View source for Talk:Hidden-variable theory

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==Introduction==

Hidden variables theory was developed after quantum theory made its debut in the late 1920's. Its most modern supporter is physicist David Bohm. It proposes that the uncertainty that characterizes quantum theory and the nature of the so-called wave function for matter is just a result of our not having a complete set of variables in order to fully describe the quantum state. If we did have the full set of variables, or so the theory goes, the new ones would make the quantum state fully deterministic rather that fundamentally indeterminate as it now seems to be. The new variables seem to be extremely well 'hidden' because modern quantum theory now accounts for all of the quantities that experimentally we seem to have a good handle on such as position, time, spin, charge, energy and momentum. 

The idea is similar to the role that atoms played in understanding thermodynamics. In the late 19th century, Boltzman proposed that heat could be understood as simply the kinetic energy associated with atoms, however, many senior physicists of the day disbelieved the idea that atoms existed. Einstein later described Brownian motion in terms of atoms bouncing off of dust, and 10 years later the idea of atoms became firmly established. 

In 1932, the great mathematician John von Neumann wrote a highly influential book on Quantum Mechanics in which this theory was treated as a purely mathematical theory as though it were a branch of mathematics. He presented in this great work, a proof that no hidden-variable theory could ever reproduce the results of quantum mechanics. This is where the discussion remained until David Bohm, then in Brazil in the 1950's, refuted von Neumann's proof and wrote two papers which presented a specific model in which hidden-variables could exist, and in which quantum mechanics as we know it was preserved. However, each individual system is in a precisely definable state determined by definite laws. Quantum probabilities are a practical necessity, not a reflection that there is a lack of complete determination of the properties of matter. In other words, quantum mechanics was just another form of classical mechanics free of probabilities. indeterminism and all the other enigmas of the quantum world. 

What Bohm had done is to find a statement by von Neumann that was true most of the time, but that under certain circumstances would not hold. This mathematical statement was the crux of his proof that hidden-variable theory was impossible. Bohm found an exception to this statement, and developed his model of a hidden-variable theory to occupy this logical niche in von Neumann's otherwise correct proof. 

In the early 1960's the physicist John Stewart Bell and his physicist wife went to work at Stanford University. John Bell had always been intrigued and even a bit obsessed by the foundations of quantum theory, von Neumann's work, and the so-called Einstein-Podolsky-Rosen experiment, and he took this new opportunity to investigate this hazy area in physics. What he ultimately came up with was a surprisingly simple experimental test which defined in rather absolute terms just what kind of theory quantum mechanics is, and what the possibilities would have to be for ANY challenger to it. 

Bell's Theorem, expressed in a simple equation called an 'inequality', could be put to a direct test. It is a reflection of the fact that no signal containing any information can travel faster than the speed of light. This means that if hidden-variables theory exists to make quantum mechanics a deterministic theory, the information contained in these 'variables' cannot be transmitted faster than light. This is what physicists call a 'local' theory. John Bell discovered that, in order for Bohm's hidden-variable theory to work, it would have to be very badly 'non-local' meaning that it would have to allow for information to travel faster then the speed of light. This means that, if we accept hidden-variable theory to clean up quantum mechanics because we have decided that we no longer like the idea of assigning probabilities to events at the atomic scale, we would have to give up special relativity. This is an unsatisfactory bargain.

([[User:Caroline Thompson|Caroline Thompson]] 22:48, 30 Jun 2004 (UTC)) But there exists another kind of hidden variable theory that can explain the observed experimental results.  The [[Bell test loopholes|loopholes]] in the experiments mean that there is no compulsion to accept that Bell's inequality really has been violated.  The necessary auxiliary assumptions for the modified versions of the test ( [http://freespace.virgin.net/ch.thompson1/Tables/CHSHvCH74.htm the CHSH or CH74 test]) used in practice may well not be met.  This opens the door for theories that Einstein et al would have been happy with -- that are completely local and do ''not'' involve signals faster than light.  Adopting such a theory does mean, though, challenging the correctness of the quantum-mechanical predictions for separated particles.  As someone wrote in another Talk page (the one on quantum entanglement): "... if EPR were right, then QM wouldn't just be incomplete, it would be downright wrong."

([[User:Cema|Cema]] 04:21, 3 Dec 2004 (UTC)) I got redirected to this page from the Hidden variables. These are important in statistics. Instead of redirecting them here, as now, I suggest to make that page a disambiguation page.

link to EPR paper; goes to registration-required site.  Suboptimal.

Is it intended that text on the Talk page go into the article? The Talk page is more informative and better written than the article.[[User:67.118.119.253|67.118.119.253]] 05:08, 19 Jan 2005 (UTC)
:The edit history shows that the Talk commentary was written by the original contributor of the article. As it stands, the original commentary shows that Bohm's hidden variable theory is ill-founded. (See, for example, the last two sentences, ending in ''unsatisfactory bargain'') But the last word has not been written on this topic. [[User:Ancheta Wis|Ancheta Wis]] 06:34, 19 Jan 2005 (UTC)

Yes! E.g. "This leads to the strange situation where measurements of a certain property done on two identical systems can give different answers." (from the main article) desperately needs a reference or redaction.  AFAIK, this is only true if 'identical' is redefined as 'not MEASURABLY different', which is IMO NOT its normal meaning!  (And s/identical/not MEASUREABLY different/ results in a MUCH weaker statement!  Bell's claim/'discovery' mentioned above also desperately needs a reference.  I'm skeptical of the claim...

== Albert Einstein's effort ==

"In 1927, Einstein produced a hidden-variables interpretation of Erwin Schrödinger's wave mechanics.  But he abandoned the effort prior to publication when he found that even his own hidden-variables interpretation involved a kind of failure of spacial separability that Schrödinger later dubbed "entanglement".

From elsewhere in the article:  this effect is due to identical particles being indistinguishable.  (The wave equations are local.)

"Albert Einstein as a Philosopher of Science", by Don A. Howard, ''Physics Today'', December 2005

[[User:David R. Ingham|David R. Ingham]] 23:57, 30 January 2006 (UTC)

Apparently, his intention was to formulate a different theory that used the same Schrödinger equation.  If he were only interested in a philosophical interpretation of quantum mechanics, he would not have hoped to get rid of entanglement.  [[User:David R. Ingham|David R. Ingham]] 03:32, 31 January 2006 (UTC)

== Cleanup ==

This article looks like a bunch of informative sections without much cohesion. Please expand the intro and make the article more coherent and less ambiguous. (I'd do it myself but I don't know much about the topic.) Thanks --[[User:Zoz|Zoz]] 23:26, 3 March 2006 (UTC)

:I agree.  As it stands, it's quite informative and well-written, but the cohesion could be improved.  And it needs better references.  I'll put it on my watchlist and come back to it this weekend.  I'd like to find some peer-reviewed resources on this topic (for or against doesn't matter to me - I just want to learn more and have the current state of knowledge on this topic properly represented in the article).  Cheers, [[User:Astrobayes|Astrobayes]] 22:22, 27 June 2006 (UTC)

==Merge with [[Bohmian mechanics]]==
Any objections?  --[[User:MichaelCPrice|Michael C. Price]] <sup>[[User talk:MichaelCPrice|talk]]</sup> 01:38, 24 August 2006 (UTC)

I have copied over and merged with [[Bohmian mechanics]]. This article will now redirect to [[Bohmian mechanics]] --[[User:MichaelCPrice|Michael C. Price]] <sup>[[User talk:MichaelCPrice|talk]]</sup> 22:16, 1 September 2006 (UTC)

I've added a link from here to [[Bohm interpretation]] - otherwise it's difficult to find the article... [[User:Deadly Nut|Deadly Nut]] ([[User talk:Deadly Nut|talk]]) 14:24, 29 October 2008 (UTC)

== Dependent or Independent Variables? ==

When Einstein spoke of "hidden variables" he didn't say whether he meant independent variables or dependent variables.  The usual understanding is that he meant "dependent".  But "hidden independent variables" is just another way of saying "hidden dimensions".  Perhaps a connection with current research does exist.

== Local Hidden Variables ==

The sentence: ''"Later, Bell's theorem would prove (in the opinion of most physicists and contrary to Einstein's assertion) that local hidden variables are impossible."'' is technically misleading.  Most readers will not click the link and will assume based on the context of the paragraph that local hidden variables ~= hidden variables.  It would be more helpful to say something like ''".. Belle's theorem would prove that any hidden variable theory that is consistent with quantum mechanics is lon-local"''.  I'm not sure what the best way to phase this is to capture the fact that HVT isn't strictly ''impossible'' but rather inconsistent with relativity while still being totally accurate and including good wikilinks.

Any ideas?

[[User:Olleicua|Olleicua]] ([[User talk:Olleicua|talk]]) 05:15, 29 November 2009 (UTC)

ATTENTION: the article makes an incorrect statement: "Assuming the validity of Bell's theorem, any hidden-variable theory which is consistent with quantum mechanics would have to be non-local, maintaining the existence of instantaneous or faster than light acausal relations (correlations) between physically separated entities."

This is technically incorrect: it is possible to construct local hidden variable theories consistent with QM. See for instance the work of Itamar Pitowsky or Robert Van Wesep. However, in these theories, the hidden variable space is not like a phase space for classical mechanics, in the sense that the set of values of a hidden variable which corresponds to a certain property cannot be a Lebesgue measurable.

In conclusion: there are no classical local hidden variable theories, but there are non-classical local hidden variable theories!  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/86.193.243.54|86.193.243.54]] ([[User talk:86.193.243.54|talk]]) 23:44, 20 May 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

Another point, because there can be a variety of hidden variable theories and Bell's inequality is only valid on a certain class of local hidden variable theories, it is unclear as if EPR experiments invalidated Einstein's claims.  Unless, if we know what kind of hidden variable theory Einstein specifically chose.  <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/218.253.54.64|218.253.54.64]] ([[User talk:218.253.54.64|talk]]) 08:42, 18 October 2011 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

2 years passed and still no reaction to the comment above? I was about to state the same. Bell's theorem applies only to a certain class of local hidden variable theories, hence local hidden variables theory is still possible.~~  <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/176.199.13.117|176.199.13.117]] ([[User talk:176.199.13.117|talk]]) 22:30, 17 March 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

== SECTION: EPR Paradox & Bell's Theorem ==

Regarding ''"This rules out local hidden variable theories, but does not rule out non-local ones (which would refute quantum entanglement)."''  I don't get the parenthetical.  I would be inclined to say the non-local ones would support quantum entanglement.  Maybe someone lost a "not"?  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/67.183.113.131|67.183.113.131]] ([[User talk:67.183.113.131|talk]]) 21:32, 8 September 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

== Some comments ==

1. Unless I missed it, the article does not say who used the term first. Quoting EPR with a parenthesis is no good. von Neumann used ''"hidden" parameters''. 

2. In the lead,  think the reference to God's dice is irrelevant. [[User:Myrvin|Myrvin]] ([[User talk:Myrvin|talk]]) 06:46, 18 April 2011 (UTC)

3. In the intro, the statement that proponents of hidden variable theorems think that QM is incorrect is not precisely true-- they think it is incomplete.  <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/129.2.129.86|129.2.129.86]] ([[User talk:129.2.129.86|talk]]) 09:40, 1 May 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

== Contradiction ==

If De Broglie-Bohm "is in fact just a reformulation of conventional quantum mechanics obtained by rearranging the equations and renaming the variables" (from the intro) and "nevertheless it [De Broglie-Bohm] is a hidden variable theory" (also from intro) then the statement (from Motivation section) "in a system of trapped ions, quantum mechanics conflicts with hidden variable theories regardless of the quantum state of the system" CANNOT also be true.  Otherwise, in a system of trapped ions, a reformulation of conventional quantum mechanics that is also a hidden variable theory would conflict with hidden variable theories regardless of the quantum state of the system.  At least one of the three statements above, as written, must therefore be false.  I think this article needs the attention of an expert.
[[User:Ross Fraser|Ross Fraser]] ([[User talk:Ross Fraser|talk]]) 07:31, 16 July 2011 (UTC)

The statement "It is in fact just a reformulation of conventional quantum mechanics obtained by rearranging the equations and renaming the variables." is biased because it suggests interpretations of quantum mechanics should come up with new equations.  This is a wrong understanding of what "interpretation" really does.  <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/218.253.54.64|218.253.54.64]] ([[User talk:218.253.54.64|talk]]) 08:39, 18 October 2011 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

==Other approaches==

Do we want to extend coverage to other fringe theories with hidden variables? [[User:John Pons|John Pons]] ([[User talk:John Pons|talk]]) 07:30, 7 November 2011 (UTC)

== Recent addition ==

Recently added:
<blockquote>The designation of variables as underlying “hidden” variables depends on the level of physical description (so for example "if a gas is described in terms of temperature, pressure, and volume, then the velocities of the individual atoms in the gas would be hidden variables".</blockquote>
To me this sentence says that there are some variables that are getting "designated" (whatever that may mean in this context), and their designation asserts that they underlie some other variables that are called "hidden variables," and that the first act of designation is in some way dependent on the level of physical description involved. 

Maybe the sentence is intended to assert:
<blockquote>Declaring variables to be "hidden variables" that underlie other (known, measurable, or predictable) variables '''can be''' dependent on the level of physical description being employed. Thus the values of positions and momenta of individual atoms in a gas, while determinable according to classical physics, would be regarded as "hidden" in cases where only the temperature, pressure, and volume of a gas are measured and the more fundamental measures are only to be inferred.</blockquote>

As it stands the passage quoted is likely to confuse and frustrate our intended readership.[[User:Patrick0Moran|P0M]] ([[User talk:Patrick0Moran|talk]]) 18:57, 21 January 2012 (UTC)

If there are no objections, I am going to make the changes indicated above.[[User:Patrick0Moran|P0M]] ([[User talk:Patrick0Moran|talk]]) 09:02, 23 January 2012 (UTC)

Over-all, I find the new statement less understandable than the previous one, yet the initial words in your formulation are certainly an improvement. Proposal:
<blockquote>Declaring variables to be "hidden variables" that underlie other (known, measurable, or predictable) variables depends on the level of physical description; so for example "if a gas is described in terms of temperature, pressure, and volume, then the velocities of the individual atoms in the gas would be hidden variables".</blockquote>
Could you agree? --[[User:Chris Howard|Chris Howard]] ([[User talk:Chris Howard|talk]]) 16:53, 23 January 2012 (UTC)

:I don't think so. To begin with, I have some doubt about what the original passage was intended to convey. I also have growing doubts about whether anything about "hidden variables" that are not at present unavailable to empirical discovery should be put into an article about variables that are only assumed to exist because people like Einstein could not accept the alternative. To do so sets up a situation in which a physical "reality" that is accepted by people who believe in classical physics and which has gas atoms of measurable velocities as part of its picture is presented as an analog for a physical "reality" that has macro-world determinable values (e.g., where a photon shows up on a detection screen) and may or may not have determinations that we are unaware of that determine where that photon had to show up. So the plausibility of the classical picture of gasses composed of atoms or molecules with determinate trajectories argues for the plausibility of an EPR picture of reality in which there are "real" factors analogous to the aforesaid trajectories that determine where psi-functions will collapse, etc.   

:If I have managed to grok my way through to whatever the original meant, then I think it has one main problem. It says:  (1) "The designation of variables as underlying 'hidden' variables '''depends on''' the level of physical description," is an ungrounded assertion of whoever wrote that sentence. There is no proof offered, either by reason or by the authority gained by citing some qualified source, that what is hidden depends on the level of physical description. Saying that Hiram Poor is located in the United States does not make the place from which he is now making a cell phone call "hidden." Rather than (1), it is possible that some variables are hidden for other reasons. EPR said, in effect, "It's got to be there, even if we cannot possibly measure it." They didn't say, "It's there, whether we bother to pay attention to it or now."

:Your proposed statement has a problem, also shared by the original, in that it asserts that the level of physical description used causes experimenters to declare some variables as hidden. All that experimenters do when they use the "temperature, pressure, volume" picture is to measure and work with these variables and '''ignore''' anything else they may happen to know about. So your version should conclude with the words: "then the velocities of the individual atoms in the gas would be '''ignored''' variables." But EPR were forced to assert the existence of hidden variables because there were no merely glossed over variables that they could bring forth to account for the appearance of there being some "spooky action at a distance." And the Bell inequality argument indicates that there are not even any variables there to be discovered at some time in the future when measurement technologies improve. So there is, in other words, nothing to put in place of the trajectories of gas atoms or molecules as understood in classical mechanics.[[User:Patrick0Moran|P0M]] ([[User talk:Patrick0Moran|talk]]) 19:44, 23 January 2012 (UTC)

::I have given it some further thought. It may be preferable to work out this point explicitly in the article. Now-suggested text:
::<blockquote>"From the point of view of hidden variable theories, a ''hidden variable theory'' description of the ''quantum mechanical system'' can be seen in analogy to a ''classical statistical mechanics'' description of the ''thermodynamics of a classical gas'' where the positions and momenta of the gas atoms play the role of "hidden" variables of the gas." [as reference any of Ref1 or Ref2 or Ref3 below] [[John Stuart Bell|Bell]] has emphasized concerning the hidden variables of quantum theory that “these variables, by hypothesis, for the time being, cannot be manipulated at will by us”. [as reference Ref4 below]</blockquote>
::As references see for example:
::Ref1: ''"The fact that the photons had actual polarizations at all time would be a variable hidden from quantum mechanics, in the sense that the actual positions and momenta of gas atoms are hidden from classical statistical mechanics."'' ([http://books.google.de/books?id=pwrBp3ZGaUYC&pg=PA242])
::Ref2: ''"Since the microstate is unknown, we may also think of the <math>\lambda</math> as a [sic] hidden variables of the kind postulated in hidden variable interpretations of quantum mechanics"'' ([http://philosophy.wisc.edu/forster/reduction%2812%29.pdf] p. 8)
::Ref3: ''"The hidden variable theory is similar to the classical description of atoms in a gas. Since we can never know all the positions and momenta (the “hidden variables” in this case) of all the atoms in a gas, we must accept a partial, but for all practical purposes sufficient, probabilistic description. Hence we are perfectly happy in only knowing the average quantities (pressure, temperature, density, etc.) since that is all we need to design practical devices. Similarly, one may presume the existence of hidden variables in the quantum theory, where the wave function is the result of some average over the hidden variables."'' ([http://dspace.mit.edu/bitstream/handle/1721.1/36431/30822175.pdf?sequence=1] p. 19).
::Ref4: "The usual nomenclature, ''hidden variables'', is most unfortunate. Pragmatically minded people can well ask ''why bother about physical entities that have no effect on anything?'' Of course, every time a scintillation occurs on screen, every time an observation yields one thing rather than another, the value of a ''hidden'' variable is revealed. Perhaps ''uncontrolled'' variables would have been better, for these variables, by hypothesis, for the time being, cannot be manipulated at will by us." ([http://books.google.de/books?id=FGnnHxh2YtQC&pg=PA92])
::What is your view on this suggestion? --[[User:Chris Howard|Chris Howard]] ([[User talk:Chris Howard|talk]]) 19:12, 25 January 2012 (UTC)

==Removed speculative paragraph==

I've deleted this recent addition that was made to the article:

<blockquote>In late 2013 an experiment was described which tested a version of the double slit paradox from the famous [[Bohr-Einstein debates|Bohr-Einstein debates]]<ref>Momentum Transfer to a Free Floating Double Slit: Realization of a Thought Experiment from the Einstein-Bohr Debates, L. Ph. H. Schmidt et al. Physical Review Letters Week ending 2013. See also the article on [[Bohr-Einstein debates]].</ref>, in which a single projectile repeatedly behaved like a particle which not only went simultanously through both "slits" and produced interference, but also apparently "interacted" with them both (and likely also, with yet other areas in case of a photon, with the shutter between the slits). If such worldview is proved better &ndash; i.e. that a particle is in fact a [[Cardinality of the continuum|continuum]] of points somehow capable of acting independently but under a common wavefunction &ndash; it would support rather theories such as the [[De Broglie-Bohm theory|Bohm's one]] (with its guiding towards the centre of orbital and spreading of physical properties over it) than interpretations which presuppose full randomness, because with the latter it will be problematic to demonstrate universally and in all practical cases how can a particle remain coherent in time, in spite of non-zero probabilities of its individual points and areas getting separated (through a [[Cardinality of the continuum|continuum]] of different random determinations).<ref>An alternative possibility would be to assume that there is a finite number of instants/points within a given time or area, but theories which try to quantize the space or time itself seem to be fatally incompatible with the [[special relativity]].</ref> This could be disastruous to the [[Copenhagen interpretation]] and the like; the remaining view, [[Philosophical realism|realism]] &ndash; in connection with the continuity of trajectories as set by the [[special relativity]] and Feynman's [[Path integral formulation#The path integral and the partition function|deduction of the classical principle of least action]] &ndash; would lead to a theory that is [[Almost all|almost always]] deterministic.<ref>It can be argued, on the basis of mathematics and the [[Continuous function#Definition in terms of limits of functions|definition of continuity]], that any subset of points within a [[Interval (mathematics)|range]] where a certain function (i.e. momentum) is continuous is the value of a deterministic function, such as a linear function or an arc; and thus when (under the assumption of [[Philosophical realism|realism]]) e.g. physical position or energy keeps being continuous, it can be defined as a deterministic function on that range.</ref></blockquote>
{{Reflist}}
Besides much of it reading as original research, the experiment it references does not support the interpretation of its results.  The authors of the paper reporting the experiment concluded (boldface added):

<blockquote>In conclusion, we have observed Young-type interferences behind a free-ﬂoating isotope-labeled molecular double pinhole and measured the momentum transfer. <b>Consistent with Bohr’s arguments, a quantum mechanical description of the molecular slit dynamics is appropriate to describe the observed interference phenomena. Moreover, it is sufﬁcient to completely deﬁne the system dynamics; no additional treatment of the scattered projectile is necessary to describe the interference phenomena.</b> Momentum transfer from the projectile to the slit is shown to modify the interference features in full agreement with predictions from quantum modeling the kicked-molecule slit dynamics. <b>As an alternative to a quantum mechanical description of the slits, our results show that a classical description of the slits according to Einstein’s original viewpoint of the thought experiment is still possible. In that case one has, however, to assume a delocalized nonclassical interaction.</b> Interestingly, for the speciﬁc pathway-symmetric thought experiment of Fig. 1(a) this net interaction would not lead to a recoiling of the slits.</blockquote>
[[User:J-Wiki|J-Wiki]] ([[User talk:J-Wiki|talk]]) 03:57, 25 October 2014 (UTC)

----

:In their "quantum analysis", correct in general and not involving such or other interpretation, they have looked only at the effects of collision on HD+; note also that there are hardly any equations. They are not interested in quantum description of the whole process but only on what happened with the HD+ from which they read about used slit(s). But please respond, does the hellium go through the slits as a wave or as a particle? The Copenhagen interpretation discretizes experiments: during one, it must be either the former or the latter. If it is a particle, then it has a position or momentum during measurement (subject to uncertainty; they "arise" upon measurement, according to orthodox Copenhagen, and arise randomly). Then, there are also things such as momentum transfer etc. which are usual for particles. If it is a wave, however, then it can interfere, and also it can be in many places at a time during measurement. But in this experiment both momentum transfer and wave effects happen '''during one process of leaving a slit'''. So please admit that the experiment shows something that is against the orthodox Copenhagen interpretation. '''Already for this reason it is worth mentioning here'''(!), but there is one more point.

:If you take the Bohm's interpretation (which spreads properties such as charge or mass in space, if the [[De Broglie-Bohm theory|article]] is not mistaken) and then apply the guiding equation not to one selected point, but to all [[Cardinality of the continuum|continuum]] of points within the orbital, then you can easily explain how can something that acts as a particle go through both slits at a time. The interference pattern will arise due to similar effects as in Huygens' principle; momentum transfers from points (integrated, of course, because normally they will have only something like density of mass and thus density of momentum) will also follow normally. This looks like a quite natural explanation of the phenomenon, especially that photons most likely encounter the same thing when they bounce from shutters between the slits, etc. A very natural explanation is, then, that the apparent "particle", subject to all QED equations etc., '''acts proportionally "with its whole body"''' (can be normalized to 99% like with orbitals, so that the body does not extend infinitely in space). Every point follows its own way, when confronted with potentials of external fields, for instance (as in QED), though they have a common wavefunction and this makes them one and the same "particle."

:But this emergent interpretation, so natural and obvious, will never be compatible with the Copenhagen interpretation and the like, which assign certain probabilities to different outcomes of a measurement. This is why CI ''needs'' the distinction "acts as a wave" -- "acts as a particle" in experiment; in case of a particle you will have 1 position or momentum, subject to Heisenberg's, and in case of a wave you don't take these into account, so no problem! But never, in CI, you have a [[Cardinality of the continuum|continuum]] of measurements for a certain wave function; because, then, without any collapse in between, ALL POSSIBILITIES would have to occur, otherwise I don't know how do you understand the word "probability." You will not have an explanation why these other points are still "with" the wavepacket and have not flown elsewhere. For such an explanation, you would have to introduce a causal component which actually cancels all your probabilities and, thus, all the individual life of the points of an orbital. This causal component exists in the Bohm's interpretation (applied separately to the points), because the guiding equation will make the points go in such a way that the "centres of probability" are observed in choosing direction, and thus the points will keep close to the orbital, they will not escape.

:Thanks for reading this and please restore the paragraph, maybe with some deletions, because it enriches the article and is even easy to understand and admit. '''Don't hide the facts.''' And this is not so much of a speculation, because first and foremost the [[De Broglie-Bohm theory|article on Bohm's interpretation]] says they assume a kind of spreading of properties (such as mass or charge) in space: see "The ontology." So this philosophical or interpretational note is not my invention but is rooted in existing thought (even though BI usually uses only one guiding equation per particle; in this case it was insufficient).

:[[Special:Contributions/83.9.142.208|83.9.142.208]] ([[User talk:83.9.142.208|talk]]) 12:08, 26 October 2014 (UTC)
:----

::In the paragraph you have added to the article, you are stating that the referenced paper documents an experiment that is incompatible with the Copenhagen interpretation, but is consistent with Bohmian mechanics.  However, the authors of the paper make no such claim.  Instead, they specifically state that the results are consistent with Bohr's arguments -- and Bohr's arguments are, of course, representative of the Copenhagen interpretation.  They also state that the results are consistent with a non-local classical (realist) interpretation, which Bohmian mechanics is.  This is not surprising in the least, since the predictions of Bohmian mechanics are intentionally isomorphic with those of the Copenhagen interpretation; they are stating the same thing using a different language.  Which one is favored is just a matter of one's philosophical taste.

::You may think the experimetal results are inconsistent with the Copenhagen interpretation, but that's not what the paper says.  What you have written appears to be original research, not based on any peer-reviewed source, and Wikipedia is not a place to publish original research.[[User:J-Wiki|J-Wiki]] ([[User talk:J-Wiki|talk]]) 05:57, 27 October 2014 (UTC)

:::I expect that you will soon come with some admins who are your friends and who sent you here, due to surveillance on me, and ban my whole ISP (80% of this country) or lock the whole article, right? Anyway, the fact that an experiment was found where the principle of wave-particle complementarity was violated is important and should be said here.

:::I will also note that deterministic theories which explain the evolution of orbitals/"wavepackets" on a point-by-point basis do not need such complementarity principle and can still explain the phenomenon well basing on Huygens-Fresnel principle in this case ("wave") and natural self-compression of orbital ("particle") in other cases. The latter annotation can perhaps be removed if you hate it so much, but the experiment which violates one of fundamental postulates of the CI should not be hidden and is relevant here. [[Special:Contributions/83.9.139.176|83.9.139.176]] ([[User talk:83.9.139.176|talk]]) 03:07, 28 October 2014 (UTC)

::::No need for paranoia.  You claim that the principle of complementarity was violated by the experiment.  The researchers who performed the experiment apparently did not think that this was so.  For this to stay in the article, you'll need to find a peer-reviewed source that agrees with you (or get it through peer review yourself).  Otherwise, it has no importance for the article.[[User:J-Wiki|J-Wiki]] ([[User talk:J-Wiki|talk]]) 04:54, 28 October 2014 (UTC)

== misleading or wrong sentences in the lead ==

The lead of the article contains the following sentences:

:::::[[Albert Einstein]], the most famous proponent of hidden variables, objected to the fundamentally probabilistic nature of quantum mechanics,<ref name="Born-Einstein1971">{{cite book|title=The Born-Einstein letters: correspondence between Albert Einstein and Max and Hedwig Born from 1916-1955, with commentaries by Max Born|year=1971|publisher=Macmillan|page=158}}, (Private letter from Einstein to [[Max Born]], 3 March 1947: "I admit, of course, that there is a considerable amount of validity in the statistical approach which you were the first to recognize clearly as necessary given the framework of the existing formalism. I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance. ... I am quite convinced that someone will eventually come up with a theory whose objects, connected by laws, are not probabilities but considered facts, as used to be taken for granted until quite recently".)</ref> and famously declared "I am convinced God does not play dice".<ref>private letter to Max Born, 4 December 1926, [http://alberteinstein.info/vufind1/Record/EAR000038009 Albert Einstein Archives] reel 8, item 180</ref> Einstein, Podolsky, and Rosen argued that "elements of reality" (hidden variables) must be added to quantum mechanics to explain entanglement without action at a distance.<ref>{{cite journal | last1 = Einstein | first1 = A. | last2 = Podolsky | first2 = B. | last3 = Rosen | first3 = N. | year = 1935 | title = Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? | journal = [[Physical Review]] | volume = 47 | issue = 10| pages = 777–780 | doi = 10.1103/PhysRev.47.777 | bibcode=1935PhRv...47..777E}}</ref><ref>"The debate whether Quantum Mechanics is a complete theory and probabilities have a non-epistemic character (i.e. nature is intrinsically probabilistic) or whether it is a statistical approximation of a deterministic theory and probabilities are due to our ignorance of some parameters (i.e. they are epistemic) dates to the beginning of the theory itself". See: arXiv:quant-ph/0701071v1 12 Jan 2007</ref>
{{Reflist}}

I think these two sentences are free-running editorializing, and moreover, seriously misleading or wrong. The article offers two references for the second sentence, but I think they do not provide adequate support for it. On the face of it, the EPR 1935 paper does not mention hidden variables. The arXiv reference does not mention the EPR paper. Thus, on the face of it, the references do not support the sentence.

Of course many writers fondly wish that Einstein had advocated hidden variables, because that mistaken allegation, when not recognized as mistaken, makes Einstein an easy straw man, and those writers can then feel comfortable saying 'Look there, I have proved Einstein wrong; see how that makes me cleverer than Einstein.'

One can go further. The following is from the abstract of an article by Leslie E. Ballentine:

:::::Einstein ... considered Born's statistical interpretation to be the only satisfactory one, and he was not a supporter of hidden-variable theories such as that of Bohm. ... This ... was not based merely upon his famous remark that God does not play dice, but upon some definite physical arguments which did not assume determinism.<ref>Ballentine, L.E. (1972). Einstein's Interpretation of Quantum Mechanics, ''American Journal of Physics'', '''40''', 1763–1771, [http://dx.doi.org/10.1119/1.1987060 doi: 10.1119/1.1987060].</ref>
{{Reflist}}

The sentences are faulty and need to be repaired.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 16:16, 6 October 2015 (UTC)

:But what about "elements of reality" from EPR? Intended to enrich the incomplete quantum theory, right? [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 16:27, 6 October 2015 (UTC)

::A quick response, indeed!

::If it is desired to talk about EPR's 'elements of reality', perhaps that might make a suitable topic for an article, or be discussed in the article [[EPR paradox]], or somesuch. But to try to make them into "hidden variables" is, by Wikipedia criteria, as I see it, [[WP:SYN]], or some such. With respect, I think it a serious misreading to try to make 'elements of reality' into "hidden variables". I think it a grave misreading to suggest that 'elements of reality' are "intended to enrich the incomplete quantum theory". That is to read them as far more specific than EPR intended. More plausible to suggest that they wanted to rip the whole theory up and start afresh. Whatever, I think the sentences are misleading; Ballentine directly contradicts them and may come close to being a reliable source on that. The present references are clearly inadequate. If more reliable sources are called for, beyond Ballentine, I will have a look around for such. Now that I think it over, I think a natural repair would just delete the faulty sentences.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 17:25, 6 October 2015 (UTC)

::A writer to whom "hidden variables" can more obviously be attributed is David Bohm.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 17:58, 6 October 2015 (UTC)

::As did others, such as von Neumann and Pauli, Einstein considered and rejected the idea of hidden variables. For example,  Belousek's [http://philpapers.org/rec/BELEU abstract] reads "This paper considers an unpublished manuscript written by Albert Einstein in 1927 that contains an unsuccessful attempt to provide a deterministic hidden-variable completion of quantum mechanics. After laying out the formal scheme of the manuscript and developing its interpretation, its background, context and significance are discussed, particularly in regard to the impact of the failure of the scheme on Einstein's ensuing thoughts concerning the possibility for a complete quantum mechanics."[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 18:16, 6 October 2015 (UTC)

:::Wenn ich die mir bekannten physikalischen Phänomene betrachte, auch speziell diejenigen, welche durch die Quanten-Mechanik so erfolgreich erfasst werden, so finde ich doch nirgends eine Tatsache, die es mir als wahrscheinlich erscheinen lasst, dass man die Forderung II aufzugeben habe.

::::p.323 "QUANTEN-MECHANIK UND WIRKLICHKEIT", A. Einstein 1948 "Dialectica".

:::Corpuscles, waves, and even determinism are only details, the chief thing being a generalizing notion introduced in [70], namely, local elements of a physical reality. Einstein persistently strove for a universal theory which should be completely based on such elements, and considered the quantum theory as a tentative deviation from this concept—pointing out[71] that among the known facts none excluded, in principle, a return to it. Meanwhile, such a fact was predictable, not far from the thought experiment proposed in [70], and was discovered by J. Bell[22] in 1964 as a result of his deep revision of the classical concept which now began speaking not only in words but in formulas.

::::p. 880 "Quantum/Classical Correspondence in the Light of Bell’s Inequalities", Khalfin and Tsirelson 1992 "Foundations of physics".
:::[[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 18:37, 6 October 2015 (UTC)

:: Continuing from further above, not a reply to the immediately above.

::Don Howard writes: "The 1927 Solvay meeting took place in October, one month after the Volta Congress in Como and a few months after Einstein had abandoned his attempted hidden variables model of Schrödinger’s wave mechanics."<ref>Howard, D. (2007). Revisiting the Einstein–Bohr dialog up,  ''Iyyun: The Jerusalem Philosophical Quarterly'', '''56''': 57–90.</ref>
{{Reflist}}

::Bohm didn't abandon the idea. Why not cite him instead of Einstein, who did abandon it?[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 19:35, 6 October 2015 (UTC)

::::Responding to the above from Editor [[User:Tsirel|Tsirel]].

::::The quote from "Quantum/Classical Correspondence in the Light of Bell’s Inequalities", Khalfin and Tsirelson 1992 "Foundations of physics" won't do. It doesn't directly address or support the faulty sentences; it does not contain the crucial words 'hidden variable'.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 19:44, 6 October 2015 (UTC)

:::::Well, your next stop will be, probably, "[[Albert_Einstein#Einstein–Podolsky–Rosen paradox]]"; there I see: "This principle distilled the essence of Einstein's objection to quantum mechanics. As a physical principle, it was shown to be incorrect when the Aspect experiment of 1982 confirmed Bell's theorem, which had been promulgated in 1964." :-) [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 19:50, 6 October 2015 (UTC)

::::::I am not ready for that step or stop? I need to sort this one out first. Einstein wrote "However, I do not believe that quantum mechanics can serve as a starting point in the search for this basis," and I think this shows that he thought that adding things to quantum mechanics was not the way forward. The above passage from ''Dialectica'' (1948) is translated by Irene Born thus: ("principle II, i.e. the independent existence of the real state of affairs existing in two separate parts of space R<sub>i</sub> and R<sub>j</sub>.") "when I consider the physical phenomena known to me, and especially those which are being so successfully encompassed by quantum mechanics, I still cannot find any fact anywhere which would make it appear likely that requirement II will have to be abandoned." I think this too does not give direct support so as to supply reliable sourcing.

::::::Again, I think Bohm is a straightforward advocate of hidden variables and would be a better writer to refer to than is Einstein.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 21:01, 6 October 2015 (UTC)

:::::::On page 81 of ''John S. Bell on the Foundations of Quantum Mechanics'' ("Appendix: Einstein and Hidden Variables"), John Bell defends his own characterization of Einstein as a proponent of hidden variables.  Among the quotes of Einstein he provides is this:

:::::::<blockquote>Assuming the success of efforts to accomplish a complete physical description, statistical quantum theory would, within the framework of future physics, take an approximately analogous position to the statistical mechanics within the framework of classical mechanics.  I am rather firmly convinced that the development of theoretical physics will be of this type; but the path will be lengthy and difficult.  (Einstein, ''Albert Einstein, Philosopher-Scientist'' (1949), P.A. Schilpp, ed., p. 672.)</blockquote>
:::::::[[User:J-Wiki|J-Wiki]] ([[User talk:J-Wiki|talk]]) 05:29, 7 October 2015 (UTC)

:::::::: Yes. "Die Forderung II" in Einstein 1948 (quoted above) is, independent existence of spatially separated parts of a system. Einstein emphasizes it very much. And surely, he likes "Einstein locality" (and Chjoaygame likes it, too). But these two principles, taken together, form nothing but the local realism! Call it "local hidden variables", or "counterfactual definiteness + relativistic causality" or whatever; these are logically equivalent formulations of the same idea. Thus, I fail to see any gap between positions of Einstein and Bell, quantum theory aside. [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 08:12, 7 October 2015 (UTC)
:::::::: The reservation "quantum theory aside" is important. The two principles do not mention wave functions or something like that. This is "experimental metaphysics": direct link between general principles and empirical facts, revealed by Bell inspired by EPR. [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 08:16, 7 October 2015 (UTC)
:::::::: Heuristics, how to seek new theory, are a separate matter. Just to enrich the existing quantum theory by hidden variables (like Bohm)? Or rather, find a completely fresh insight? Here views of Einstein, Bell, and others, may differ. This is deep water, indeed. But it does not invalidate the fact: Einstein hoped that Nature satisfies the two principles; Bell proved the opposite (modulo the loopholes, of course). Note that the quantum theory is not mentioned in the definition of "the fact". After a single successful experiment, the quantum theory may fail badly, but The Conclusion will remain intact. [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 08:25, 7 October 2015 (UTC)
:::::::: By the way: "independent existence" (of spatially separated parts of a system) does not mean statistical independence, of course. Shared randomness is OK. And indeed, conditioning on all parts may be needed in some probabilistic calculations. However, some authors (and editors) use conditioning as an excuse for escaping shared randomness (toward so-called "Popescu-Rohrlich boxes"). This is "contextuality". I do not believe that Einstein could support this. Contextuality means broken independent existence (in disguise). [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 09:49, 7 October 2015 (UTC)

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== Classes of hidden variables ==

Is this new section relevant? I doubt. Just technical notes from introduction to probability theory, with no special relevance here. [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 04:53, 14 August 2017 (UTC)

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==Misquote of Einstein==

The initial paragraph contains a quote from Einstein of "I am convinced God does not play dice", attributed to a private letter to Max Born, dated 4 December 1926. In my collected letters, however, the quote is "I, at any rate, am convinced that He [God] is not playing at dice". This comes from: Irene Born, transl., ''The Born Einstein Letters: Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955 with commentaries by Max Born'' (Macmillan Press, 1971), p.91.[[User:Tonyproctor|TonyP]] ([[User talk:Tonyproctor|talk]]) 17:53, 17 October 2020 (UTC)

:The quote is essentially the same, minus the conjunctive expression "at any rate".  Since the quote in the lede is given outside of the context of its full paragraph, it seems to be simply a matter of improved style to leave off the conjunction, and to convert the pronoun "He" to its referent, as is commonly done.  By the way, further down in the article, in the section "God does not play dice", the full paragraph of the quote is given, as translated in [https://einsteinpapers.press.princeton.edu/vol15-trans/437 The Collected Papers of Albert Einstein, Volume 15: The Berlin Years: Writings & Correspondence, June 1925-May 1927 (English Translation Supplement), p. 403]  [[User:J-Wiki|J-Wiki]] ([[User talk:J-Wiki|talk]]) 04:32, 18 October 2020 (UTC)

:: Then I'm afraid it's paraphrasing rather than being a direct quote, either of Einstein or of Hedwig's translation. Things like this get copied all around the Internet, and into respectable publications, because no one bothers to check the original source. I have a similar misquote of Einstein where the words are fundamentally different [[User:Tonyproctor|TonyP]] ([[User talk:Tonyproctor|talk]]) 09:34, 18 October 2020 (UTC)

::: I've now made it clear in the first reference for the sentence that this is a common paraphrasing, and added a second reference with direct link to full source letter.[[User:J-Wiki|J-Wiki]] ([[User talk:J-Wiki|talk]]) 03:10, 19 October 2020 (UTC)

== "Deterministic" in the lead ==

Hidden-variable theories are not universally "proposals to provide deterministic explanations of quantum mechanical phenomena", the addition of a complete specification of the state and properties of a system does not preclude indeterminacy. Indeed there are stochastic hidden variable theories, as a quick peruse through the literature would reveal and as is even mentioned in this article with [[Stochastic quantum mechanics]] as an example. Determinism is of course relevant historically and as a motivation for developing hidden-variable theories so it should be mentioned, but the lead is incorrect. [[User:Volteer1|Volteer1]] ([[User talk:Volteer1|talk]]) 10:58, 19 January 2021 (UTC)
: I agree. It is very misleading. [[User:Schlafly|Roger]] ([[User talk:Schlafly|talk]]) 19:31, 11 October 2022 (UTC)

== Declaration of completeness of quantum mechanics, ==

In the section "Declaration of completeness of quantum mechanics" the last paragraph vaguely discusses Einstein with this cryptic sentence: 
 ''he did challenge the completeness of quantum mechanics during informal discussions over meals, presenting a [[thought experiment]] intended to demonstrate that quantum mechanics could not be entirely correct.''

So was he challenging completeness or correctness? 

His 1953 tribute article for Born is much clearer. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 22:04, 23 August 2023 (UTC)

:Honestly I don't know why the completeness argument is in this article, but [[The case for quantum mechanics being incomplete]] redirects to this article. Of course [[incompleteness of quantum mechanics]] redirects to the EPR article ;-)
:I fixed up the section FWIW.
:{{resolved}} [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 22:26, 23 August 2023 (UTC)

== Mermin vs the lead and motivation sections? ==

As far as I can tell, the clearly reliable reference Mermin, N. David. "Hidden variables and the two theorems of John Bell." Reviews of Modern Physics 65.3 (1993): 803 contradicts the lead and motivation sections. He says hidden variables imply "a pre-existing value of the measured property" contrary to quantum orthodoxy. 

He specifically discounts determinism and uncertainty as issues. 

From his introduction: 

''"But surely indeterminism, you might conclude, is built into the very bones of the modern quantum theory. Entirely beside the point!"''

''"the uncertainty principle only prohibits the possibility of preparing an ensemble of systems in which all those properties are sharply defined"''

Bell's paper never mentions uncertainty. He does mention deterministic measurements, which Mermin breaks down in to "particles have properties" and "those properties are measurable"; without the first, the second is beside the point.

I think the motivation of the article is off base and wandering to boot. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 01:11, 28 October 2023 (UTC)
:This is not about local hidden variables, but even if it was, hidden variable theories are deterministic (even if this is not the only property that these theories have). I cannot figure out how you could have a non-deterministic theory with hidden variables, what would be the point?--[[User:ReyHahn|ReyHahn]] ([[User talk:ReyHahn|talk]]) 09:34, 30 October 2023 (UTC)
::Do you have a reference for "hidden variable theories are deterministic".  That is the kind of thing that is missing in this article.
::Mermin's point is that if there are no hidden variables, then whether they are deterministic or not is "entirely beside the point". There is no reason to spill ink over determinism for things that do not exist. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 14:52, 30 October 2023 (UTC)
:I replace the Motivation section with one based on Mermin and Bell refs.  Please review. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 02:06, 7 November 2023 (UTC)

== Von Neunmann's no-hidden variables proof ==

I think we might need a separate article or at least to work out an anchor for "Von Neunmann's no-hidden variables proof" or "impossibility proof". Many article are too mouthful, every time that we have to refer to this we have to make a long sentence instead of just linking to it. [[User:ReyHahn|ReyHahn]] ([[User talk:ReyHahn|talk]]) 11:05, 19 November 2024 (UTC)

:Maybe expand [[Hidden-variable_theory#von_Neumann's_proof]] first, add an {{tl|anchor}}, and then decide if that is enough? [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 16:27, 19 November 2024 (UTC)
::Seems fair. Let me see what I can find.--[[User:ReyHahn|ReyHahn]] ([[User talk:ReyHahn|talk]]) 16:31, 19 November 2024 (UTC)
::I am changing my mind on the location of this proof. Should "Von Neunmann's no-hidden variables proof" anchor to a section of von Neumann's book ''[[Mathematical Foundations of Quantum Mechanics]]''?--[[User:ReyHahn|ReyHahn]] ([[User talk:ReyHahn|talk]]) 18:11, 19 November 2024 (UTC)r
::{{ping|XOR'easter}} what do you think?--[[User:ReyHahn|ReyHahn]] ([[User talk:ReyHahn|talk]]) 18:20, 19 November 2024 (UTC)
:::If the goal of this page is to describe things mostly qualitatively, then it would make sense to put mathematical details in the article about the book. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 18:31, 19 November 2024 (UTC)
:I just stumbled upon [[John_Stewart_Bell#Critique_of_von_Neumann's_proof]]. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 02:50, 20 November 2024 (UTC)
::The Jeffrey Bub passage there might be [[WP:UNDUE]]. Sure there are critiques to Bell, but the citations of Bub are not comparable with the citations of Bell's work.--[[User:ReyHahn|ReyHahn]] ([[User talk:ReyHahn|talk]]) 08:23, 20 November 2024 (UTC)
Question: should I create [[Von Neumann's no hidden variables proof]] and make it a redirect to von Neumann's book article section? or just leave it as link it as <nowiki>[[Mathematical Foundations of Quantum Mechanics#No hidden variables proof|Von Neumann's no hidden variables proof]]</nowiki>?--[[User:ReyHahn|ReyHahn]] ([[User talk:ReyHahn|talk]]) 10:27, 20 November 2024 (UTC)
:{{done}}--[[User:ReyHahn|ReyHahn]] ([[User talk:ReyHahn|talk]]) 09:21, 23 November 2024 (UTC)