# Talk:Hidden variable theory

## 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.

(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 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 ( 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."

(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.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. 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

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. 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 --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, Astrobayes 22:22, 27 June 2006 (UTC)

## Merge with Bohmian mechanics

Any objections? --Michael C. Price talk 01:38, 24 August 2006 (UTC)

I have copied over and merged with Bohmian mechanics. This article will now redirect to Bohmian mechanics --Michael C. Price talk 22:16, 1 September 2006 (UTC)

I've added a link from here to Bohm interpretation - otherwise it's difficult to find the article... 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?

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! —Preceding unsigned comment added by 86.193.243.54 (talk) 23:44, 20 May 2010 (UTC)

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. — Preceding unsigned comment added by 218.253.54.64 (talk) 08:42, 18 October 2011 (UTC)

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.~~ — Preceding unsigned comment added by 176.199.13.117 (talk) 22:30, 17 March 2013 (UTC)

## 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"? —Preceding unsigned comment added by 67.183.113.131 (talk) 21:32, 8 September 2010 (UTC)

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. 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. — Preceding unsigned comment added by 129.2.129.86 (talk) 09:40, 1 May 2013 (UTC)

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. 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. — Preceding unsigned comment added by 218.253.54.64 (talk) 08:39, 18 October 2011 (UTC)

## Other approaches

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

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".

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:

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.

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

If there are no objections, I am going to make the changes indicated above.P0M (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:

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".

Could you agree? --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.P0M (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:

"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] 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]

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." ([1])
Ref2: "Since the microstate is unknown, we may also think of the ${\displaystyle \lambda }$ as a [sic] hidden variables of the kind postulated in hidden variable interpretations of quantum mechanics" ([2] 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." ([3] 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." ([4])
What is your view on this suggestion? --Chris Howard (talk) 19:12, 25 January 2012 (UTC)