Talk:De Broglie–Bohm theory

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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 interpretationde 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.


  • 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:

evolves by the Schrödinger equation into:

where and 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 of the apparatus lies either on the support of or of and when is replaced with 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 (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)


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: 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 (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 — Preceding unsigned comment added by (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)


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 (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)

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 (talk) 03:21, 2 March 2013 (UTC)


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? (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. (talk) 03:29, 15 December 2013 (UTC)David C. Anacker (talk) 21:15, 14 December 2013 (UTC)David C. Anacker (talk) 21:01, 14 December 2013 (UTC)David C. Anacker (talk) 00:19, 13 December 2013 (UTC) David C. Anacker (talk) 00:14, 13 December 2013 (UTC) David C. Anacker