cuts" (in von Neumann's lingo). According to Copenhagen- there is not a single bit of quantum theory (ie. anything that characterizes QT as such) in the description of "classical world". And here, in Bohmian int.- it is.

Btw, as an aside: I'd say that the entire page on Bohmian int. is very poorly structured. Bohm's int. vs. Copenhagen (or quasi-Copenhagen as defined by Von Neumann and Dirac): ontological vs. epistemological; quantum potential/active information vs. ordinary wave-particle and probability waves; nonlocalicty vs. locality; wholeness vs. -I dont know how to call it: particulariness ?...is presented very poorly. In his posthumous book "The Undivided Universe", Bohm has (with Hiley, and, of course, in numerous previous papers) presented ellegant and complete description of the physical world. This description is in many aspects more satisfying than the prevailing one (and I'm not saying it's flawless or "perfect" since such notions are nonsensical). Just- the weigh of habit and pragmatism keeps people stuck to the old ways (they give good description- but so does Bohm). The only thing is that non-locality is almost "emotionally" unacceptable to the majority of working phsyicists. But- this is hardly an argument.

As I've said: this article "collapses" Copenhagen orthodoxy. And- the page on Bohmian int. really deserves (even without it) more. Now, he looks like some pop-guru, which is, probably, the perception of interested outsiders-but not the truth about a serious and testifiable physical theory.

Mir Harven


 * You've got to look closely at what they mean by the "classical limit". They don't mean using pre-quantum physics, like Zernicke decoherence or whatever. They just mean the probability density. See the paragraph under equation 14. They calculate this probability density using Bohmian mechanics, and observe that it is different to the probability density calculated using the standard decoherence picture. If you look at figures 1a, 2a, 2b and 2c, you see that the Bohmian mechanics result agrees with the standard result at the experimental scale. However I have to admit that I'm not familiar with Omn&egrave;s' work. To me, the phrase "Omn&egrave;s doubts that decoherence is the answer to loss of coherence" sounds like an oxymoron.


 * Please sign your entries with ~, which is automatically converted to a name and a date. -- Tim Starling 01:40, Dec 7, 2003 (UTC)
 * Hmm...first, I apologize for a belated answer-I was lost in a maze of other, more mundane interests. But-are you sure you got their contention right ? I'll try to summarize what I've read from (and I hope not into) their article:


 * their point is that Bohmian computation agrees with the experiment (addressed earlier, at the beginning of the "Results" chapter, just below eq. (14).). So, we must stress that it's the results of the experiment they're trying to explain, not just an exercise in one way of computation or another (or, more precisely, one formalism or another). To repeat: they try to reproduce the results of the experiment.


 * they do it in two ways: Bohmian and "orthodox" (in a relaxed sense-but it is still orthodox; works by Zurek and others, i.e. references 2 and 3 in the article). Understandably, orthodox (or, better, ordinary) approach is within ordinary QM framework and doesnt employ specifically Bohmian concepts of quantum potential and active information. Just as an aside-one should mention that Bohmian approach is not new with regard to math formalism, but re interpretation of rather ordinary Sch. eq. (or, Ham.-Jac.), which simply gives a part Bohm had interpreted as quantum potential and developed a new view on QM with testifiable results. So, Bohm is (as anyone familiar with "The Undivided Universe" knows) not original re mathematical formalism (it's just a wave function in radial form, and Sch.eq. applied on it)-but in interpretation that denies central features of ordinary QM: no wave-particle dualism (electron is particle guided by quantum pot. field); no epistemological approach (i.e., quantum realism and ontology); and, most strikingly: non-locality vs. locality of ordinary QM (or any ordinary physical theory). Not to delve into intricacies further, what's at stake in this article is: there should be no non-locality in classical systems. And it is-according to the experiment and their Bohmian computation. But not in the ordinary decoherence framework. Look at this: "What it is remarkable is that this behavior even takes place in the case in which the coherence is completely lost (ô=0). This result is totally unexpected, and is due to the fact that the non–local behavior of quantum mechanics is preserved even in this case.This supports Omn`es’ suggestion that something else it is necessary, apart from decoherence, in order to make quantum mechanics exhibit a true classical behavior. In a Bohmian sense, even when interference e�ects are lost, still it is possible to distinguish between the result observed when the two slits are simultaneously opened, and those obtained from the sum of trajectories coming from each slit independently............


 * Conclusions. – By applying Bohmian mechanics to the paradigmatic two–slits experiment we have addressed a question raised by Omn`es about the possibility of decoherence theory to fully explain the appearance of classical behavior in a quantum system. Our results show that, although quantum statistics erases information about interference e�ects, there is still a strong non–local quantum correlation in the behavior of the system in the case of null coherence. This is due to non–locality in quantum mechanics, making that the probability density keeps information about the whole system. Such an information is “transmitted” to each particle, so that they “know” whether the other slit is open or not."


 * or, in everyday speech: decoherence approach (i.e. ordinary QM) doesnt explain non-local behavior of classical systems (quot. "there is still a strong non–local quantum correlation in the behavior of the system in the case of null coherence.") This non-locality is the feature completely absent in ordinary QM, and peculiar to Bohmian mechanics. What needs to be stressed again: they point to the results of the experiments-not just their calculations. More simplistically: the keywords are CLASSICAL SYSTEM and NON-LOCAL BEHAVIOR (experimentally measured). And this is explained only (in this case) within the conceptual apparatus of Bohmian mechanics, and NOT decoherence.


 * also- I do not see this corroborated by graphs, hence there is, IMO, discrepancy between their contentions and presented pictures.

Mir Harven 23:28, 13 Dec 2003 (UTC)

"It also differs in a few matters that are experimentally tested with no consensus whether the Copenhagen interpretation has been proven inadequate (and this inadequacy just glossed over due to inertia in physicist circles- not unlike the situation with cold fusion)" Excuse me, but isn't this a little bit biased of the author?

This page is a mess in explaining its subject. I edited it a little, tried to clarify. Still a mess, tho. 64.168.30.87 03:29, 24 Oct 2004 (UTC)

Here are some more archived comments. Deadly Nut (talk) 13:11, 24 November 2008 (UTC)

More old comments (24 November 2008)
These are comments which I believe have already been dealt with. If you feel there is further milage in them, please take them out of this list. Thanks. Deadly Nut (talk) 13:27, 29 October 2008 (UTC)

category change
Linas removed this article from [Category:Quantum mechanics] and added [Category:Quantum measurement]. I reverted that edit, and then he reverted mine, with a note asking not to revert his change without discussion. OK, I'm here. Why did you remove this article from the Quantum mechanics category? --goethean 19:17, 14 May 2005 (UTC)


 * Yes, I'm puzzled myself. The articles under the rubric interpretation of quantum mechanics now fall under quantum measurement. Though not quite utterly absurd, this reclassification is quite idiosyncratic.--CSTAR

Pseudoscience claim reverted and many-particle case modelled
Unsourced and probably OR claims reverted; they seemed mainly to be aimed at the lack of a many-particle treatment which is now present. --Michael C. Price talk 02:01, 6 August 2006 (UTC)

Everett's criticism
I've added Everett's critique of Bohmian mechanics:
 *  The Bohm particle(s) are not observable entities in the sense that we can remove them from the theory and still account for our observations, since Bohm regards the universal wavefunction as a complex-valued but real field. This was first noted by Hugh Everett whilst developing his many worlds interpretation of quantum mechanics, who showed that the wavefunction alone is sufficient explanation for all our observations.

All it needs is for a response to be added, which I can't do myself since I don't know of a valid rebuttal. --Michael C Price 14:29, 16 June 2006 (UTC)

Deleted "commentary"
I have delete the section "commentary" for the following reasons.

1:It is unverified.
 * It make a number of claims about the beliefs and opinions of physicists which are unsubstantiated

2:It is PoV
 * A number of the claims and clearly biased, implying motives and the like

3:It is essentially a personal essay
 * Whilst fascinating, Wikipedia does not publish original thoughts and research.

Jefffire 11:35, 14 December 2006 (UTC)

Seen as isomorphic to many worlds
The section with this title in the article is signed; that isn't normal, is it? Mcswell (talk) 00:26, 21 May 2008 (UTC)
 * It is not signed. Someone (not me) has copied a section from a FAQ I wrote into the article, and the reference includes my name.  I'll remove my name from it.--Michael C. Price talk 10:05, 21 May 2008 (UTC)

For archived comments, see /Archive 1 Deadly Nut (talk) 13:27, 29 October 2008 (UTC)

Old comments
In my view the comments in this section have already been dealt with. If you feel there is still life in any of these topics, please take it out of this section and place it in the main body of the talk section.

Bell
There's a lot of stuff about Bell appearing that should really be in the Bell's theorem article. --Michael C. Price talk 23:32, 22 August 2006 (UTC)
 * I'm ging to delete it unless its presence is explained. --Michael C. Price talk 01:36, 24 August 2006 (UTC)

Hidden variables merge
Anyone object to merging Hidden variable theory into this article? It was what Bohm originally called his theory. --Michael C. Price talk 01:36, 24 August 2006 (UTC)


 * I see someone is of the opinion that this shouldn't be called "hidden variables" and has removed some references to the term. Well that's what Bohm called it originally -- and how it is often called -- so we should mention it, even if John Bell thought otherwise.    --Michael C. Price talk 20:14, 26 August 2006 (UTC)


 * I personally think that there is a difference between the Bohm interpretation, which is one HV theory, and Hidden variable theory, which summarises several. Anyway, as there has been no movement on this in 2 years, I'm marking it as 'old'. Deadly Nut (talk) 08:24, 14 December 2008 (UTC)

Completed points from 'Sfwild's comments'

 * can be thought of as taking its cue from what one sees in the laboratory, say, in a two-slit experiment with electrons.

--- This is false. Bohm's interpretation, written after his textbook on QM, takes as its starting point certain fundamental shortcomings of the standard interpretation, and attempts to resolve the antinomies btw. Schrödinger wave equation and the Bohr-Heisenberg interpretation of such in terms of pure probabilities, e.g. radical and "unaccountable" indeterminism, or what Bohm calls "irreducible lawlessness." ---
 * I've removed this text. Deadly Nut (talk) 12:32, 26 November 2008 (UTC)

We can see localized flashes whenever an electron is detected at some place on the screen. The overall pattern made by many such flashes is governed by a pattern closely matched by simple wave dynamics. Bohm and de Broglie posited that in the world of quantum phenomena, every kind of particle is accompanied by a wave which guides the motion of the particle, hence the term pilot wave.

Note that Bohm only uses the term "pilot wave" when referring to de Broglie's work.
 * I'm removing this term as I edit that part of the article. Deadly Nut (talk) 12:32, 26 November 2008 (UTC)


 * Mathematically, the pilot wave is described by the wavefunction of conventional quantum mechanics, but with an added piloting influence on the motion of the particles. We can formulate the pilot wave's influence using a wavefunction-derived potential called the quantum potential,

The wavefunction of the early Bohm (the 50's) is virtually the same as it is for all interpretations quantum mechanics: basically it’s the S. equation. To that de Broglie first adduced the concept of the "pilot wave" which is somewhat reinterpreted by the early Bohm in terms of the "quantum potential” Mathematically it doesn't make any difference whether you add the quantum potential or not.


 * Which acts upon the particles in a manner analogous to the interaction of particles and fields in classical physics.

I don't know what the writer is saying here: that the effects of the quantum potential are analogous to classical field theory? Nothing could be farther from the truth; that's why Bohm found himself not only, in the end, dissatisfied with the paradoxes of the Copenhagen Interpretation, but even felt the need for a "new order" of physics, what he calls early on the "subquantum order," and which he would call later the "implicate order." There is no analagon in classical physics for any of this.
 * I've removed this. Deadly Nut (talk) 12:32, 26 November 2008 (UTC)

The pilot wave governs the motion of the particle and evolves according to the Schrödinger equation. Unlike the Everett many-worlds interpretation, the Bohm interpretation does not assume that the universe splits when a measurement occurs,

Why is the writer talking about Everett here? It is a digression and has no place except perhaps in a footnote...assuming that what the article is trying to do is present Bohm's interpretation in an objective, informed manner. Everett many worlds interpretation can some relation to Bohm's later cosmological thinking, but has no bearing on Bohmian Mechanics per se.
 * I've removed this, but not the comparison with the Copenhagen Interpretation, because Bohm made the comparison explicitly. Deadly Nut (talk) 12:32, 26 November 2008 (UTC)

Two-slit experiment
Thus, in this theory all fundamental entities, such as electrons, are point-like particles that occupy precisely defined regions of space at all times. When one performs a double-slit experiment (see wave-particle duality), one is concerned with noting the positions on a screen at which electrons arrive individually, one at a time. Over time, the positions at which the electrons are detected build up a pattern characteristic of wave interference. The usual Copenhagen interpretation is puzzling in that a single entity, the electron, is said to exhibit characteristics of both particle and wave. The Bohm interpretation accounts for the same phenomena by saying that both a particle and a wave do exist. The particle aspect is present because each electron traverses one slit or another, but never both. The wave aspect is present because the electron's pilot wave traverses both slits.

-- Ok, as far as this goes, but this paragraph has more to do with double slit experiment itself, and de Broglie's early interpretation as opposed, say, to Bohr's notion of complementarity. --

Thus, the Bohm interpretation resolves the puzzle quite simply and naturally. The electron's motion is guided — both in its choice of slits and its subsequent trajectory towards the screen — by the wave. The characteristic wave-interference pattern seen in the detection of the electrons arises by considering that the guiding wave exhibits interference in the familiar way one learns in the elementary physics of waves.

--- It's not so simple. What you have is S's wave equation+Heisenberg probabilities+what Bohm calls quantum potential. These are not classical waves after all. ---

One might also note that what is measured in such an experiment — the position on the screen at which each electron arrives — is itself none other than the "hidden variable" the Bohm interpretation adds to the description, as we show in the formulation below. --- How does the writer get this? Is he saying that the experimental data=the hidden variables? I think he misses the point---

It might seem that the term "hidden variables" is an inappropriate name for the positions of particles, the quantity that is apparently most conspicuously manifested in the experiment. However, the particle's position has no influence on the guiding wave and hence is unobservable or "hidden" in some sense (see criticisms). --- "Hidden variables" does not designate "positions of particles" as writer believes. And these in turn certainly do not correspond to quantities "conspicuously manifested in the experiment." Writer would make Bohm into a naive and "deterministic" realist.


 * I've rewritten this section. Deadly Nut (talk) 12:41, 1 December 2008 (UTC)

Nonlocality
Now we must address the question of nonlocality.

-- "One must"... "Now we must address"... Editor please!-- --

Within Bohm's interpretation, it can occur that events happening at one location in space instantaneously influence other events which might be at large distances: thus we say that the theory fails to obey locality, i.e., it is non-local. The response many physicists have to Bohm's theory is often related to how they regard this concept.

--This is a gross generalization of the role of non-locality in Bohm's thinking. Since one has to address the issue, why not start with EPR?--

The question of nonlocality hinges upon the attitude one takes towards the Einstein-Podolsky-Rosen paradox and Bell's theorem (see p.14 in ).

--Talk first about non-locality, intent of EPR thought experiment, Bohm's interpetatation, and then talk about Bell--

There are often two camps into which people fall regarding the issue.

--That may be true, but first explain the issues--otherwise it's all hearsay---

According to one camp, it has been shown that quantum mechanics itself is nonlocal and that this cannot be avoided by appealing to any alternative interpretation. The same Bell responsible for Bell's theorem was a member of this group (p. 196 in ): "It is known that with Bohm's example of EPR correlations, involving particles with spin, there is an irreducible nonlocality." If this is indeed the case, then the nonlocality of the Bohm interpretation can hardly be regarded as a strike against it.

--Logic? Writer identifies one "camp" with some off the cuff comments from Bell here to the effect that all quantum mechanics is non-local in order to question relevance of Bohm's model?--

Others see the consequences of EPR and Bell's theorem in a different way. They regard the correct conclusion to be related not so much to quantum theory itself, but only to deterministic interpretations of the same (i.e., to hidden-variable theories such as Bohm's interpretation).

--Again, writer makes the mistake of equating the "Bohm Interpretation" with early hidden variable interpretation with a "deterministic interpretation." I doubt he has read much Bohm, because if had, he would realize that this is a gross oversimplification

According to the people who think this way, what has been shown is that all deterministic theories must be nonlocal. For example, Niels Bohr was a member of this group.

--all very fuzzy. Bohr himself never advocated non-locality; his objections to the "thought consequences" of EPR had more to do with his appreciation of the "wholeness of the quantum phenomenon"--

This group would claim that retaining orthodox quantum mechanics — with its probabilistic character — permits one to retain locality, or at least to avoid the EPR type of nonlocality, at the expense of having no way to picture particles as objective elements of reality that occupy definite regions of space at all times. Armed with such a viewpoint, these physicists tend to be less receptive to Bohm's interpretation.

This simply doesn't follow. Is he saying that the same folk who believe all deterministic theories are non-local (not so many actually) are the ones who favor the probabilistic character of the standard interpretation? It's true that in the Bohr-Heisenberg approach, what Einstein called "spookiness" of non-locality is avoided, but there are deeper things going on...  Whole discussion dividing discussion into two camps, and then misinterpreting the viewpoints of each camp, trivializes a very important chapter in the history of QM. And then what about Vigier, and the Alain Aspect experiments and such? Not a word

Sfwild 04:11, 11 June 2007 (UTC)

I've rewritten the section on Nonlocality, and named it EPR, to fit the logic of the article better. I've also added a mention of Alain Aspect's work. Hopefully this addresses most of Sfwild's comments on the section. Deadly Nut (talk) 10:44, 2 December 2008 (UTC)

I edited the EPR section softening the language "Bell shows" -> "Bell asserts/argues". Bell's arguments rely on a proof by contradiction. Deriving a contradiction does not "show" which of the set of mutually inconsistent premises is false. It shows that one of them is. That one need not be locality hence he has not "shown" non-locality in QM. Indeed the choice of "which assumption to keep" is intimately tied to the choice of interpretation. Regards, James Baugh (talk) 16:42, 14 July 2009 (UTC)

A Non-Specialist Writes
I am not clear as to where Bohm's theory stands at the moment from this article. If its not been 'proven experimentally' or rather, as the articles suggests, its been disproven experimentally, then presumably its dead? Or is it the case that no Theory, including the Copenhagen and Multiple Worlds Theories have been proven experimentally either?

Also, the article suggests that Bohm viewed the theory as a starting point for experimentation rather than a finished theory. If he thought it could be adapted/enlarged then presumably it isn't dead?

Also, as a real non-Specialist, for a knuckle-head like me, is the Theory basically saying that everything is exchanging 'information' with everything else through waves and thus interacting in a way which is not dependent upon measurement and 'wave collapse'?

If this theory is 'disproven', where does that leave Bohm's other ideas? ThePeg (talk) 17:49, 16 November 2008 (UTC)


 * Presumably the article is not being clear enough; Bohm's theory is an interpretation, so it is neither dead (disproven) nor alive (proven over the alternatives) but rather in a state of limbo with many others. --Michael C. Price talk 19:18, 16 November 2008 (UTC)


 * I think ThePeg has an important point - thank you. I've tried to highlight this at the highest level of the article.  I've also tried to clarify the basic ideas of the theory, and to remove the Benefits section, which should now be represented in the section labelled Results. Because I've changed the content of Benefits quite drastically, I've removed the POV notice - please reinstate it if it still applies. Deadly Nut (talk) 13:01, 24 November 2008 (UTC)

Critcism ? Or ignorance
Although personally I dont think Bohmian interpretation will bear much fruit-when criticised, it must be on fair basis. And, at least half of "criticisms" are, to put it mildly- lame. I've deleted, now, only the 1st point, since "inelegance" is personal preference, and, judging from the majority of opinion- this would be the last objection re Bohmian view. As for redundance-current physical theories are full of variables that are not directly verified and are props that may very well turn out to be just concoction: for instance, Higgs boson and dark matter. Other cristicism will be reviewed in due time, but, weaknesses of Bohm's interpretation cannot be addressed in such a manner, teeming with half-truths, since Copenhagen formulation abounds with even more "unacceptable" or concocted notions (anyone remember problems with classsical-quantum division, "healed" by Bohr's Correspondence pronciple-pure scholasticism, not provable at all). Bohm's "sin", if any, is that he was too timid and not radical enough. Mir Harven 12:57, 29 Oct 2004 (UTC)

Everett's Criticism
The response to Everett's criticism looks like original research, with the claim that Everett's theory requires extra assumptions -- also such issues about other interpretations should really be dealt with on their respective talk pages (e.g. Talk:Many-worlds_interpretation) rather than here, so I propose we delete this claim.

Focusing on Bohm's theory and role of the particles, I don't think the response actually addresses the issue of the unobservability of other universes (empty parts of the universal wavefunction), although of course adherents of the various interpretations are never going to agree about this. Can we say that followers of Everett (who hold the non-collapsing wavefunction is sufficient to account for all observations) see the Bohm particles as superfluous, whilst others regard them as necessary to realise one possibility from amongst many? --Michael C. Price talk 21:21, 1 October 2006 (UTC)

The response is not original, just a brief summary of Bohm's own critique of MWI. See e.g. §13.6 of The Undivided Universe:


 * If we adopt DeWitt's approach, then, as we have seen, it is necessary to supplement this with some further principles involving an as yet unavailable definition of complexity and further equations determining just how this would determine the splitting of universes. On the other hand, if we adopt Everett's approach or indeed that of the many-minds interpretation, we have to do something similar with regard to the splitting of awareness. In this connection a complete and consistent expression of these interpretations would, as we have seen, require new principles and assumptions of a speculative nature going beyond our present knowledge of awareness and its possible relationship to Hilbert space. (p. 315)

Regarding how one possibility is realized from among many, it would be misleading to give the impression that one theory needs to explain this and the other doesn't. Both Everett and Bohm recognized that they have to explain it, they just did so in different ways. Everett used the splitting of universes (or awareness), so he didn't need the particles. Bohm used the particles, so he didn't need the splitting. Any comparison of the two theories ought to bring out this parallelism. —Were-Bunny 17:16, 9 October 2006 (UTC)


 * Thanks for supplying the Bohm quotation, this demonstrates that this particular claim about the necessity of particles is not original research -- what it doesn't show is that this is universally accepted, especially by adherents of other interpretions (as you would expect). Hence the qualifer "in Bohm's view" is required to WP:NPOV it.  --Michael C. Price talk 00:01, 10 October 2006 (UTC)

Bohm's interpretation is not universally accepted, so it is highly unlikely that his views on this particular point (or any other point) of his interpretation are universally accepted. But that's irrelevant to the issue at hand, which is the question of how Bohm responded to Everett's criticism of the Bohm interpretation—i.e., a question about what Bohm thought, not aboout whethter others agree with him. If universal acceptance were the requirement for explaining the features of the Bohm interpretation, the whole page would have to be empty. Since The Undivided Universe is Bohm's most authoritative work on his interpretation, no further evidence of his views is needed here. Furthermore, the redundant qualifiers ("in Bohm's view," "Bohm maintained that," "in Bohm's view") also are not needed because the reader already knows that the whole page reflects Bohm's views, except where otherwise noted. A qualifier is needed only once following someone else's views, to alert the reader to the transition. —Were-Bunny 22:12, 10 October 2006 (UTC)


 * You misunderstand my point (or rather the Wikipedia guidelines). No one is saying that Bohm's views are inappropriate in the article -- but it must be made clear where they are Bohm's views and where they are views endorsed by the wider community.  All statements in Wikipedia articles should be explicit about their sourcing if challenged; the qualifiers are not redundant, placing a single qualifier is not sufficient since this article (like others) contains statements which vary with their acceptance from statement to statement.  --Michael C. Price talk 01:41, 11 October 2006 (UTC)

You are misapplying the Wikipedia guidelines in this case. This paragraph makes no mention of general opinion. It states that Everett made a criticism of the Bohm interpretation (e.g., that particles are not needed) and that Bohm responded to that criticism by explaining why they are needed. These are claims of fact, not opinion--i.e., the fact that Everett and Bohm did or did not make the respective statements. To verify the accuracy of these facts, all that is needed is to cite the appropriate writings of Everett and Bohm. Other people's acceptance doesn't matter because no claim is being made about whether the expressed views are generally accepted. If you think the paragraph makes some additional claim about general opinion, the burden is on you to point out specifically what it is. If there is such a claim, it should be clearly identified as such. At present it is not; all opinions are attributed to either Bohm or Everett. —Were-Bunny 20:01, 11 October 2006 (UTC)


 * I must have been unclear -- I have no problem with Everett's and Bohm's views being reported: it was those opinions that were not clearly attributed and that could be misinterpreted as general statements of scientific fact that concerned me. Best wishes, --Michael C. Price talk 20:10, 11 October 2006 (UTC)

You're being extremely vague and unclear. Please try to be much clearer. I've asked you to identify specifically which opinions you believe are not attributed to either Bohm or Everett. Please do so as clearly as possible. —Were-Bunny 16:46, 12 October 2006 (UTC)


 * I find your requirement rather odd. I have already corrected the article by adding the appropriate attributions, which you originally objcted to.  So to be completely explicit: I am happy with the article as it is since the questionable statements (i.e. opinions) are appropiately attributed.  --Michael C. Price talk 19:26, 12 October 2006 (UTC)

Criticism section
I am not sure if Bohmian mechanics are just really insecure, but the `criticism' section truly is a fiasco. Surely there is some Wikipedia policy or guideline against having criticisms each followed immediately after with a `response'. In many cases, moreover, the `responses' have a whiff of original research, or at least original syntheses from existing literature, and many of them don't actually address the criticisms in any meaningful way (probably because no such way exists). I don't want to edit the article and disturb the equilibrium that tends to develop around these sorts of topics, but could a regular please try to sort this out? Rosenkreuz 08:50, 11 January 2007 (UTC)
 * The point of the criticism section is to inform the reader: this is what the critics say, and this is how the adherents defend their position. Whether the responses are adequate is left for the reader to judge.  (I wrote one of the responses and I'm not a Bohmian.)--Michael C. Price talk 08:58, 11 January 2007 (UTC)


 * I understand as much. Only most similar articles don't have such `response' opportunities, I don't think...the reader judges the validity of the criticisms based on the content of the theory as discussed in the article itself, not on a list of possible fixes.  Having such a list, moreover, invites an endless cycle of criticisms and counters, surely?  It seems like a bit of a `POV-trap', to me, which is wide open to abuse. Rosenkreuz 09:07, 11 January 2007 (UTC)
 * Yes, but interpretations of quantum mechanics are a particularly controversial area, even amongst leading researchers who care to venture an opinion. Controversial topics often (but not always) have a criticism section.  That's not POV abuse, provided all viewpoints get to be expressed (whether or not they are valid -- which Wikipedia has no opinion about, of course). Any controversial subject will attract an endless cycle of criticisms and counters -- the criticism section is an attempt to channel this more productively. --Michael C. Price talk 09:13, 11 January 2007 (UTC)
 * I know that. I don't object to a criticism section at all: that much is necessary.  It is the responses which are misplaced, I think.  For example, the article on the relative state idea contains an `acceptance and criticism' section &mdash; which is good &mdash; but it doesn't have a list of comebacks by the Everites to every point raised in objection to the theory &mdash; and nor should it.  Why should the same rules not apply to the Bohm interpretation?  Rosenkreuz 09:19, 11 January 2007 (UTC)
 * Hmmm.. Heh, I helped write the MWI criticism section. I guess that section has a more unified approach than here.  I hesitate to remove the "response"s here because I'm sure someone will object.  And I admit I'm too lazy to do the complete rewrite you seem to be suggesting. --Michael C. Price talk 09:26, 11 January 2007 (UTC)


 * A nonspecialist reader says: the criticism/response format is VERY helpful; please don't delete it. —The preceding unsigned comment was added by 72.70.250.127 (talk) 02:26, 2 April 2007 (UTC).


 * I am not a physicist, either (not even an armchair physicist ^^), and while the "criticism" section certainly is interesting, I agree with Rosenkreuz that it's suboptimal at best - the way it's written gives undue weight to the Bohmians' responses by always letting them get "the last word". I think it'd be better to rewrite this section entirely, as an actual text instead of a bulleted list; I feel I'm not qualified to do it myself, but it definitely needs work, since right now, it reads as if it was lifted straight from a pro-Bohmian website. -- Schneelocke 17:31, 13 April 2007 (UTC)


 * I am a physicist but not an expert in Bohm mechanics. As a reader, I did get the impression that each point in the criticism section was rushed through, in order to get as fast as possible to the subsequent rebuttal of it. It is more sounding as a biased advocacy of Bohmian mechanics, whereby (unfortunately) criticism may be raised and must be rebutted immediatetely, than as a neutral exposition of different viewpoints. As it is, the section would be more appropriately entitled "Rebuttal of Criticisms" than "Criticisms". The rebuttals do sound as the central issue and reason of existence of the section. I agree that it is fair in general to have both the criticism and the rebuttal, but the section cannot stand in the present form (at least equal balance is needed). Overall, the whole article does not look as citing all necessary sources either (incidentally, not one single statement in the criticisms section is sourced, in either verse, thus raising doubts about WP OR policy issues). --209.150.240.231 01:05, 5 July 2007 (UTC)


 * I am a physicist, too, and I read various articles about different interpretations of quantum mechanics. Most of the critics in the criticism section show a misunderstanding of Bohm mechanics, and the "rebuttals" are more an explanation what Bohm mechanics really says. For example, look at the topic "scientific theory", "collapse", "observables", "non-locality", "spin", "decoherence", "quantum potentials and trajectories". All of these critics are based on misunderstandings of Bohm mechanics. I know it would be provocative, but replacing the header "Criticisms" by "Resolving misunderstandings" would be more accurate.87.163.97.82 10:54, 3 October 2007 (UTC)
 * More accurate, yes, but definitely more provocative. --Michael C. Price talk 11:45, 3 October 2007 (UTC)

I'd love to see a reference for each criticism and response. Some of the responses probably should have counter-responses too.--Per Abrahamsen (talk) 20:12, 19 May 2008 (UTC)

I agree with rosenkreuz above wholeheartedly. This section needs total cleanup. It's not written for readers but rather for people who like to argue. counter-responses would make it even worse. There is no reason to have more than one description per side, and even *that* is pushing it, since the *rest* of teh article should function as the "for" argument. Keep the pro-Bohmian stuff in the rest of the article. Make the critism section succinct and one sided, *unless* there is a very large and valid point that sounds more intelligent than "no, you're wrong", cause that's how a lot of the responses sound right now, simply stating taht the critisism is unfounded, and using lots of words to do so. —Preceding unsigned comment added by 84.12.134.165 (talk) 20:49, 19 May 2008 (UTC)

Criticisms section renamed as FAQ
I've rearranged this as a Frequently Asked Questions section, and tried to simplify (and shorten) the content. I have tried not to lose information in the process; however,


 * I really did not understand the last two points, and I have removed them. If either of these has a serious point, please reinstate it and rewrite the question (and preferably the answer) so I can understand it.  Thanks.


 * The last point says that Bohm's particles are not observable entities, but surely they are - what hits the detectors and causes flashes? After making the edit, I realised that Hugh Everett raised this point, so I need to take it seriously.  Does someone have a reference, to help me understand it?


 * Some of the points made look speculative.

Deadly Nut (talk) 09:20, 14 November 2008 (UTC)
 * Should I remove the style marker, or will someone else do that if the improvement is enough?


 * I will happily rewrite the answers of the two points you deleted, if you would be so kind as to reinstert the text. As for a reference for the last point (Everett's criticism), you will find that elsewhere in the article, but I am happy to add that as well to the reinserted text when it reappears. --Michael C. Price talk 11:22, 14 November 2008 (UTC)
 * Thank you for the offer, Michael. I've reinserted the text. Deadly Nut (talk) 18:28, 14 November 2008 (UTC)
 * Okay, I see the text. I like the way you phrased the question -- I think I'll use that in the FAQ section. --Michael C. Price talk 21:03, 14 November 2008 (UTC)

Article Cleanup Co-Ordination Point
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 * the article is very short and might need expanding, removal or merging with a broader article

As part of the cleanup process, the automated bot PocKleanBot has generated this notice as a focus of cleanup efforts, and also contacted several contributing editors of the article to bring their attention to the problem. You should use this section to discuss possible resolution of the problem and achieve consensus for action. Only when there is a consensus that the article is now cleaned up should you then de-list it by deleting the cleanup tag from the article, this causes the article to drop off the monthly cleanup-needed list page.
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Discussion

 * }

Uhh, this request for cleanup is confusing and unclear. Is there some specific complaint? linas 04:39, 13 December 2006 (UTC)

Pockleanbot has been removed, so unless a real person has something to say, I'd say to ignore it. Fephisto 01:10, 14 December 2006 (UTC)

I restored the cleanup template (I was not the one who put it there the first time). The problem is the overall tone throughout the entire article. It's exceedingly didatical, in a manner that accentuates the "feeling" that the article assumes Bohm interpretation to be correct, and adds greatly to its POV. The problem is most obvious in (but not exclusive to) the Introduction and the Criticism section. It had been pointed out by others, albeit not in these words. Perhaps a complete rewrite or copyedit tag would be more appropriate. AoS1014 17:00, 19 May 2007 (UTC)

Sfwild's comments
Please find below general comments on the opening "Background" secion of article on "Bohm Intepretation"

There are big problems with this article!

I've moved some of sfwild's points, which I believe have been dealt with, to the 'old comments' section. Please bring them back if they are still current. Deadly Nut (talk) 08:24, 14 December 2008 (UTC)

Article name
The Bohm interpretation--

"The Bohm Interpretation" is not an accepted usage. Rather one speaks either "Bohmian Mechanics" (as they do in Europe) or one speaks of Bohm's early "Hidden Variables Interpretation," or a bit later, the "Causal Interpretation" or, finally, the "Ontological Interpretation" of QM. Sometimes one hears, in a more general way, of the "de Broglie-Bohm" interpretation. Not a good start!---

Causality and determinism
And unlike the Copenhagen interpretation it is both objective and deterministic. It says the state of the universe evolves smoothly through time, with no collapsing of wavefunctions. Thus, Bohm called the hidden variable or pilot wave the quantum potential force.

Here again, the author obviously misunderstands (or deliberately misleads?) the reader when he says, broadly, that the Bohmian interpretation is "deterministic." This may be to some extent true in the very early presentations, but after Causality and Chance, and throughout the middle and late period, Bohm is adamant that "causal" is not the same as "deterministic." Any accurate presentation of Bohm's theories needs to address this. Sfwild 04:11, 11 June 2007 (UTC)


 * I'll bear this in mind. For the time being, I've just substituted the word "causal". Deadly Nut (talk) 08:17, 3 December 2008 (UTC)
 * When Micheal C Price reverted this, I looked it up - I note that Holland (1993) describes the Causal Interpretation as deterministic, (but points out that there is a non-deterministic variant proposed by Bohm and Vigier in 1954). Deadly Nut (talk) 08:17, 3 December 2008 (UTC)

Vigier and Aspect
Is there anything published about Vigier and Alain Aspect with respect the Bohm interpretation?--Michael C. Price talk 16:14, 5 July 2007 (UTC)


 * There is too much published--Google it! Vigier worked closely with Bohm first in Brazil and then in regular collaboration during the summers in Paris.  They published a number of articles together, extending Hidden Variable approach.  In the European discourse, one hears all the time of the "de Broglie-Bohm-Vigier interpretation" or what is sometimes called the Causal Stochastic Interpretation of QM. The '82 Aspect experiments come right out of this approach. Note that results were first published as a realization of the ERPB (B=Bohm)Gedankenexperiment defined in terms of violation of Bell Inequalities.  The Aspect exeriments are important because they brought the discussion of non-locality out of the realm of the purely theoretical into the realm of the experimentally verifiable.  There is no shortage of literature on the subject.

Sfwild 15:52, 6 July 2007 (UTC)

It's an idealogical dispute, not an encyclopedia article
I think all this will be hopeless, this article is bounded to remain non-neutral forever, for reasons that have nothing to do with Science. I've been around in wikipedia lately and I can see perfectly well what's going on here and eslewhere. What is going on is that we have a worldview of philosophers who base all their speculations about what we are on the bet that the current understanding of quantum physics is completely wrong. This page is all too important to them, and it will always have support in a somewhat biased way. I see something weird. Arxiv papers put on a par with peer reviewed papers. That is telling. We have sixty years years of tons of published peer-reviewed work on the one hand, in the development of reliable quantum field theory that has made astonishing predictions and justified the attribution of a dozen Nobel prizes, against two non peer-reviewed Arxiv papers that we have to believe on faith. --Gibbzmann 03:20, 28 October 2007 (UTC)


 * I think Gibbzmann is right in that the debate here is embedded in deep ideological disputes, though what I find objectionable is the presentation of what is called the "Bohm interpretation" purely in terms of the rather limited approach of what is sometimes called "Bohmian mechanics." To argue, for instance, that Bohm's interpretation of QMis "deterministic" is to seriously misunderstand what Bohm is trying to say. It is, as it were, a naive misreading of the very early '52 papers. That is why I continue to believe the article should be re-written and the positions clarified as being not Bohm's interpretation but the derivative interpretation of some of his latter-day followers. In other words, pure POV. Bohm himself hated the word "mechanics" and almost never used it; he would certainly be shocked if someone informed him beyond the grave that his legacy is being so confused.

Sfwild (talk) 19:35, 25 November 2007 (UTC)


 * You're aware, of course, that those predictions are matched by the Bohm-de Broglie theory right? Also, I find it rich when defenders of orthodox (Bohr-Heisenberg) QM accuse others of letting unwarranted philosophical assumptions get in the way of the formalism. I'm not a Bohmian (Bohmite?), but this kind of attack is not very fair. -- Ekpyrotic866 —Preceding undated comment added 19:27, 8 June 2009 (UTC).

Gleason
The article about Gleason's_theorem seems to use quantum logic to imply that no hidden variables theories can exist. Is this tackled in the criticisms anywhere? —Preceding unsigned comment added by 65.96.162.192 (talk) 04:22, 22 February 2008 (UTC)

Article cleanup
I have cleared out the old comments in this discussion because I'm planning to make some improvements to this article. Here's what I'm planning to do:

Improve the structure. I suggest this contents list:
 * Overview
 * Background
 * Principles
 * Benefits
 * History
 * Beyond Bohm
 * Examples
 * The Uncertainty Principle
 * The Two Slit Experiment
 * EPR
 * Mathematical foundation
 * Bell's simplification
 * Bohm's formalism
 * Computational Bohmian Dynamics
 * Criticisms
 * See also
 * References
 * External links

Improve the History and Principles sections, with references.

Try to make sure that any subject discussed in this article has references to back it up.

The Criticisms section seems very long, and it has attracted a lot of criticism. Can we reduce it to those criticisms that are published?

Generally, make sure information is covered by references.

I'd be most interested in your feedback on this proposal, especially on the new contents list. Thanks. Deadly Nut (talk) 13:27, 29 October 2008 (UTC)
 * The Criticisms section has also attracted praise. Please try to improve rather than delete. Also note that a lot of science material in Wikipedia is unreferenced -- that doesn't make it useless or incorrect, just in need of a citation tag, perhaps. --Michael C. Price talk 05:16, 30 October 2008 (UTC)

Response
joliverst (talk 10/31/08) I have recently taken an interest in this page and would also like to change things.
 * I see you're much better qualified than me to do this. I've come to this theory recently, and was trying to take this article off the bottom rung, as a way to clarify my understanding.  Why don't you take the initiative here, and ask me for help if I can provide it.  I've started by researching the history, so I may be able to write something on that.  I've also written a rather brief piece on de Broglie's pilot wave theory recently (it was a stub before I did that).  it's a bit light on mathematics, because I haven't followed up the right references yet to be able to tell which were de Broglie's contributions and which were due to Bohm.  Perhaps you'd like to look it over. Deadly Nut (talk) 08:29, 5 November 2008 (UTC)

I would organize it as having the theory first. Start with the simple idea: this is a theory about particles whose motion is governed by the wave function. At all times, these particles have definite positions and velocities though they are generally inaccessible to measurement. Next state the simple formulation for R^1 with scalar-valued wave functions. Then expand to R^3N, then add spin-valued wave functions. Finish with words that this generalizes to very general spaces such as manifolds and sections of a vector bundle, giving a reference. I would not do Bohm's version here, but rather the simple version that generalizes, i.e., the velocity formula and Schrodinger's equation. The quantum potential part is unneeded and can be relegated to the history section.
 * Sounds like a good plan. Deadly Nut (talk) 08:29, 5 November 2008 (UTC)

One thing to get across is that this is a theory, not an interpretation. One should present as such. Is it possible to get this renamed? Bohm interpretation makes this into philosophy. It is not. It is a physical theory and it should be treated as such. It is distinct from quantum mechanics though they have the same empirical predictions, in as much as quantum mechanics has predictions.
 * I agree in principle; however, to be a distinct theory, it must be possible to prove that this is right and that the Copenhagen Interpretation is wrong. What tests would allow this? Deadly Nut (talk) 08:29, 5 November 2008 (UTC)
 * I agree that the name looks wrong; I gather Bohm wouldn't like the current name. However, I don't see a consensus on what's right.  My nomination is the De Broglie-Bohm theory, but I'd guess you'd prefer Bohmian mechanics. They both get forwarded to the right place. Deadly Nut (talk) 08:29, 5 November 2008 (UTC)

I would also recommend removing the criticisms. If there are places where this is located, then point there. If not, perhaps one should write a paper, get it published, and point there. I would rather see that the points that need to be made to defend against criticisms be made simply in the article as relevant without it being from a defensive posture.
 * I agree in principle. However, (1) there are criticisms made by Pauli. von Neumann and others that are part of the history.  Also, (2) I note Michael C Price's response that people find these critcisms useful.  My inclination is to keep them for the time being as "frequently asked questions", and try to condense them.  Later when the article is superbly clear and well structured, we won't need them.  At the moment, I feel the criticisms are a disproportionate percentage of the article. Deadly Nut (talk) 08:29, 5 November 2008 (UTC)

On the same note, I would think that a Benefits section is also inappropriate. It is a theory, state what it is, where it came from, and what it does. Let others draw the conclusion as to why it is useful. You can mention in the history a few of these things, but minimal is better.
 * I agree - I was keeping it in only because I wanted to remove it later rather than now.

My ordering:


 * The theory
 * Intuitive ideas
 * Single particle on a line
 * Spin-less particles on R^3
 * Spin
 * Generalizations
 * Understanding Quantum Mechanics
 * The Uncertainty Principle
 * The Two Slit Experiment
 * EPR (Bell's version)
 * Identical particles
 * Measurement and Quantum Equilibrium
 * Computational Bohmian Dynamics
 * History
 * Derivations
 * Action
 * Current
 * Invariance
 * Planck's formula
 * No Hidden Variable proofs
 * Extensions
 * Nonlocality
 * Curved Space-time
 * See also
 * References
 * External links —Preceding unsigned comment added by Joliverst (talk • contribs) 13:11, 31 October 2008 (UTC)
 * Looks generally good to me. I'm not sure that nonlocality is an extension - I thought it was a feature of any theory of quantum mechanics... Deadly Nut (talk) 08:29, 5 November 2008 (UTC)


 * Let others draw the conclusion as to why it is useful. I disagree, since the merits of this interpretation (and it is usually called an interpretation since it is experimentally indistinguishable from other interpretations) are subtle and discussed in the literature we can report on them here.
 * Perhaps the criticism section could be renamed. It's purpose is to elucidate the interpretation by clearing up common misconceptions. --Michael C. Price talk 09:51, 12 November 2008 (UTC)

Contents rearrangement
I've rearranged the article to follow the sequence of Joliverst's suggestion for the contents list. I haven't changed the content, to make later changes more obvious. To follow this principle, I've left in Criticisms and Benefits, but moved them to a less conspicuous part of the article. Deadly Nut (talk) 08:08, 12 November 2008 (UTC)

History section
I've added a History section. Deadly Nut (talk) 08:52, 25 November 2008 (UTC)

The Theory
I've tried to make the 1-particle bit easier to read. I still need to check that it really represents the essence of Bohm's and de Broglie's theory. I've removed the section entitled Mathematical Foundation because it was off-topic. Deadly Nut (talk) 12:41, 26 November 2008 (UTC)

I've rewritten the Principles section, to try to make it really clear. I've also moved a couple of the paragraphs to the Extensions section because they don't seem to be part of the basic theory. I got the $$p=\nabla S(x,t)$$ bit from Bohm's 1952 paper, but it puzzles me because it looks like if you know the position accurately, you can get an accurate momentum from the wave function - but I thought position and momentum were complementary? Deadly Nut (talk) 13:35, 28 November 2008 (UTC)
 * That is the whole point of Bohm's approach; that position and momentum of his hidden variables are simultaneously defined. --Michael C. Price talk 15:39, 28 November 2008 (UTC)
 * Good point! Also, thank you for the adjustments to this section. Deadly Nut (talk) 11:11, 30 November 2008 (UTC)

In the section on quantum potential, Cmdulya has put "equating real and imaginary parts". This isn't correct. I've responded by describing what we do as separating R from S (this is the same operation as separating magnitude and phase). I hope this is clearer. To aid clarity to people not familiar with this kind of mathematics, I've written the functions in full instead of abbreviating them (e.g. $$R(\mathbf{x},t)$$ instead of R). I've also added a step (Bohm has this in his original paper) to make it clearer. Deadly Nut (talk) 10:12, 11 December 2008 (UTC)

Determinism
I've made this a separate subject, because there's some really important stuff in here, and it needs to be resolved. Deadly Nut (talk) 09:10, 17 December 2008 (UTC)

I see you have replaced "deterministic" with "causal". Bohm's theory is deterministic since there is no wf collapse; what is your objection to the word? --Michael C. Price talk 14:19, 26 November 2008 (UTC)
 * I was going on SFWild's comment (see above), 'Here again, the author obviously misunderstands (or deliberately misleads?) the reader when he says, broadly, that the Bohmian interpretation is "deterministic." This may be to some extent true in the very early presentations, but after Causality and Chance, and throughout the middle and late period, Bohm is adamant that "causal" is not the same as "deterministic."  Any accurate presentation of Bohm's theories needs to address this.'  I was taking his words on trust, but I don't know what his credentials are... Deadly Nut (talk) 12:21, 27 November 2008 (UTC)
 * If is precisely because "causal" is not the same as "deterministic" that the article should describe it as "deterministic". Given the particle's position and momentum at some time it is defined for all other times.--Michael C. Price talk 15:39, 28 November 2008 (UTC)

Thank you Deadly Nut for serious improvements to the flow of the article. With regard to Michael Price's comments above, I still take issue with the assertion that the Bohm Interpretation in toto can be described as "deterministic." While it is true that the initial '52 presentation was concieved as a more-or-less deterministic alternative to the a-causal assumptions of the standard model, Bohm is very careful not to use the word "deterministic" to describe his approach. In Chance and Causality he explicitly objects to the notion that his theory is any way a return to Classical deterministic mechanism, and posits a continuum between the two poles of chance and necessity, with neither being absolute. For Bohm, the question of determinism is always dependent on context, so that while the motions of the particles at the quantum level can be seen as being more determined than the standard theory allows (namely by the motions of the sub-quantum hidden variables), those motions are themselves subject to random fluctuations, similar to Brownian motion. Indeed, Bohm himself suggests that there is in fact a deeper kind of Indeterminism than the familiar Heisenberg relations, relating specifically to the chance fluctuations (see Chance and Causality, Chapter 4, Section 2). This is basically the model he persued with Vigier in the sixties. Further, Bohm's notion of causality is considerably richer than the standard definitions of determinism allow (eg Kant), and in Wholeness and the Implicate Order he extends his notion of causality in ways that closely parallel the older Aristotelian notions of formal and final cause, or what he calls "formative causation." It is impossible to reconcile this kind of quasi-teleological thinking with any accepted definition of "determinism." Moreover, insofar as non-locality plays a role, such non-local interactions can be described as causal, but hardly deterministic. In the end, Bohm felt he had to give up even the sobriquet of the "causal interpretation" precisely because it smelled too much of determinism, opting instead for the term "ontological interpretation." While he developed the model in both a causal and stochastic form, it's pretty clear that his own thinking trended away from any sort of deterministic approach. The work with Hiley in the eighties explicitly embraces a stochastic model. See Chapter 9 Section 5 of Undivided Wholeness, and Chapter 14, where he writes "this general approach implies a certain kind of limit to determinism...So ultimately our overall world view is niether absoltuely determinsitic nor aboslutely indeterministic. Rather it implies that these two extremes are abstrations which constitute different views or aspects of the overall set of appearances." While it is true that Bell and others, based on a reading of the early '52 papers, have made the claim that the theory is deterministic, this is not a view held by Bohm himself. Sorry to be long-winded, but I believe this is an important clarification because claiming in an unqualified statement that "the Bohm interpretation is deterministic" is a gross over-simplification and leads to all kinds of confusion, such as is found frequently in the popular literature, where it is sometimes stated that Bohm's theory represents a step backward to the model of Classical determinism and mechanism, which is certainly not the case. Sfwild (talk) 20:01, 12 December 2008 (UTC)


 * Thanks for this, sfwild. So far, I've read Bohm's 1952 paper, but only parts of the Undivided Universe, so I'd find it tricky to explain all this to a lay reader... I think it needs a statement in the Principles section, and probably some changes to the One-particle formalism section. I'll have a go at the principles if you don't do it first, but I'd appreciate it if you checked the One-particle formalism section to see if it properly reflects the theory. Deadly Nut (talk) 09:25, 14 December 2008 (UTC)


 * I've written the History section up to about the 1952 paper. Sfwild - would you be able to take it further, describing the development of the theory and some of the more important collaborations? At present, I don't have the knowledge to do this. Deadly Nut (talk) 09:25, 14 December 2008 (UTC)


 * @Michael C Price - I'm persuaded by the level of detail that sfwild knows what he's talking about here. Also, there are hints in Bohm's 1952 paper that the trajectories might not be exactly what you get by integrating $$v=\nabla S/m$$.  I know you're pressing for determinism here, but sfwild has persuaded me that something more complicated is going on. Deadly Nut (talk) 09:25, 14 December 2008 (UTC)


 * This subject is too complicated for the introduction, so I've removed this paragraph. Even if the statement is accurate, it doesn't look like a very useful form of determinism! Deadly Nut (talk) 09:25, 14 December 2008 (UTC)


 * The Bohm interpretation is deterministic in that, if we knew what the current state of a system is, we could predict what its future would be. However, we cannot measure this state beyond the limits imposed by the uncertainty principle, so although the theory is deterministic, we cannot predict an outcome accurately.

I've just been trying to see what the references say. I notice that some people take The Quantum Theory of Motion as the definition (this book calls it the "de Broglie-Bohm theory"). My impression from skimming the book is that it describes the theory as deterministic. Others (including sfwild) take The Undivided Universe (this book calls it the "Causal Interpretation" or "Ontological Interpretation"). Sfwild is clear that Bohm describes a non-deterministic model even when he's not discussing the stochastic model. Both books were published in 1993. Here's an example: the paper arXiv:quant-ph/0206196 describes an experiment that disproves the de Broglie-Bohm theory, and takes as its reference The Quantum Theory of Motion - indeterminism would invalidate the result of this experiment.

What I'd like to do is this:
 * Nominate The Undivided Universe as the definition of the theory and point out its indeterminism.
 * Describe an "extension" (defined by The Quantum Theory Of Motion) that is deterministic.

Any comments on this plan? Am I right, or have I misunderstood completely? Deadly Nut (talk) 09:09, 17 December 2008 (UTC)

It did occur to me that one of the difficulties in talking about the "Bohm Interpretation" is that there is really no definitive statement as to what that interpretation is. Bohm's interpretation evolves over time and presents a number of different forms or “extensions.” Bohm was always clear that he saw the model as continuous work-in-progress, rather than merely a counter-example to the usual model. Part of the confusion here is that many workers who identify themselves as "Bohmians" or "Bohmites" adhere to a strict "Bell interpretation" of Bohm's work. And if you read Bell and Holland, they are quite clear that their interest is only in the early papers. So I think Deadly Nut hits the question dead-on: Is the "Bohm Interpretation" the interpretation mediated by Bell and which is sometimes expressed as “Bohmian Mechanics” (Durr, Goldstein et al.)? Or is the Bohm Interpretation the interpretation Bohm himself worked on, from ‘52 onwards, sometimes alone and sometimes with collaborators such as Vigier and Hiley, right up until his death in 1992? My vote is obviously for the latter, taking Undivided Wholeness as the most developed or “evolved” form. Either way, clarification is in order, and referencing the workgroups associated with “Bohmian Mechanics” in the extensions seems a reasonable approach. Sfwild (talk) 19:08, 17 December 2008 (UTC)
 * I don't think it appropriate to make a judgement on what is the definitive version of the theory. Why not just report all the variants?  For me the papers Bohm wrote in the 1950s are the clearest.  If there are later developments then we can report those as well, but there is no need to lose the earlier stuff. --Michael C. Price talk 21:35, 17 December 2008 (UTC)
 * Thank you, sfwild and Michael C Price, for clarifying this for me. I think Michael is right, that we shouldn't sideline widely used versions of the theory, but I was a bit spooked by the article I took as an example, because it claims to invalidate the theory but (and it doesn't state this explicitly) only if it's deterministic.  Anyway, I've added the section Name and Evolution to try to clarify this and to bring it to the reader's attention. I'd have liked to put more detail in the Bohm paragraph, but I'd need to do a bit more research to get it right. Deadly Nut (talk) 09:20, 18 December 2008 (UTC)
 * I think this is the biggest issue with this article. There definitely needs to be a decision and agreement on whether this article is about Bohmian Mechanics, the theory that happens to share a name with David Bohm, or about the various inter-related interpretations of quantum mechanics presented by David Bohm throughout his career. If this article ends up being about the latter, then I motion to delete it for lack of notability or add it as part of the article about Bohm, then I would suggest we start on an article about Bohmian Mechanics, since that's is a theory that's actually still getting talked about in the literature. Honestly, this article appears (to me) to be extremely deceptive, since "the Bohmian interpretation" is often used as another way of referring to Bohmian mechanics, but this article seems to be about the evolution of David Bohm's personal view. Imagine Einstein had eventually withdrawn his support from the theory of relativity and said that, instead, he thought that spacetime was completely classical and there were just certain optical phenomena caused by some as-yet-unnamed force exerted by certain celestial bodies. We certainly wouldn't want to add, to the Relativity article, the claims that spacetime is classical and that there exists some strange optic force which makes it look like our experiments confirm relativity. We would obviously reject arguments of the form "This article is about Einstein's theory, and I have a quote here from him saying that his theory says this" if the arguer was referring to sources containing Einstein's later position. It looks like the only relevant difference in this case is that the Bohmian Interpretation happens to include the author's name. 67.85.191.28 (talk) 22:32, 22 December 2008 (UTC)
 * As I understand it, this article is about Bohmian Mechanics - the science in it should apply to any of the theories that carry Bohm's name. However, it was a great surprise to me that Bohm was a heretic in his own religion, and I feel that the reader who is new to the subject should be warned about this.  The one major feature that is different between different versions is determinism - I was alerted to the problem by a debate about determinism, and it is apparent to me that there are 'supporters' of both Bohmian Mechanics and the Ontological Interpretation among the contributors to this article; for that reason I feel it is important to reflect the different views in the presentation. Deadly Nut (talk) 07:29, 24 December 2008 (UTC)
 * I am a little confused by your first sentence. Bohmian Mechanics is the name of a theory. If Bohmian Mechanics is the subject of this article, then the science in it should apply to, and explain, Bohmian Mechanics. The fact that there may have been other theories that bore Bohm's name, or were the product of his research, or garnered his explicit endorsement does not mean they are the subject of this article. I understand that we have advocates of one view and advocates of the other each trying to tailor the article to their respective pet theories. The solution to this problem is not to present two different theories as if they were one either very vague or totally self-contradictory theory (we already have more than enough of this kind of theory in Quantum Mechanics, *coughCopenhagencoughMany-WorldscoughConsistentHistoriescough*). The solution would be to make two articles, one for Bohmian Mechanics and one for Bohm's Ontological Interpretation. (I will withhold my biased and rather snobbish opinions about whether the Ontological Interpretation is notable enough, or dealt with enough in the literature, to justify having its own article). It's a shame that a search for "Bohmian Mechanics" redirects to this *pejorative* of an article, especially since Bohmian Mechanics is such a simple and intuitive theory, explaining it in a wikipedia article should be a walk in the park, not the nightmare it seems to have become. 71.225.239.182 (talk) 04:24, 25 December 2008 (UTC)

I agree too that we don’t want to loose any of the earlier material. In its current form, I think the presentation beginning with the reformulation of S. equation and One Body and Many Body systems works rather well. It gets trickier as the theory develops. For instance, there is undoubtedly a tension between the earlier deterministic-local (100% “causal”) interpretation and the early stochastic model, where the random fluctuations play a greater role. In response to some of the debates around this issue, Bohm would probably say: “well if the formalism of the strictly causal formulation is unappealing, you can always try the stochastic model” (See Undivided Universe, Chapter 3, Section 5, with reference to Stationary States). Then there is the whole question of non-locality, and how to present that aspect of the theory. All commentators agree that non-locality is an important feature of the “Bohm Interpretation” (or whatever you want to call it). But Bohm actually does not talk about non-locality in any of the early papers except perhaps as implied by the non-Classical features of the quantum potential, or in terms of EPR entanglement. The basic model for this period was still presented as Hidden Variables existing within a sub-quantum domain. It’s only when Bell starts promoting the theory in the sixties and seventies that the issue receives attention. Based on the Bell work, the Bohmian research project takes on a whole new life, leading to the Aspect experiments, Bohmian Mechanics, and other things. Based on that work, Bohm comes back to the theory in the eighties and, for the first time, comes to terms with non-locality, so that the overall theory is modified/enriched in ways that were not self-evident in the original papers (See Undivided Universe, Chapter 7). There are other important developments as well. For instance, in the later presentation of the ontological (“post-causal”) formulation, he effectively replaces the earlier notion of the “quantum potential” with the concept of “active information,” so that the guiding wave or force becomes an informational “in-forming” wave which communicates information about the whole system. This is an important feature which is generally overlooked in the literature. And then of course there are concepts or “extensions” such as the Implicate Order, or later, at the level of the second quantization, the “Super-Implicate Order”—all of which have to be addressed somehow.

Enough said! I think the article is coming along so I’ll desist from further commentary for a while. Meanwhile, here’s a link to a very richly documented paper by Olival Freie, a Brazilian scholar, who relates the evolution of Bohm’s thinking during the Brazil period and his collaboration with Vigier:

http://www.fis.ufba.br/dfg/pice/controversia/index_arquivos/Freire-Bohm-HSPS.pdf. My understanding is that there is also a collection of Vigier’s early papers and presentation of the “Causal Stochastic” interpretation in a collection edited by Stanley Jeffers, where the thing is called the “de Broglie-Bohm-Vigier Interpretation” (just to confuse things a bit further). Sfwild (talk) 18:29, 18 December 2008 (UTC)

Computational Bohmian Dynamics
When I looked at this, the contents looked like extensions to the theory, so I moved it to the Extensions section. Deadly Nut (talk) 13:35, 28 November 2008 (UTC)

Understanding quantum mechanics
I've worked on the Uncertainty Principle, hoping to clarify it a bit. Deadly Nut (talk) 11:11, 30 November 2008 (UTC)

It seems to me that section on the 2-slit experiment requires only a statement of what the experiment is and how the Bohm interpretation describes it. I agree with sfwild's comments about hidden variables, but this is also not the place a reader would expect to find the topic; I have added a comment on hidden variables to the Principles section. Deadly Nut (talk) 12:41, 1 December 2008 (UTC)

The section on Nonlocality seemed a bit awkward here. I've covered these topics by discussing EPR and how Bohm interpretation deals with it. I've also added a section on measurement of spin because it seemed relevant, especially for people new to the subject. Deadly Nut (talk) 10:44, 2 December 2008 (UTC)

Thank you, 70.137.138.141 for the paragraph on indeterminacy. I've tried to simplify the prose without losing the meaning. Deadly Nut (talk) 09:45, 14 December 2008 (UTC)

Introduction
Thank you sfwild for an excellent opening paragraph. I've added links to other Wikipedia articles. Deadly Nut (talk) 08:35, 7 December 2008 (UTC)

Remove advocacy FAQs, replace FAQ with "criticism" section
The FAQ sections basically reads as advocacy for the Bohm interpretation. Since this is a physical theory which is not supported by experimental evidence and on which there is no consensus in the physical community (or rather, the consensus is that the theory is unnecessary and has serious conceptual problems), I believe this is unacceptable in Wikipedia. This is supposed to be an encyclopedia, not an advocacy site for definite stands in scientific disputes. I therefore introduced a "disputed" sign on this section. Please do not remove until such time as the section reflects the general consensus in the physical community. 84.238.81.116 (talk) 18:15, 15 November 2008 (UTC)

More on the FAQ section: I find these two utterly unconvincing and not up to any encyclopaeding or scientific standards:

''Q: While orthodox quantum mechanics admits many observables on the Hilbert space that are treated almost equivalently (much like the bases composed of their eigenvectors), Bohm's interpretation requires one to pick a set of "privileged" observables that are treated classically — namely the position. How can this be justified, when there is no experimental reason to think that some observables are fundamentally different from others?''

''A: Positions may be considered as a natural choice for the selection because positions are most directly measurable. For example, one does not actually measure the "spin" of a particle in the Stern–Gerlach experiment, but instead measures the position of the light flashes on a detector. Often the observed quantities are positions, e.g. of a measuring needle or of the particles making up a computer display. And so there is justification for making position privileged.''

"Often" the observed quantities are positions? Yes, and often they are not. And how is the question of whether the result of a measurement is decided by the reading of a position (e.g., of a measuring needle) related to whether position should be considered a "privileged" observable for particles described by quantum mechanics? But this is immaterial - my point is that this argument is easy to reverse: Often the observed quantities are NOT positions, so there is justification for NOT making position privileged. Just as logical, and just as imbecile.

Q: Why should we consider this to be a separate theory when it looks contrived, and gives the same measurable predictions as conventional quantum mechanics?

''A: Bohm's original aim was to demonstrate that hidden-variables theories are possible, contrary to the belief (due to von Neumann) that they are not. To accomplish this aim it was necessary that the predictions of the two theories be the same. However, Bohm's hope was that this demonstration could lead to new insights and experiments. Bohm's theory can be extended in ways that cannot even be contemplated in the conventional theory[citation needed], and these extensions may lead to new measurable predictions.''

I inserted the "citation needed". One question: can't conventional quantum theory be extended, and hasn't it actually been extended in various ways over the course of the last decades? Another question: Are we to accept Bohm's theory on the grounds that in the future it "may" be extended to lead to measurable predictions? In other news, the Moon "may" turn out to be a green cheese after all. Who, after all, is to say it may not?

A third question: Is this article really up to encyclopaedic standards? I'm going to place an "expert-subject" tag on the whole article - I have half a mind to delete all "advocating" FAQs, but that'd more or less wipe out the whole section. I think this article should contain a clear exposition of the theory (which it also does) together with a clear exposition of the various criticisms raised, in such a way that it neither comes away as advocacy for Bohm's theory nor for the criticism raised against it by Einstein, Bohr, Heisenberg, etc. 84.238.81.116 (talk) 18:57, 15 November 2008 (UTC)


 * Regarding your objections to the first question, I believe you are correct that position is not privileged. Nevertheless it is a POV I have heard prominent Bohmites (such as Hilley) espouse, and hence is reportable here.  Regarding your second question, the contrived nature of the theory is frequently commented on and needs addressing.  I believe Bohm made the response much as it appears here in the book, Ghost in the Atom, in an interview with Paul Davies. --Michael C. Price talk 02:24, 16 November 2008 (UTC)


 * There do seem to be duplicated questions; 2 that address the issue of wavefunction collapse and 2 that address the issue of non-locality.--Michael C. Price talk 02:53, 16 November 2008 (UTC)


 * The reformulation of the answer to the second question above is much better, thank you. Regarding the first question, in that case it should rather be formulated in terms of referring the Bohmites' position, accompanied by a reference, rather than just apparently asserted. I mean, instead of " Positions may be considered ..." we should have "Proponents of the Bohm theory contend, that positions may be considered .... &lt;ref&gt;see, e.g., Hilley (somewhere)&lt;/ref&gt;". (I'm sorry just to appear with criticism on the talk section, but unfortunately I can't offer to revise this section myself - I simply don't have the time to locate the references). 84.238.81.116 (talk) 13:15, 16 November 2008 (UTC)

The first FAQ - Q: Quantum field theory has been verified experimentally remarkably well. Since locality is essential to quantum field theory, how can it be reconciled with Bohm's interpretation? - is covered by the fifth - Q: The Bohmian models are nonlocal; how can this be reconciled with the principles of special relativity? However, the first question is unfair (Surely QFT is non-local, and you're asking a non-relativistic interpretation to reproduce a relativistic theory) and its response is weak and defensive. I've therefore removed it, moving the references to the fifth question, where the answer is better. Deadly Nut (talk) 09:06, 7 December 2008 (UTC)
 * I haven't looked at the article yet, but QFT is definitely local due to relativity. Locality is enshrined on the Canonical commutation relations in QFT. Non-relativistic Bohmian QM can get away with being non-local because it is non-relativistic. --Michael C. Price talk 17:20, 7 December 2008 (UTC)
 * My understanding is that although the wave equations of QFT are Lorentz-invariant, there are still non-local effects that disobey the letter but not the spirit of relativity.
 * Bell's theory shows that with entangled particles, the statistics of the experimental results depend on the orientation of the detectors for both particles. In Bell-test experiments, you can alter the orientation of one detector outside the light cone of the other; you therefore get non-local effects even if the wave equation is Lorentz-invariant.  Check out Bell's Theory of local beables (in Speakable and Unspeakable in Quantum Mechanics), where he says (at the start of section 5) "Quantum mechanics, however, gives certain conditions which do not satisfy the locality inequality."

I've combined the two collapse-related questions and collapsed the answers. The last para of the second (about quantum chaos) looked to me more like an extension, so I've moved it to extensions - quantum chaos. HOWEVER, it looks to me like something that BM can't handle and it has no references.


 * Please would someone tidy up the section and give references to work on the subject.  Specifically, we need to know how the Bohm interpretation fits in with it.  If no one does this in the next couple of weeks, I'll delete it. Deadly Nut (talk) 15:01, 7 December 2008 (UTC)

I've taken this out because it has serious problems:


 * Q: The Bohmian interpretation has subtle problems with incorporating spin and other concepts of quantum physics: the eigenvalues of the spin are discrete, and therefore contradict rotational invariance unless the probabilistic interpretation is accepted.


 * A: This criticism is based on the false assumption that the particle position variables in Bohm's equations must carry spin. There are natural variants of the Bohm interpretation in which such problems do not appear. In these, spin is a property of the wave only; the particle variables have no spin in the mathematical formulation.

The question is quite technical, and I don't understand it - classical spin is a vector, and I can't see how it can be rotationally invariant. I know that quantum spin is more complicated than classical spin, but it's still got an axis and I still wouldn't expect it to be rotationally invariant. So if the question is a reasonable one, could we please have a reference to help us understand it? The answer is a disaster, and is the reason I'm taking this out. Anyone can see that position variables don't carry spin - they're position variables... The second sentance says that the Bohm interpretation can be extended to answer the question. If we're talking about a properly thought-out theory it out to answer the question itself without needing to be extended.

If anyone would like to reinstate this question, please: Thanks. Deadly Nut (talk) 09:09, 15 December 2008 (UTC)
 * give a reference in the question so that people who don't understand it when reading it can follow up the reference and see what it means. If you can, say who asked it.
 * explain in the answer either why the question is invalid or how the Bohm interpretation we've got addresses it.

Disproven?
The Comparison with experimental data sections says:
 * The Bohm pilot wave theory has been disproven experimentally. An important prediction of the Bohm theory is that the electron in the ground state of a hydrogen atom is in rest, as the quantum force introduced by Bohm balances the classical electromagnetic potential.

But this seems incorrect. If the forces balances then particle(s) will be merely non-accelerating, not at rest. Surely??? On a general note, it is easy to prove that Bohm's interpretation reproduces all conventional results. Therefore such a simple disproof must be incorrect. --Michael C. Price talk 19:58, 18 November 2008 (UTC)

I've tagged it "disputed" for the moment. I'd like to see better links and/or references so that the claim can be analysed. --Michael C. Price talk 20:05, 18 November 2008 (UTC)


 * How could the bound lepton be non-accelerating and moving with relativistiv velocity and still confined to the atom at the same time? As a matter of fact, the prediction of that s-electrons are at rest is a well-known feature of the Bohm-de Broglie theory and is stated already in Bohm's original article from 1952. Direct measurements will yield the same momentum distribution as predicted by quantum mechanics, though, but according to Bohm's theory, direct measurements of momentum will disturb the bound lepton, causing it to move and yield the quantum mechanical result.


 * Why does the Bohm theory predict that ground state electrons are at rest? Because "the momentum of Bohm's "hidden variable" particle is defined by" the gradient of S, the phase function. But s states are spherically symmetrical, so the phase is constant (QED).


 * I suggest we remove the "disputed" tag. Agger (talk) 12:17, 19 November 2008 (UTC)


 * Okay, I think I see the resolution. The muon "disproof" involves relativity and time dilation, yet Bohm's theory only reproduces the non-relativistic Schrodinger equation.  Therefore there is no discrepancy, since all we have shown is that relativistic leptons do not obey the Schrodinger wave-equation -- which is hardly surprising.  So no problem for Bohm's non-relativistic theory.  I have removed the disputed tags and explained this in the article. --Michael C. Price talk 13:21, 19 November 2008 (UTC)


 * Except that relativity is not involved in the claim that s state electrons are at rest and relatvistic wave functions as used in the relativistic Bohm theory also have spherical symmetry. So there is still a big problem for the Bohm theory: Relativistic or non-relativistic, it predicts that ground state electrons are at rest, and the time dilation in muon decay experiments show they are not. —Preceding unsigned comment added by 80.163.95.210 (talk) 14:52, 19 November 2008 (UTC)
 * No, your logic is wrong. There is no problem because Bohm did not construct a relativistic theory.  Therefore there is no theory to refute.  If stationary electrons in the s state are a prediction of the as yet non-existent theory then there would be a problem; but since such a theory does not exist yet it is not a problem.
 * So the question is: would a relativistic Bohm theory predict stationary electrons in the ground state orbital? Not whether the ground state orbitals are spherically symmetric (of which there is no dispute).
 * I note you claim that there is a relativistic Bohm theory. Where is the calculation showing that ground state electrons are stationary in it? (Such a demonstration exists in the 1952 papers -- but they are non-relativistic.)--Michael C. Price talk 19:20, 19 November 2008 (UTC)

I posted some general criticisms on this discussion page last year, but if anything the article has become muddier. What is needed, before getting into a lot of the minutia or later experimental proofs or disproofs (this last section is especially problematic), is a clear exposition of Bohm’s Hidden-Variable-Causal-Ontological Interpretation(s), including the evolution/elaboration of that interpretation in its historical context. A more direct approach would be helpful to the casual reader who simply wants to know what the Bohmian interpretation is all about, and how it differs from other interpretations. Sfwild (talk) 19:26, 27 November 2008 (UTC)

Requested move post-mortem

 * The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

Moved Vegaswikian (talk) 02:49, 13 November 2009 (UTC)

Bohm interpretation → de Broglie-Bohm theory — After reading this discussion, it looks like the name "de Broglie-Bohm theory" is most accepted among the discussion participants. But because this was such an utterly nuanced debate, I want to make sure that this is the title you want. @harej 04:34, 31 October 2009 (UTC)
 * Okay with me.--Michael C. Price talk 06:42, 31 October 2009 (UTC)
 * Word. ZRPerry (talk) 16:18, 31 October 2009 (UTC)

Go for it! From an historiographical perspective, proposed name change has the backing of no less an authority than Einstein himself, who already in '52 (referencing the early version of the theory) speaks of the "de Broglie-Bohm approach," adding that he does not believe such an approach to be very hopeful.Sfwild (talk) 18:34, 31 October 2009 (UTC)
 * The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

New Name and New Page History
On 11/13/2009, the page received a new name. It is fitting to have a long discussed and desired rewrite of the page. A first attempt has now been posted.

Reorganized the whole page based on the principles of say what the theory is, what the results are, where it comes from, and a little history.

More refinement and citations need to be added.

Added:
 * Different theory extensions
 * A total of 5 Derivations
 * Classical Limit mentioned
 * QEH
 * Quantum formalism substantially reworked
 * History section largely preserved with rearrangments.

In terms of deleted material from the current page:
 * Deleted Quantum Chaos--seems irrelevant
 * Principles were reincorporated elsewhere
 * Comparison with experimental data--it did not seem sensible to me and would want a reference to published material covering the implication to this theory
 * Q&A were reincorporated for the most part though the questions were removed.
 * The full derivation of Bohm's approach was removed though the main equations were left as being irrelevant to most people's needs.

Need: A good review of nonlocal extensions, preferably a paper to reference. If not exist, we should write one. Jostylr (talk) 13:34, 13 November 2009 (UTC)


 * I dig. I've been making little edits here and there to try and smooth out some of the rough edges in some of the older content that we're keeping. A structural suggestion that I'd be interested in hearing some opinions on: I think the Results section should be trimmed down to the essentials, and then moved so that it appears before the Extensions. In its current form, the extensions look like a part of the theory at large, which obfuscates both the simplicity of the core theory, and the fact that you can get the results listed later in the article without bringing in the extensions to the theory that are mentioned before them.
 * If we want to promote understanding, I think the ideal form would be one where the advantages of the stated theory are listed first and then the extensions discussed only once the limitations of the unmodified version are brought to light.
 * However, this is as small a quibble as a quibble can be while still qualifying for quibble-hood. On the whole, I am very pleased with the current rewrite, and I look forward to improving on what is already a great start. Regards, ZRPerry (talk) 20:59, 13 November 2009 (UTC)

I think that is a very reasonable approach. The difficult task to tackle is trimming the Results section (important regardless of placement). I think the extensions are important enough to try to keep them from not being too far away from the top since they presumably will form the foundation of future directions of the theory and they address some misconceptions about the limitations of the theory. I guess just try it out and see how it goes. One idea might be to split the results section somehow though I do not have a great feeling about that. Perhaps pull the two slit experiment out and enhance that that description to ensure that it highlights all the essential features--quoting Feynman about the essential mysteries being in that one experiment. Since Bell and Stern Gerlach require spin, it makes logical sense to have that stuff after the spin extension. But in any event, go for it while the forge is hot. Jostylr (talk) 22:04, 13 November 2009 (UTC)

Oh and I like the refinements made. I hope more such refinements are on their way. Jostylr (talk) 22:05, 13 November 2009 (UTC)


 * I agree with ZRPerry. I've been lurking and monitoring this page for a long time, thinking that a truly massive re-write was necessary to correct the convoluted, misleading, and confused earlier version.  Jostylr's version is a huge huge step in the right direction!  In general, I think the beginning part of the article is a little too mathematical and technical -- it's not that it's too rigorous, but rather that it might be a little hard for (say) an undergraduate physics major to really understand what this theory is, how it relates to ordinary QM, why one might be interested in taking it seriously and/or learning more about it, etc.  If people think that's a good point I can try to work up a slightly more friendly/qualitative/accessible introduction at some point.  For now, I'm going to make some minor edits basically just to clarify some points that are worded somewhat awkwardly in the present draft.  Tnorsen (talk) 13:01, 14 November 2009 (UTC)

I have put a version with a simple overview at the beginning. It starts with the equations with minimal verbage. Then it has the double-slit experiment. I think adding to that section and making all of the issues crystal clear in the two-slit experiment could be very helpful. Schrödinger's cat, spooky action at a distance might also be reasonably added, i.e., any topic that is in the popular conception of qm might go there while the more technical version (collapse, EPRB) could go later. I think the name of the section (Overview) might need to be replaced, but I am not sure what else to call it.

The reason to have the equations come so prominently and early is to emphasize that this defines the theory. A gentle verbal introduction that obscures these equations does a disservice to this theory. But Tnorsen is right that the mathematics of it should be minimized so as not to obscure the results.

I also hope we can work towards shortening this article.Jostylr (talk) 18:01, 14 November 2009 (UTC)

Great job has been done by Jostylr on this page. I would add a formal definition of the conditional wave function of a subsystem and give some explanation of when such conditional wave function evolves by Schrödinger equation and when it doesn't. I would also add a more detailed explanation (with formulas) of how the familiar wave function collapse emerges from the theory. Something like:

$$\psi^0_{\text{system}}(q_1)\psi^0_{\text{apparatus}}(q_2)$$

evolves by the Schrödinger equation into:

$$\psi^1_{\text{system}}(q_1)\psi^1_{\text{apparatus}}(q_2)+\psi^2_{\text{system}}(q_1)\psi^2_{\text{apparatus}}(q_2)$$

where $$\psi^1_{\text{apparatus}}$$ and $$\psi^2_{\text{apparatus}}$$ have macroscopially disjoint supports in the configuration space of the apparatus. In standard quantum theory, one of the terms in the sum above has to be removed "by hand". In the de Broglie-Bohm theory, the actual configuration $$Q_2$$ of the apparatus lies either on the support of $$\psi^1_{\text{apparatus}}$$ or of $$\psi^2_{\text{apparatus}}$$ and when $$q_2$$ is replaced with $$Q_2$$ one of the terms in that sum vanishes and one obtains a collapsed conditional wave function for the system (which from now on evolves unitarily and guides the particles of the system).

I'm not sure exactly where to add some explanation of this sort in the article.Dvtausk (talk) 02:09, 15 November 2009 (UTC)

Hey guys,

I think Jostyrl did a good job of presenting the formalism as it is taught by Duerr, Goldstein, et al. But let’s be honest: this is an article about “Bohmian Mechanics” in its current iteration, and as such represents a somewhat narrow approach. Most disturbing is the lack of grounding in the historical foundations of physics discourse. It is at least a bit odd that an article that presents itself as the de Broglie-Bohm Theory makes no attempt to explain what De Broglie’s or Bohm’s approach was about. What the reader gets instead is a wallop of Bohmian Mechanics. If this is the goal then why not simply re-direct to Goldstein’s SEP article? As currently presented, the “Theory” falls from the air without any context, and then cites Duerr and others as authorities. For instance, to assert right up front that the theory starts with the guiding equation, and that the S-equation “completes” the theory, is a highly partisan approach which only the proponents of Bohmian Mechanics adhere to. At the very least, there needs to be referencing of sources eg. Bell, Holland, the early articles of Duerr et al. and some qualification that such is the understanding which emerged among workers in the field during the latter part of the last century. Also it should be pointed out that relatively newfangled conceptualizations such as “the quantum equilibrium hypothesis” (aka Born Rule) and “Conditional wave collapse” come right out of the Bohmian Mechanics toolbox, and have little or no relation to the theory as it evolved from, say, 1927 to 1993. I know that there are folks who believe passionately that this is the “right” approach, but I doubt it serves the innocent “gentle reader” who simply wants to know what the Bohm Interpretation or the De Broglie-Bohm Theory is about.

Other issues include the misuse of the term “ontology,” statements to the effect that the probability distribution is only an “additional postulate” in standard QM (it’s really the other way around; it is central to standard QM and something of an assumption in Bohm), confusing presentation of the quantum potential as a “derivation” of the theory, presentation as solely a theory about the motion of particles (whereas Bohm starts with notion that the field is primary and indeed, most “real”), a rather superfluous discussion of the Heisenberg indeterminacy relations which fails to bring out the essential difference between BB and standard QM, and a mouthful of “extensions” which lead to rather minor developments in the theory (eg. “Quantum Trajectory method”, Valentini’s speculations on quantum heat death etc. etc. ).

In sum, if this is to remain an article on Bohmian Mechanics, then why not rename it “Bohmian Mechanics” and discuss the theory that way, referencing the “authorities” of that school. That would at least be an honest way to go about it. Alternatively, if it’s to be an article on De Broglie-Bohm (my preference), then talk about the major contributions of De Broglie (pilot wave), Bohm (esp. ’52 articles), Bell etc., referencing the primary sources and the historical context , with the Bohmian Mechanics formalism presented as a kind of extension. To offer a reading which is essentially straight-up Bohmian Mechanics and then call it the “De Broglie-Bohm Theory” is problematic, and only serves to perpetuate the current confusion in the literature, while according to the theory itself a kind of “counter-factual” misplaced concreteness which isolates it from its historical context.

I would also suggest archiving the earlier discussion pages. Sfwild (talk) 20:19, 15 November 2009 (UTC)


 * I agree with the archiving. Anyone know policies and procedures on that?


 * I would not object to a separate article on Bohmian mechanics. Is that an option? I was under the impression that the powers that be would not allow this as they would say that all these fine distinctions you make between the different eras and versions are really just all talking about the same theory and should be on one page. Is your claim that Bohmian mechanics is a different theory or is it the same theory? What exactly do you think this theory is?


 * The discussion on the name rejected Bohmian mechanics because of de Broglie's primacy on the matter. Your claim would say that he is not primary nor even is Bohm, but rather Bell because Bell is the one that promoted the derivation of it from probability density currents which is what Bohmian mechanics focuses on. I think most would disagree and say that de Broglie put the first version of Bohmian mechanics out there. Since we have a refined and clear version of this theory, that is what we should use rather than be tied to the first beginnings of a theory. Why should history prevent us from presenting a clear theory to those who wish to know what this alternative to standard quantum mechanics says? As far as I know, most readers interested in theories of physics would first want to know what that theory is about and then, maybe, the historical evolution of it. That is what motivates the current version of the article. What evidence do you have that history should be presented first in Wikipedia articles on physics? I would think a description of the physics (and its mathematics) is the most important part of any encyclopedic article on a topic in physics.


 * Furthermore, I believe that Bell is the one that coined the name de Broglie-Bohm theory. As such, the theory he discusses should be given primacy. And this is exactly the theory presented in this article. It is not de Broglie's theory. It is not Bohm's theory. It is the theory that came out of the two as understood and promoted by Bell under this name. And it is also the theory of current research and scrutiny. I see no reason to not present the theory of Bell, the one theory with the name associated with this page. Not that I am agreeing that these are different theories.


 * Also please explain exactly what mathematically is the difference between these theories? As I understand it (and I am no expert in historical matters, but using your own statements in the naming discussion), de Broglie's version is exactly specifying the velocity in more or less the same way. The derivations might have been different (I think he focussed on the action?), but as far as I understand it, we have the same objects evolving in exactly the same way in the different versions. So please explain what the differences are. And a great place to do that is in the history section. I should think that that section could use more expert care for it then I can give it. So please modify it as you seem to have a passion for the history of science.


 * The main point of the rewrite is to clearly explain what the theory is. A historical analysis, coming first and which obscures and confuses what the theory is, does not do any reader any good. If you have a clear version of the theory that differs from what is presented, then please write it down and present it. But make sure that it presents the theory with crystal clarity. This is an article on physics, not history. Nor are physical theories tied to the whims of their authors. If Bohm and de Broglie chose to pursue other theories later, well, good for them. Write articles about their later theories if such theories fall outside the scope of de Broglie-Bohm theory (the one of Bell).


 * As for your snippet about pointing to SEP, you seem to miss the entire point of Wikipedia. The whole point of this site is to write stuff that already exists out there. Your argument should be able to apply to any well written Wikipedia article. Of course a good Wikipedia article is irrelevant since one could just give a list of a couple of good references for any topic and say "Go read it". I think your ability to easily cite other resources for this version of the page is a testament to it being reflective of what is out there rather than one person's viewpoint.


 * Also, the bit referring to the fact that this is in line with the literature, however confused it is in your opinion, is, in fact, supportive of this version according to Wikipedia rules. The best way to address this confusion, is to have a section on it in which you cite published journal articles that go into detail what this confusion is, assuming that it is important enough to be put into this article. That can be a useful subsection of the history portion.


 * But ultimately, the way wiki works, as far as I know, is that you should write down your version, then the rest of us can see the merits of it and modify it or revert to our version and incorporate your relevant points depending on exactly what you write and do. If you want to, you can begin by writing a very clear section in the history portion saying very clearly with good citations as to why these theories are all very different from each other. And feel free to, throughout the article, add and cite other resources that explain how this theory accounts for all the quantum phenomena. I cite Durr et al because 1. Their papers are in refereed journals; I do not know that books such as the Undivided Universe or Holland's book went through the same kind of scrutiny. 2. They have very clear mathematical precision in what they say about this theory. 3. I am very familiar with their work and way of thinking.  In regards to 3, I would be quite happy if you can add balance to the article for the other schools of thought by citing other research articles describing the results and analysis of this theory.


 * I have to admit that I do not have current access to Bohm's 1952 papers. But I think he discussed the psi-squared distribution of particles; is that not how he obtained agreement with measurements? And if he did, then the quantum equilibrium hypothesis is just a short skip away and is a modern, precise version of what Bohm wrote which is what I tried to suggest in that section. If I am wrong, then make the suitable modifications to the article.


 * Also, other than your insistence on historical context being essential to describing a physical theory (I wholeheartedly disagree with that point of view), I think you should do your best to make the changes you talked about and we can see what comes of it. I would say that the current first section presents both particles and waves in an even way. Later sections perhaps have a bias towards treating particles as more important (hey, this is a theory about particles, after all). If you think that's inappropriate, rewrite them. You can put Schrodinger's equation first if you like. Make the changes.

Be Wiki, Be Bold. Jostylr (talk) 02:05, 16 November 2009 (UTC)

I have no objection to renaming this article "Bohmian Mechanics". But, I have to say that it would be very confusing to the readers of Wikipedia if "Bohmian Mechanics" (as presented by Dürr et al.) and "De Broglie-Bohm Theory" (as presented by Bohm himself, for instance) were presented as two distinct theories. The modern presentation of Dürr et al. is much cleaner and more intelligent than the original presentation of Bohm. Also, Dürr et al. have clarified many points of the theory. But it is not really a new theory.

I'm a mathematician and when I look for mathematical definitions/proofs/theories in Wikipedia I hope to find the most clever/clean and up to date presentation of the modern approach, not the original approach that was invented several decades ago (which is usually unnecessarily convoluted, uses old notation and terminology, etc). The same happens when I look for Physics articles. Of course, some people might be interested in the history and it is ok to keep some presentation of the original approach around.Dvtausk (talk) 02:20, 16 November 2009 (UTC)


 * You are right that it would be confusing to have two articles. And I think it is reasonable to accept de-Broglie Bohm, particularly given the literature search results cited by Plumbago.Jostylr (talk) 12:31, 16 November 2009 (UTC)


 * As I said previously, I think Jostylr's re-write of this page was a massive and desperately needed step in the right direction. That said, I actually agree with a lot of Sfwild's comments above.  It would be good to have a section on the history of the theory which discusses de Broglie and Bohm and Bell more explicitly.  (Of course, the focus of such a section would be to show how, despite different formulations and emphases, their ideas really were fundamentally the same as what is presented in the article -- that is, I share Jostylr's confusion about Sfwild seeming to think that there are actually several distinct theories here.  I definitely agree with Dvtausk that there should not be several different pages, for "Bohmian Mechanics", "de Broglie Bohm theory", etc.)  In general, as I said previously, I would lobby for a more qualitative/historical opening to the article so as to make clear to (say) undergrad physics majors what the theory is all about so the important messages don't get "buried in the formalism" (to steal Einstein's characterization of Podolsky's EPR paper!).  And it would be good to add some material to the Born Rule (or Quantum Equilibrium) section discussing other current approaches to this such as Valentini's dynamical approach to equilibrium ideas.  And there are a lot of other things like that, too.  I guess the point is that I think Sfwild makes some good suggestions for things it would be useful to add, and there is no need for that to be taken as any kind of fundamental criticism of the new and massively-improved article.  Jostylr wrote this whole thing by himself and it's only been up for a couple of days... of course there will be things that can be improved.  So there is no need, it seems to me, for any hostility or ill-feeling here.  People like Sfwild who see ways it can be improved should just go ahead and improve it.  Tnorsen (talk) 12:47, 16 November 2009 (UTC)

Waleswatcher has a good point: the repetition of the guiding equation (it appears both in the overview and in the description of the theory) is weird. Suggestion: the first overview could be completely formula free, addressed at curious readers with no background in undergraduate math. Perhaps just some description of the sort: "the theory is about the motion of particles, guided by the wave function of standard quantum mechanics".Dvtausk (talk) 16:45, 16 November 2009 (UTC)


 * That is probably fine. But the struggle I have with it is that one of the great features of de Broglie-Bohm is how simple the theory can be stated. I would want that impression to not be lost. Being able to say "here is the theory" in four lines is nice. But it seems most seem to think equations up front are inappropriate in this article and/or physics. Make the changes and see how it works out.


 * In response to Waleswatcher, doesn't that user have to say on the talk page what the problems are in order to justify placing the "needs expert"? I am not saying this article is perfect yet, but how can we address the concerns unless we know specifically what they are? It does say to see the talk page, after all.Jostylr (talk) 19:12, 16 November 2009 (UTC)

I have a rather minor and technical question: Shouldn't the Schr&ouml;dinger equation in the section on "Spin" contain a vector potential? Tumulka (talk) 17:21, 16 November 2009 (UTC)


 * Yes that would be appropriate. I tend to overlook that since I always think of it in terms of the covariant derivative. Please add it.Jostylr (talk) 19:12, 16 November 2009 (UTC)

I have changed the introduction a little bit, with the main purpose to shift from the case of particles to the more general concept of configurations. While this is not necessarily the way dBB is usually presented, it is clearly more natural and simplifies the presentation of generalizations. And it is clearly not a new way to present dBB, so, not "original research". Given that the first relativistic field theory (EM) version is already part of Bohm's original paper, it seems not justified to restrict the approach to nonrelativistic particles only. Then, I don't see that relativistic variants have a tendency to become stochastic. This is only true for variants with particle ontology, not for variants with field ontology. I'm not sure what means "nonlocal extensions" - dBB is nonlocal anyway - and have removed this. Another minor correction: the ontology is different from the classical one, contains also the wave function. Ilja Schmelzer (talk) 12:11, 7 January 2010 (UTC)


 * I deleted the paragraph referencing Brown & Wallace. Dr. Brown and Dr. Wallace, it is not right to advertise your own research papers on Wikipedia. The conclusions you reached in that paper are hardly cited (other than by yourselves) and totally unsupported by any (other than yourselves). People interested in resurrecting such an obviously biased paragraph please at least cite more respectable sources. Duduong (talk) 23:15, 5 May 2010 (UTC)
 * Why you thought the material was introduced by Brown & Wallace I have no idea - it wasn't;see the long and heated discussion that accompanied its development. Please note that I have had to revert every alteration you made to the Occam's section - it was all erroneous and unsourced.  I shudder to think what damage you have done to the rest of the article -but I'm not going to even look; not good for my blood pressure. --Michael C. Price talk 19:39, 25 September 2010 (UTC)

"Im" is used. I assume it means "the imaginary component of..." but unlike "ln" is it not standard enough to consider it "defined". "Im" is arbitrarty-seeming. It might be two variables or anything else, unless you define it. —Preceding unsigned comment added by 70.66.1.110 (talk) 07:36, 21 September 2010 (UTC)

Human role in standard quantum mechanics is misrepresented
From the article as of 15 Feb 2011: "However, while standard quantum mechanics is limited to discussing experiments with human observers, de Broglie–Bohm theory is a theory which governs the dynamics of a system without the intervention of outside observers (p. 117 in Bell[10])."

The statement that "standard quantum mechanics" requires a human observer is not accurate. Feynman states explicitly (but I have not found the reference, sorry) that a consciousness is not required for the measurement process, only the existence of some perhaps microscopic or distant effects left behind by an experiment, which might in principle be used to reconstruct in retrospect what happened. In other words, effecting a "measurement" means leaving behind a track of some kind, whether or not it can feasibly be interpreted to yield the desired information. In this, Feynman's point of view seems so sensible as to appear obvious. I am not aware of any challenge to it. Dratman (talk) 23:53, 15 February 2011 (UTC)

Correct me if I am wrong, but standard quantum mechanics says that the state of a system is given entirely by the wavefunction. So the trace of information possibly referred to by Feynman must be in the wavefunction for standard quantum mechanics. So how does the wavefunction evolve? Most agree it evolves most of the time by Schrodinger's equation. But the point of Schrodinger's cat is that if we only use that linear evolution of the wavefunction, then there is no single macroscopic track to read off from the wavefunction. All probable outcomes happen, but we only see one. That is why something more must be added. Standard quantum mechanics deals with it by asserting that a measurement collapses the state of the system into something well-defined enough that it is obvious how to read off the result of the experiment. But what qualifies as a measurement is Bell's point/question. And the implied answer to that in standard quantum mechanics seems to be the eventual observation by an experimenter. The real issue is not that there are human observers, but that the theory is designed to only apply in experimental situations which are, however, not explicitly defined. Hence Bohr's emphasis on the splitting of the world into a macroscopic part and a microscopic part. Of course, where is the split? It could be argued that one could change "human observers" to "classical observers", i.e., a system that is not governed by quantum rules for some reason. But what systems qualify for that? And who would believe that? Hence the pursuit and existence of quantum theories without observers, such as dBBt. Jostylr (talk) 03:00, 17 February 2011 (UTC)

Test
The article confidently states that dBB agrees with standard QM, but this article states that it has failed an experimental test. 1Z (talk)

So it does, but the claim is well-known to be utterly spurious, as was demonstrated in at least the following three references:

"Two particle interference in standard and Bohmian quantum mechanics", E. Guay and L. Marchildon, J. Phys. A: Math. Gen 36, 5617 (2003).

"Comment on 'Bohmian prediction about a two double-slit experiment and its disagreement with standard quantum mechanics'", W. Struyve, W. de Baere, J. de Neve, and S. de Weirdt,J. Phys. A: Math. Gen. 36, 1525 (2003)

"Comment on 'Experimental realization of a first test of de Broglie-Bohm theory'", O. Akhavan, M. Golshani, J. Phys. B 37, 3777 (2004).

Zicovich (talk) 15:08, 7 March 2011 (UTC)

On the experiment section it talks about a simulation of the model using fluid dynamics of droplets of oil as if it is an experiment, but it isn't. It is a physical simulation, right? Maybe it should be clarified. But I'm no expert, so I'm not gonna edit.179.223.145.88 (talk) 09:14, 25 January 2023 (UTC)

Photon trajectory research
This paper: http://www.aip.org.au/Congress2010/Abstracts/Monday%206%20Dec%20-%20Orals/Session_3E/Kocsis_Observing_the_Trajectories.pdf has some bearing on the article but I do not have the expertise to update it. As a stopgap, I threw a reference to the paper in at the bottom of the page in hopefully correct style :) — Preceding unsigned comment added by 173.57.43.182 (talk) 04:20, 3 June 2011 (UTC)


 * After reading your post, I've added it on weak measurement for the moment.
 * --Chris Howard (talk) 14:50, 3 June 2011 (UTC)

These results have also been published at Science http://www.sciencemag.org/content/332/6034/1170.abstract — Preceding unsigned comment added by 212.128.169.142 (talk) 16:36, 8 November 2011 (UTC)


 * Update: I have added it now, together with the paper of P.Ghose, also to this article: to the section on "Relativity". This looks like an appropriate place for it, given that the development of the notion of trajectories for photons is, as such, a new and remarkable development in causal theory. --Chris Howard (talk) 12:57, 20 November 2011 (UTC)

Nonlocality
This sentence puzzles me: "Because the known laws of physics are all local, and because non-local interactions combined with relativity lead to causal paradoxes, many physicists find this unacceptable." All the known laws, except QM... Am I missing something? I just wanted to get feedback before changing it. Paxfeline (talk) 21:41, 21 May 2012 (UTC)

I was going to make exactly the same comment! In fact I was tempted to put a "citation required" on the main article, but because of my extreme non-expert status I decided to defer. The existing text is a strong statement about a subject of current debate...acrimonious debate at that. It deserves justification. — Preceding unsigned comment added by 76.115.88.202 (talk) 02:06, 8 July 2012 (UTC)


 * Indeed your criticism concerns this edit of 30 Jan 2012 that did not improve the article - to be reverted or at least re-worded. --Chris Howard (talk) 19:37, 8 July 2012 (UTC)

All the laws of physics are local, yes, except those that are significant at scales of the size of an atom and below. In this tiny regime, the laws of physics are distinctly nonlocal. This was shown by Bohm, who defined the Schrödinger equation as the deterministic nonlocal field guiding the trajectories of particles, or spins, or whatever quantum state is being represented. This fact of tiny nonlocality was confirmed by Bell, who (just in case anyone still doubted the deterministic approach of Bohm) explicitly wrote about his admiration for Bohm's theory: "I saw the impossible done". Many details about Bell and nonlocality are in the article, "John Bell and the most profound discovery of science". David Spector (talk) 01:49, 25 November 2021 (UTC)

Bell and De Broglie–Bohm theory
I may be wrong, but there might be an error in this section. The text currently reads: "Bell showed that von Neumann's objection amounted to showing that hidden variables theories are nonlocal, and that nonlocality is a feature of all quantum mechanical systems" (emphasis mine). However, my interpretation of the preceding material is that it should actually read: "... showing that hidden variables theories are local ..." (emphasis mine). Otherwise it reads as if von Neumann was objecting to hidden variable theories because they shared nonlocality with actual quantum mechanical systems. Which wouldn't really be an objection at all. Perhaps I'm missing something subtle here? Anyway, I'll change it if I don't hear anything to the contrary. Cheers, --P LUMBAGO 14:15, 25 February 2013 (UTC)


 * The hidden variables theories that the Bell Test disproves are those that are local, that is, more or less classical in nature, but with unknown or "hidden" effects added. These were the theories that Einstein hoped would be correct, since he didn't like wave function collapse, probability as axiomatic, and other mysterious aspects of Bohr's theory. But the pilot wave theory that David Bohm proposed in 1952 converted de Broglie's local theory into a nonlocal theory, one that still reproduced the probabilistic effects of the Copenhagen Interpretation. All of the strange nature of QM was now located just in the guiding equation (part of the Schrödinger wave function), which Bohm viewed as a nonlocal quantum force that would guide particles in a wavelike way, taking the entire experimental configuration (both slits) into account. Then the subsequent trajectories of particles in the two-slit experiment were the results of interaction with that force, in a classical way. So, yes, there was an experimental objection, and yes, John Bell liked the way Bohmian mechanics used a nonlocal force to resolve the local hidden variables error. David Spector (talk) 13:02, 30 July 2020 (UTC)

A hydrogen atom ground state in Bohmian mechanics
I tried to apply a Bohmian equation to a hydrogen atom. I got that an electron falls into the nucleus along a helical path at a constant speed. After that I took into account uniformly increasing magnetic field, with decreasing radius of the electron trajectory. In this case, an electric field arises, which is directed against of the decreasing of the radius of the trajectory. In this case, there are no electromagnetic waves, so there is no loss by radiation. Thus, we have a stationary orbit for the ground state of the hydrogen atom. The same way you can consider the deuterium nucleus, using the Yukawa potential and taking into account relativistic corrections, and thus, learn more about the nature of intranuclear spin interactions. Mark L. Gurari — Preceding unsigned comment added by 76.10.139.212 (talk) 03:21, 2 March 2013 (UTC)


 * An interesting theory. Unfortunately, there is no place in Wikipedia for original research. This must be discussed in other fora, such as Stack Exchange/Physics or arXiv. David Spector (talk) 13:07, 30 July 2020 (UTC)


 * Indeed, the failure of the hydrogen atom to spontaneously collapse was one of the first clues that nature works in a quantized way in the very tiny regime. Observation failed to confirm the naive theory that atoms were like our solar system, with electrostatic attraction substituted for gravity. David Spector (talk) 01:54, 25 November 2021 (UTC)

Foliation
I removed the link between the term "foliation of space-time" and the article "frame of reference". Foliation is used several times here in reference to Relativity, but remains totally unexplained and undefined in either article. The term does not appear at all in the Frame of Reference article. Using that as a reference is really poor authoring/editing. I expect that the two concepts are heavily related, but unless someone wants to EXPLAIN the relationship, it is simply obfuscation to add a link that explains nothing. It is just as poor a practice to use a term with virtually no explanation. Can someone FIX this absurdity?173.189.78.18 (talk) 16:44, 15 July 2013 (UTC)

Upon further reflection I have tried (as of 12/14/2013, 7:30 pm) to remove all personal edits regarding internal inconsistency in De Broglie - Bohm theory. 64.134.238.142 (talk) 03:29, 15 December 2013 (UTC)David C. Anacker 74.62.13.50 (talk) 21:15, 14 December 2013 (UTC)David C. Anacker

74.62.13.50 (talk) 21:01, 14 December 2013 (UTC)David C. Anacker

74.62.13.50 (talk) 00:19, 13 December 2013 (UTC) David C. Anacker 74.62.13.50 (talk) 00:14, 13 December 2013 (UTC) David C. Anacker

de Broglie disagreed with Bohmian mechanics
The following is a quote by de Broglie clearly stating he disagreed with Bohmian mechanics. Mpc755 (talk) 11:29, 23 May 2014 (UTC)

"My first reaction on reading Bohm's work was to reiterate, in a communication to the Comptes rendus de l' Academie des Sciences, the objects, insurmountable in my opinion, that seemed to render impossible any attribution of physical reality to the $Ψ$ wave, and consequently, to render impossible the adoption of the pilot-wave theory. —Louis de Broglie"




 * The quote does not say that he disagreed with Bohmian mechanics. It says something from which you synthesise that he disagreed with Bohmian mechanics. See wp:NOR and wp:SYNTH. - DVdm (talk) 12:00, 23 May 2014 (UTC)


 * de Broglie wanted to develop a causal explanation for QM, which is precisely what David Bohm achieved (with a few minor corrections by himself and others in the years following his original 1952 two-part paper). It may very well be true that de Broglie objected to Bohm's trajectory determinism, or to his interpretation of part of the Schrödinger equation as a "pilot wave" guidance equation for particle trajectories in the two-slit experiment. I don't believe that these two physicists ever had a chance to meet and discuss these issues, and the application of Occam's Razor to QM interpretations, much less to work together. There is a certain inertia to ideas and theories in physics, such that the general adoption of Bohr's Copenhagen Interpretation (as well as the fact that Bohm was a former Communist who refused to name names before HUAC, and that he worked for many years with the mystic philosopher Krishnamurti) tended to cast Bohm's ideas into relative darkness. Unfortunately, nothing specific can be said about their possible differences in Wikipedia, since these differences, if any, are not really known. David Spector (talk) 15:42, 29 July 2020 (UTC)

Bouncing droplet experiments
I think this article http://newsoffice.mit.edu/2014/fluid-systems-quantum-mechanics-0912 also has some relevance to the topic and might add value to the discussion. I cannot incorporate it into the main article due to the lack of expertise. It is also refrenced here: http://www.sciencedaily.com/releases/2014/09/140912120634.htm. — comment added by EricBright (talk • contribs) 18:51, 14 September 2014 (UTC)


 * Yes, the bouncing droplet experiments can replicate some aspects of QM (double-slit). But, so far, it is not clear whether the nonlocal effects shown by these experiments use the same mechanism as nature does in the very tiny regime. For now, it is simply a very convenient (though delicate) model, one that is currently being explored. David Spector (talk) 02:00, 25 November 2021 (UTC)

Referenced Polls are useless
An early paragraph in this article mentions two polls that are meant to show that the de Broglie-Bohm theory is taken seriously by physicists, and has footnote 2 and 3 attached. If you follow the footnotes, the first "poll" involved 8 physics students in a hut in the forest. This sample size is far too small to be meaningful. Furthermore, physics students are hardly experts on the subject. The second "poll" had only 33 respondents and the paper specifically stated that the poll the purpose of the poll was "not so much of finding a “truly representative sample”. — Preceding unsigned comment added by 129.63.129.196 (talk) 16:58, 29 October 2014 (UTC)

Infinite or Finite Universe?
"The main fact to notice is that this velocity field depends on the actual positions of all of the N particles in the universe"

1) Is the theory readily generalisable when dealing with an Infinite universe (some people would clearly ask what an 'infinite universe' would actually entail). 2) The Velocity field equation in this case does NOT indicate HOW all the particles in the universe affect the velocity field, only that they do,  according to the diff eqn. that is, the wavefunction is arbitrary. ASavantDude (talk) 15:43, 12 September 2016 (UTC)

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de Broglie Bohm theory proved wrong/dead
An article by Partha Ghose proposed an experiment which results differ in dBB and QM. The experiment was carried out in Turin. QM was shown to be right and dBB to be wrong. This puts the end to dBB as a prominent physical theory. — Preceding unsigned comment added by Ilper (talk • contribs) 20:43, 31 May 2017 (UTC)


 * I'm afraid the situation is not this simple. I have been in communication with Dr. Ghose and other physicists on ResearchGate, and this particular experiment appears to have had a flaw that brings its results into question. In addition, a more recent experiment, "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer", by Sacha Kocsis and six others, 2011, includes this quotation: "In the case of single-particle quantum mechanics, the trajectories measured in this fashion reproduce those predicted in the Bohm-de Broglie interpretation of quantum mechanics."


 * I then asked the physicist who gave me this citation whether he would agree that the experiments to date do not yet support either interpretation of QM over the other, and he said, "In my humble opinion: yes."


 * It is clear that dBB is still a "prominent physical theory", one that is vastly simpler and more deterministic than the accepted Copenhagen Interpretation. Until experimental evidence is clear one way or the other, Occam's Razor currently gives a clear preference to Bohmian mechanics. David Spector (talk) 12:47, 30 July 2020 (UTC)

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What is a hidden variable?
I feel this is a very stupid question, which has to be asked. It appears that the name 'hidden variable' is actually a misnomer (though the theory should give rise to hidden information, and it would make some sense to call such information a 'hidden variable', but I don't think that the article indicates what information will necessarily be hidden from the experimenter in this theory). Scott Aaronson's paper ("Quantum Computing and Hidden Variables I: Mapping Unitary to Stochastic Matrices") states that "a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a stochastic matrix that maps the initial probability distribution to the final one in some fixed basis.", which specifies what a whole hidden variable theory would be (though I'm not too sure about the precise details). According to the same paper: "In the de Broglie-Bohm theory, the trajectories of particles are introduced as ontic [real] hidden variables, and they are piloted by the wave function that obeys the Schrodinger equation". So am I to take it that the deterministic configuration space particle trajectories ARE the hidden variables? How does the deterministic de Broglie Bohm theory give rise to random variables that are observed? Is the introduction of Random Variables into a theory inherently indeterministic? I'm guessing that the last answer to this question is NO, but I hope someone can offer some explanation for this.

A verbal explanation of what the hidden variables are (and the fact that they are not absolutely hidden) is given at: https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory#Hidden_variables BUT this does not go into mathematical details concerning what information is 'hidden' in the theory (assuming that the name 'hidden' within 'hidden variable' is a non-confusing title to use).

The 'Hidden variables' section indicates that the particle is not actually hidden. So is its trajectory hidden? Which particle properties "cannot be observed with arbitrary precision (within the limits set by uncertainty principle)"? This last question seems vacuous to me as, from my limited understanding, NOTHING can be measured beyond the limits set by the uncertainty principle. Is this a possible issue with the wording of the article?

Apologies if I have misunderstood the obvious. ASavantDude (talk) 20:29, 23 September 2017 (UTC)

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Re: What are hidden variables? I don't know about "hidden variables" in general, but in Bohmian mechanics the so-called hidden variables are the positions of the particles (see https://plato.stanford.edu/entries/qm-bohm/). Paxfeline (talk) 08:22, 16 July 2018 (UTC)


 * In reply to these two questions, the "hidden variables" in Bohmian mechanics are the initial positions of the particles.


 * Look at it this way: if you know you have a particle moving in a force field, how can you possibly determine its trajectory without knowing its initial position? You can't.


 * In Bohmian mechanics, the Schrödinger equation provides the force field, but this leaves the paths of the particle as nondeterministic. By adding the initial position of the particles, David Bohm shows that the paths are now deterministic, and indeed have been verified by experiments.


 * This simplicity is astounding, yet is routinely overlooked by physicists who haven't examined what Bohm said. His 1952 two-part paper is very easy to read. David Spector (talk) 11:42, 30 June 2021 (UTC)

"the latter depends on the boundary conditions of the system"
The Hartle–Hawking state page indicates that "the Hartle–Hawking state universe has no beginning...it simply has no initial boundaries in time nor space." The De Broglie–Bohm theory page states that "the latter depends on the boundary conditions of the system". Do these two observations, put together, imply that there is no non-local hidden variables theory that is compatible with the idea of the Hartle-Hawking state? (presumably the Hidden variables theory needs boundary conditions given that it is deterministic - but the Hartle-Hawking state article seems to negate this possibility). ASavantDude (talk) 20:29, 23 September 2017 (UTC)


 * A very clever question. While Schrödinger's equation is frequently accompanied by claims of its application to the entire universe, what is actually meant is that the environment of a QM experiment must be considered as being a conceptual and very real part of the experiment. This is clearly shown in the two-slit experiment when a measurement is added to reveal which slit a particle went through. The measurement itself has high enough energy and interaction to perturb the paths of the particles enough to destroy the interference pattern due to the two slits. The measurement may be considered a part of the universe "outside of" the two slits, but in this case must be considered as part of the configuration of the experiment itself. However, a subway train moving 300 meters away from the experiment is observed to have a negligible effect (in this experiment). So, while any event in the entire Universe may be said to "have an effect" everywhere else, that effect for most forces falls off at least with the square of the distance, and can certainly reach zero. However, I'm not sure this question itself is relevant to this article, which may account for its getting no response in 2 years. David Spector (talk) 16:20, 29 July 2020 (UTC)

Possible Equation Typo
The article states :

$$-\frac{\partial\rho}{\partial t} = \nabla \cdot (\rho v^\psi)$$

But the idea of $$ v^\psi $$ seems like a typo to me. Did the contributor of this forumula intend the following instead?:

$$-\frac{\partial\rho}{\partial t} = \nabla \cdot (\rho v\psi)$$

Any response appreciated. ASavantDude (talk) 20:01, 21 March 2018 (UTC)

Ontological clarification
I've been trying to understand how this theory accounts for wave function collapse, and had some trouble finding the answer to my question here. I thought I'd start a discussion here in case my brand of confusion is common, and since I don't believe myself qualified to make relevant edits.

At the end of the day, I think I was confused because there seem to be two aspects of wave function collapse that need explaining. One is how it happens at all, and the other is how a state is randomly chosen. I feel like I've heard before that a measurement has a distinct effect on a system from the evolution according to the Schrödinger equation. The explanation given to this point seems to be: "it's not distinct. If you factor in all the interacting parts, it's still just the Schrödinger equation". Meanwhile, the way this theory accounts for "random choice" seems clear enough.

Anyway, if anyone with more expertise has any input as to whether my approach to the subject can be reasonably expected from other readers, or whether I've gotten the right ideas about this theory, I'd be eager to hear. I'm also curious how much the response to the former issue is similar to other QM interpretations. Could the article be improved by such clarification? Student298 (talk) 06:12, 26 July 2020 (UTC)

Just had a chance to think about it some more, and here's what's actually bugging me: isn't the whole idea of this theory that what's being measured is the actual particle? But since it says in the ontology section that particles (or the configuration thereof) don't give any feedback to the wave equation, how can a particle be measured such that it has physical consequence? Student298 (talk) 06:39, 26 July 2020 (UTC)


 * Well, how can any macroscopic object be measured? The only basic difference between classical measurements and QM measurements is given by the Heisenberg Uncertainty Principle, a simple observational limitation easily provable from the Fourier Transform. "Wave function collapse" is motivated by the apparent wave-like nature of certain experiments having small dimensions. It is found that after a period of time, or after some experimental intervention to achieve a measurement, this unknowable, mystical wave-like situation appears to "collapse" into a simple deterministic situation involving particles.


 * However, this article shows that Bohmian mechanics, in contrast to the accepted Copenhagen Interpretation, provides a simpler explanation, one fortunately a bit more in accord with classical physics in that particle paths can be considered deterministic, determined by a guiding equation derived in a simple way from the wave function that describes the experimental configuration. It is the guiding equation that contains the wavelike nonlocal nature that is observed in the experiment.


 * It may be worthwhile to add that Bohm considers that particles have, at all times, precise values of location and momentum. This is what he means by a deterministic trajectory. It is just that these cannot be simultaneously measured in a tiny experimental regime due to the way measurement interactions work.


 * So, Bohm doesn't have to describe wave function collapse, because in his interpretation it never happens. Only the guiding equation, which is nonlocal (and thus nonclassical) is needed. What this means is that the particles themselves always remain particles and move as particles. The only difference in the regime around the distance of the radius of a small atom is that the wave function acts as a mechanical force, not merely a probability function (de Broglie may not have liked that interpretation, but it works).


 * Experiments that seem to show "collapse" upon measurement don't appear to pay attention to the fact that measuring a tiny particle to magnify its position or momentum all the way to our observational regime must impart a substantial momentum kick to the particle in order to measure it. It is fundamentally that kick that produces the effects that seem to show a collapse from the wave-like domain to the particle domain, a collapse that Bohm shows never actually happens. David Spector (talk) 16:53, 29 July 2020 (UTC)


 * I'm not sure this entirely addresses my question. I understand that in this theory, the wave function evolves on its own, and it creates forces which guide the particles. But if the particles themselves don't influence the wave function in return, how do they influence anything (measurements included)? Student298 (talk) 01:28, 9 August 2020 (UTC)


 * The particles influence other particles via the wave function. The velocity of each particle depends on the position of all of the other particles because the R^3N point that we evaluate the wave function and its gradient is the actual configuration point of all the particles. This is the main non-locality in the theory and the bit that makes people legitimately cringe though Bell's work shows there ought to be something cringe worthy in the theory. Also, the wave function is not creating forces, but rather directly dictating the velocities (minor language quibble). Jostylr (talk) 13:41, 13 June 2021 (UTC)


 * Just to clarify that the last comment by Jostylr is correct: the wave function contains the entire trajectory description (other than the initial conditions, which are the "hidden variables"). The wave function is a "guiding equation" for deterministic "trajectories", not a force that causes particle accelerations. The Schrödinger equation, used in this way, gives all the measured experimental effects (the "trajectories") for its entire nonlocal domain, which properly includes the experimental apparatus, some model of the measuring devices, and some model for the external environment (when needed). David Spector (talk) 02:15, 25 November 2021 (UTC)

Zitterbewegung
A derviation of pilot waves has been demonstrated from purely classical Maxwell’s electrodynamics and published recently in a high impact factor journal (https://doi.org/10.1007/s11071-020-05928-5). I am the author of the paper, and therefore I am not the person allowed to upload the reference, since a COI is at stake. But perhaps, if someone finds it interesting, he could introduce a section entitled “Zitterbewegung” with something similar to this:


 * Charged extended particles can experience self-oscillatory dynamics as a result of classical electrodynamic self-interactions \cite{}. This trembling motion has a frequency that is closely related to the zitterbewegung frequency appearing in Dirac's equation. The mechanism producing these fluctuations arises because some parts of an accelerated charged corpuscle emit electromagnetic perturbations that can affect another part of the body, producing self-forces. Using the Liénard-Wiechert potential as solutions to Maxwell's equations with sources, it can be shown that these forces can be described in terms of state-dependent delay differential equations, which display limit cycle behavior. Therefore, the principle of inertia, as appearing in Newton's first law, would only hold on average, since uniform motion can become unstable through a process of symmetry breaking of the Lorentz group. Consequently, pilot waves would be necessary attached to any electrodynamic body. Alvaro12Lopez (talk) 12:38, 29 September 2020 (UTC)
 * Dear Alvaro12Lopez. I am following this site. Your explanation of your publication is very interesting, and I like it very much. However I am not a learned enough physisist to judge the veracity of your publication´s content.  So if another expert user, understanding e.g. the "Lienard-Wiechert" potential, or any (peer-review?) commentator to your publication asserts it´s correctness, I will support the addition of a text, similar to that one you proposed.
 * KR, from Vienna (so nice: "Zitterbewegung" sounds to us Austrians very natural...) FrankBierFarmer (talk) 07:12, 30 September 2020 (UTC)
 * That's a terrible idea, it would be giving WP:UNDUE weight to a fringe point of view. Wikipedia should report on notable research, but what Alvaro12Lopez is trying to do is make his research notable by including it in Wikipedia. It doesn't work like this. The relevant paper has only ever been cited by himself, and he's been trying to  include it everywhere in Wikipedia. Tercer (talk) 09:07, 30 September 2020 (UTC)


 * I totally agree with Tercer. Alvaro12Lopez (talk) 10:00, 30 September 2020 (UTC)
 * is correct. Wikipedia is not the place to bring attention to novel ideas; we summarize the scientific consensus as it exists. XOR&#39;easter (talk) 16:33, 30 September 2020 (UTC)
 * Even though that according to scientific consensus De Broglie-Bohm's theory is a rather redundant interpretation of quantum mechanics for geeks. And even though that the present work is the most serious classical proof in favor of pilot waves that has ever been provided, by the property of transitivity, I have to claim that XOR'easter is totally right as well. For if I say that Tercer is right, and XOR'easter says that Tercer is right too, I must conclude the XOR'easter is right as well. And I am sure that Tercer agrees with Tercer and, for this reason, with XOR'easter. Oh my god!!! We have an equivalence class here, gentlemen. Isn't that beautiful? Let's found a club together. Sincerely, Alvaro12Lopez (talk) 07:42, 1 October 2020 (UTC)

Inadequacy of "Bohmian mechanics"
The section "Bohmian mechanics" is woefully inadequate.

For example, it fails to mention the very heart of Bohmian mechanics, that particle trajectories can be made deterministic simply by adding the intial velocities of the particles to the wave function. While the wave function describes with precision all the effects of an experimental geometry, it leaves much mystery under the Standard, or Copenhagen Interpretation of quantum mechanics. You cannot trace a particle trajectory even if you know the force field acting on it without the initial position of that particle.

Bohmian mechanics is not based on Born's Rule, as stated in this section, but derives it from first principles, analogous to the Maxwell-Boltzmann derivation of black body temperature.

Bohmian mechanics has been verified by several experiments, in which the trajectories of particles through one slit of the double-slit experiment have been experimentally determined. They agree with the predictions of Bohmian mechanics. The randomness comes from the variation in location of the particles as they enter the slit, and the "wave interference" distribution comes from the Bohmian force field determined by the Schrödinger equation. There is a widely-published computer generated image of this force field, and it is very interesting to see clearly how it determines the screen pattern.

We may be irritated by the apparent influence of Slit 1 when a photon passes through Slit 2, but this nonlocality is truly the way QM works, and reaches its peak of strangeness with QM entanglement, in which separate particles share a common QM state.

Our commonsense view of physics was determined by our senses, which operate in the standard size regime. But physics is not limited to the standard regime. For example, we want to understand how Nature works in fundamental particles, which behave strangely in the tiny regime.

The Standard Interpretation of QM was pushed on physics by Neils Bohr and has survived intact in spite of its basis being a set of axioms that must not be questioned or investigated. It enshrines wave/particle duality, wave function collapse, and many other aspects of QM as strange principles that must be accepted instead of investigated. David Bohm was free of such restrictions, and his 1952 theory has held up well in spite of the hand-waving prejudice against it. John Bell, who famously disproved all local "hidden variables" theories, wrote near the end of his life that Bohm's nonlocal "hidden variables" theory passed his test. David Spector (talk) 11:29, 30 June 2021 (UTC)

Merger
It seems to me that these pages need to be either merged or distinguished:

https://en.m.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory

https://en.m.wikipedia.org/wiki/Pilot_wave_theory

There is a lot of different information in each, but they seem to be the same topic. Etomology (talk) 18:27, 24 November 2021 (UTC)

Agree with Merging
The two articles both seem to discuss exactly the same topic: the interpretation of quantum mechanics and theory behind quantum mechanics first proposed by David Bohm in his two-part paper in 1952.

I would urge that these two articles be merged, using appropriate WP synonyms (redirects) for search purposes. I recognize that merging these articles may be a major project, one which I may not be able to find the time to undertake.

I would further urge that a distinction be drawn between the local hidden-variables theory of de Broglie and the later nonlocal hidden-variables theory of Bohm. In brief, Bell proved that de Broglie's theory (initially favored by Einstein) was incorrect and that Bohm's theory was correct.

To this day the confusion caused by lumping together the incorrect early pilot-wave theory with the later correct pilot-wave theory has been one of several obstacles to the widespread acceptance of Bohm's theory.

Another obstacle to acceptance was Bohm's getting in trouble with the House Committee on Un-American Activities, which, under the leadership of Sen. J. McCarthy hunted Communists as being the primary evil of our times. Appearing before the Committee was in many cases enough to brand a person as a Communist, regardless of actual membership in the party.

And another obstacle was Bohm's long-time interest in the philosophy of nonduality in general and of J. Krishnamurti in particular. But note that Erwin Schrödinger himself agreed with nonduality enough to write a book that was mostly about it.

I would like to see some additions to the merged article: an explicit discussion showing how Bohm eliminates the need for the axioms required by the Copenhagen Interpretation, and examples showing how the Bohm theory removes nondeterminism from at least the three following experiments: double-slit, light-polarizing filters, and the silver atom or electron spin effects of sequentially-connected Stern-Gerlach interferometers. David Spector (talk) 20:37, 24 November 2021 (UTC)

I'm not sure how article titles work (particularly with a merger), but for some context, I compared the terms "Pilot Wave Theory," "Bohmian Mechanics," and "de Broglie-Bohm Theory" Google ngram (mostly books) gives the order of frequency as Bohmian Mechanics, de Broglie-Bohm Theory, and Pilot Wave Theory respectively

https://books.google.com/ngrams/graph?content=Pilot+wave+theory%2C+bohmian+mechanics%2C+de+Broglie-bohm+theory&year_start=1927&year_end=2019&corpus=26&smoothing=0&case_insensitive=true&direct_url=t4%3B%2CPilot%20wave%20theory%3B%2Cc0%3B%2Cs0%3B%3Bpilot%20wave%20theory%3B%2Cc0%3B%3BPilot%20Wave%20Theory%3B%2Cc0%3B%3BPilot%20wave%20theory%3B%2Cc0%3B.t4%3B%2Cbohmian%20mechanics%3B%2Cc0%3B%2Cs0%3B%3BBohmian%20mechanics%3B%2Cc0%3B%3BBohmian%20Mechanics%3B%2Cc0%3B%3BBOHMIAN%20MECHANICS%3B%2Cc0%3B.t4%3B%2Cde%20Broglie%20-%20bohm%20theory%3B%2Cc0%3B%2Cs0%3B%3Bde%20Broglie%20-%20Bohm%20theory%3B%2Cc0%3B%3BDe%20Broglie%20-%20Bohm%20theory%3B%2Cc0

while Google trends (search data) gives the order as Pilot Wave Theory, Bohmian Mechanics, and de Broglie-Bohm Theory respectively

https://trends.google.com/trends/explore?date=all&geo=US&q=Pilot%20wave%20theory,Bohmian%20mechanics,De%20Broglie%E2%80%93Bohm%20theory Etomology (talk) 00:48, 25 November 2021 (UTC)


 * Thank you for the comparison. Too bad there isn't a clear winner, but I think the choice of main title isn't too important, as WP redirects would provide appropriate search targets and since the most common/popular name for this theory/interpretation is likely to change with time, as physicists start taking it more seriously. David Spector (talk) 21:36, 2 December 2021 (UTC)

History
It seems the current article's organization doesn't follow the traditional style of putting the history as one of the first topics (it's currently at the bottom). I suggest this to be changed to fit what seems to be the more traditional organization of Wikipedia articles.

Momergil (talk) 03:22, 16 September 2022 (UTC)