Talk:de Broglie–Bohm theory

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:

$\psi _{\text{system}}^{0}(q_{1})\psi _{\text{apparatus}}^{0}(q_{2})$

evolves by the Schrödinger equation into:

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

where $\psi _{\text{apparatus}}^{1}$ and $\psi _{\text{apparatus}}^{2}$ 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 $\psi _{\text{apparatus}}^{1}$ or of $\psi _{\text{apparatus}}^{2}$ 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 Schrödinger 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)

Updated 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 [1].

--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)

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, --PLUMBAGO 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)

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)

Updated Research

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)

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)

External links modified

Hello fellow Wikipedians,

I have just modified one external link on De Broglie–Bohm theory. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive https://web.archive.org/web/20060613191814/http://www.mth.kcl.ac.uk:80/%7Estreater/lostcauses.html to http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XI

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{Sourcecheck}}).

Y An editor has reviewed this edit and fixed any errors that were found.

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 00:21, 9 December 2016 (UTC)

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)

External links modified

Hello fellow Wikipedians,

I have just modified 3 external links on De Broglie–Bohm theory. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive https://web.archive.org/web/20110626194505/http://www.aip.org.au/Congress2010/Abstracts/Monday%206%20Dec%20-%20Orals/Session_3E/Kocsis_Observing_the_Trajectories.pdf to http://www.aip.org.au/Congress2010/Abstracts/Monday%206%20Dec%20-%20Orals/Session_3E/Kocsis_Observing_the_Trajectories.pdf
• Corrected formatting/usage for http://www.mth.kcl.ac.uk/~streater/lostcauses.html
• Added archive https://web.archive.org/web/20110626194505/http://www.aip.org.au/Congress2010/Abstracts/Monday%206%20Dec%20-%20Orals/Session_3E/Kocsis_Observing_the_Trajectories.pdf to http://www.aip.org.au/Congress2010/Abstracts/Monday%206%20Dec%20-%20Orals/Session_3E/Kocsis_Observing_the_Trajectories.pdf

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 00:32, 7 September 2017 (UTC)

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)

---

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)

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 [2], 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)

Tercer is correct. Wikipedia is not the place to bring attention to novel ideas; we summarize the scientific consensus as it exists. XOR'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)