Talk:Bell's theorem

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[edit] Re: Valid derivations

Re: CT's claim The derivation of the CHSH inequality that is presented is suspect.

Come on CT, you have to do better than that.

In fact, by the law of large numbers, the proof currently in the article is identical to the proof in Bell's 1971 paper with one small difference: in Bell's paper, he also allows instruments to contain hidden variables. However, this introduces no new ingredients into the proof, since the average values are still going to be in the closed interval -1, 1. In CT's proof this fact is not made clear. Aside from the that, as I said, both proofs are mathematically equivalent.--CSTAR 17:47, 23 July 2005 (UTC)

I strongly dispute your claim that the proofs are equivalent. The failure to allow for components of hidden variable associated with the detectors is no minor matter. A more important failure, though, is the omission of any mention of the hidden variables which were are the heart of the EPR debate. Furthermore, the whole structure of the thing is unrelated to that of the actual experiments. Surely we want a derivation that does apply to the real world? Bell's original version did not quite fit the bill (it required the assumption that when polarisers were parallel you necessarily got 100% agreement. This is a quantum-theoretical idea that, although usually approximately true in practice, is not required to be always true under local realism.) His later derivation was designed for use in real experiments and has been used for this purpose, though, unfortunately, it is generally misinterpreted in a manner that may turn out to be critical (see CHSH inequality page).

I've just been reading part of Nick Herbert's "Quantum Reality" and confirmed my suspicions that there are quite a number of invalid proofs of Bell's theorem around, mainly in popular books but also in serious articles. His derivation is restricted to cases where there is rotational invariance and there are no missing values. It, too, does not explicitly mention hidden variables.

These various derivations, valid only in very special circumstances, will not help readers understand the actual experiments. The derivations will make it hard to understand even the detection loophole, which is intrinsically very straightforward. People reading popular books are left with the impression that something absolutely impossible has been demonstrated, whereas the truth is that no loophole-free test has yet been done and the question of whether or not local realism is true is wide open.

Why does wikipedia have to play this game? Why can't it present an derivation that Bell himself supported instead of a pseudo-derivation invented later?

Caroline Thompson 09:49, 24 July 2005 (UTC)

Owwww, this is indeed painful. There is some merit to sticking to the historical version of the proof, and I admit the formulation as integrals over lambda is how I remember the proofs being given. As to the validity of a derivation... Naively, the derivation given in the current article appears to obey the standard assumptions of probability theory. Admittedly, probability theory has somewhat shaky axiomatic/(non-)constructive foundations; some things, like differential equations involving two or more random variables, remain undefined to this day. The axiomatic foundations of "hidden variables" are probably in much worse shape. However, these concerns don't seem to have a direct impact on Bell's theorem; at the survey level taken here, it all seems to be "sufficiently correct" to me.

Thus, naively, much of the debate here is bordering on "original research": If a derivation is flawed in some subtle way, possibly due to an inconsistency in the axiomatic foundation of probability theory, that deserves a journal article, not a WP article. If alternative derivations, which give the same result, can be distinguished by performing some experiment, then that experiment should be written up and published in a journal. It should not be debated on these pages. This is the wrong forum for such arguments. linas 19:22, 24 July 2005 (UTC)

[edit] Re: Valid derivation (bis)

In the previous section I made the claim by the law of large numbers, the proof currently in the article is identical to the proof in Bell's 1971 paper with one small difference. I have made similar arguments in discussions with Drezet. OK here's the proof of this claim. The following text has been produced (using Xemacs global replace mostly) from a portion of the article with additional editing inserting line breaks for readability, replacing use of averaging over sequences with integrals over a sample space and inserting a definition of a hidden variable model. (Note that in the article in its current version, I was using an informal model referring the reader to other articles where formal models were discussed).The proof is mathematically identical to that given by Bell's 1971 paper (e.g. prove that a certain random variable has value ≤ 2 and integrate) Now of course I don't expect CT to accept this, but I argue that any fair minded person with the knowledge of the Law of Large Numbers and access to Bell's 1971 paper will see the equivalence.

[edit] Bell's thought experiment

Bell considered a hypothetical setup in which two observers, now commonly referred to as Alice and Bob, perform independent measurements on a system S prepared in some fixed state. Each has a detector with which to make measurements. Moreover, on each trial, Alice and Bob can choose between various detector settings; after repeated trials Alice and Bob collect statistics on their measurements and correlate the results. In one version of this setup, Alice can choose between two detector settings to measure one of A(a) or A(a′), and Bob can choose between detector settings to measure either B(b) or B(b′).

There are two key assumptions in Bell's analysis: (1) each measurement reveals an objective physical property of the system (2) a measurement taken by one observer has no effect on the measurement taken by the other.

In the language of probability theory, one would say that a series of measurements corresponds to a set of samples of a random variable. Depending on how the electrons were prepared, one might expect the measurement of one electron to somehow correlate with a corresponding measurement of the other: the random variables are assumed to not be independent, but linked in some way. None-the-less, because of the independent measurements, there is a limit to the amount of correlation one might expect to see. The Bell inequality expresses that maximum amount of correlation one should expect.

A version of the Bell inequality appropriate for this example is given by Clauser, Horne, Shimony and Holt, and is called the CHSH form:

$(1) \quad \mathbf{C}(A(a), B(b)) + \mathbf{C}(A(a), B(b')) + \mathbf{C}(A(a'), B(b)) - \mathbf{C}(A(a'), B(b'))\leq 2,$

where C denotes correlation.

Experimental tests of Bell inequalities, such as the above, on quantum mechanical systems, show a correlation in excess of this limit. Thus, one seems to forced to conclude that one or both of the assumptions fails for quantum mechanics. The first assumption is roughly analogous to the assumption of local realism; the second corresponds to the idea that no hidden message is exchanged between the particles or the particle detectors at the time of the measurement, the one particle "telling" the other how it should get measured.

[edit] Statement of Bell's theorem

In statistics, the correlation coefficient of random variables X, Y is

$\frac{1}{\sigma_X \sigma_Y} \bigg(\operatorname{E}(X Y) - \operatorname{E}(X) \operatorname{E}(Y)\bigg),$

where σ_X is the square root of the variance of X. However, in this article, we will refer to the closely related, but unnormalized quantity

$\mathbf{C}(X,Y) = \operatorname{E}(X Y)$

as the correlation.

We assume there is a hidden parameter space Λ and the observed outcomes by both Alice and Bob result by random sampling of the parameter λ ∈ Λ. Moreover, we assume that observed values are functions of the local detector settings and the hidden parameter only.

Value observed by Alice with deterctor setting a =A(a, λ)

Value observed by Bob with deterctor setting b =B(b, λ)

In particular, the hidden parameter space Λ has a probability measure ρ and the expectation of a random variable X on Λ with respect to ρ is written

$\operatorname{E}(X) = \int_\Lambda X(\lambda) \rho(\lambda) d \lambda$

where for accessibility of notation we assume that the probability measure has a density. Bell's theorem. The CHSH inequality (1) holds under the hidden variables assumptions above.

For simplicity, let us first assume the observed values are +1 or −1. ; we remove this assumption in Remark 1 below.

Let λ ∈ Λ. Then at least one of

$B(b, \lambda) + B(b', \lambda), \quad B(b, \lambda) - B(b', \lambda)$

is 0. Thus

$A(a, \lambda) \ B(b, \lambda) + A(a, \lambda) \ B(b', \lambda) +A(a', \lambda) \ B(b) - A(a', \lambda) \ B(b', \lambda) =$

$A(a, \lambda) (B(b, \lambda) + B(b', \lambda))+ A(a', \lambda) (B(b, \lambda) - B(b', \lambda)) \leq 2.$

and therefore

$\mathbf{C}(A(a), B(b)) + \mathbf{C}(A(a), B(b')) + \mathbf{C}(A(a'), B(b)) - \mathbf{C}(A(a'), B(b')) =$

$\int_\Lambda A(a, \lambda) \ B(b, \lambda) + \int_\Lambda A(a, \lambda) \ B(b', \lambda) + \int_\Lambda A(a', \lambda) \ B(b, \lambda) - \int_\Lambda A(a', \lambda) \ B(b', \lambda) =$

$\int_\Lambda \bigg\{A(a, \lambda) \ B(b, \lambda) + A(a, \lambda) \ B(b', \lambda) +A(a', \lambda) \ B(b, \lambda) - A(a', \lambda) \ B(b', \lambda)\bigg\} \rho(\lambda) d \lambda =$

$\int_\Lambda \bigg\{A(a, \lambda) (B(b, \lambda) + B(b', \lambda))+ A(a', \lambda) (B(b, \lambda) - B(b', \lambda)) \bigg\} \rho(\lambda) d \lambda \quad$

$\leq 2.$

Remark 1. The correlation inequality (1) still holds if the variables A(a, \lambda;), B(b,\lambda;) are allowed to take on any real values between -1, +1. Indeed, the relevant idea is that each summand in the above average is bounded above by 2. This is easily seen to be true in the more general case:

$A(a, \lambda) \ B(b, \lambda) + A(a, \lambda) \ B(b', \lambda) + A(a', \lambda) \ B(b, \lambda) - A(a', \lambda) \ B(b', \lambda) =$

$= A(a, \lambda) (B(b, \lambda) + B(b', \lambda)) +A(a', \lambda) (B(b, \lambda) - B(b', \lambda)) \quad$

$\leq \bigg|A(a, \lambda) (B(b, \lambda) + B(b', \lambda)) +A(a', \lambda) (B(b, \lambda) - B(b', \lambda) ) \bigg| \quad$

$\leq \bigg|A(a, \lambda) (B(b, \lambda) + B(b', \lambda), \lambda)\bigg| +\bigg|A(a', \lambda) (B(b, \lambda) - B(b', \lambda), \lambda)\bigg|$

$\leq |B(b, \lambda) + B(b', \lambda)| +| B(b, \lambda) - B(b', \lambda)| \leq 2.$

To justify the upper bound 2 asserted in the last inequality, without loss of generality, we can assume that

$B(b, \lambda) \geq B(b', \lambda) \geq 0.$

In that case

$|B(b, \lambda) + B(b', \lambda)| +| B(b, \lambda) - B(b', \lambda)| =B(b, \lambda) + B(b', \lambda) + B(b, \lambda) - B(b', \lambda) = 2 B(b, \lambda) \leq 2.$ .

Remark 2. With the extension given in Remark 1, CHSH inequality still holds even if the instruments themselves contain hidden variables. In that case, averaging over the instrument hidden variables gives new variables A(a, λ), B(b, λ) on Λ to which we can apply the previous remark

This is a great improvement, but it is still, I'm afraid, misleading. Do re-read Bell on the subject. The variables we measure don't take on any value between -1 and +1. They do frequently, however, take the value 0. The reason that the average for given λ is not always +1 or -1 is not merely that you sometimes get the opposite of what you'd expect but because many of the values are 0.

Incidentally, do we need to have the general definition of a correlation given here? Isn't it enough to say that what Bell looked at was the quantum correlation? We could even (says she, hopefully!) get away from any use of X and Y notation! And (dare I say it?) Latex. Personally, I much prefer the smaller font of ordinary text.

Another point: I've always understood Bell's theorem to have two parts: an inequality that is obeyed under local realism plus the observation that QM infringes it. Caroline Thompson 09:06, 25 July 2005 (UTC)

Misleading? Look at equations (8) in his 1971 paper. Compare them to eq (7). --CSTAR 13:04, 25 July 2005 (UTC)

Caroline, +1, -1 and 0 are elements of the set "any value between -1 and +1". Assuming a smaller, restricted set does not change the math. So I don't understand what you are complaining about. As to quantum correlation, that article is horrid, and needs to be deleted or re-written to actually say something meaningful. Right now, its completely garbled. linas 14:04, 25 July 2005 (UTC)

CSTAR and Linas: I'm interested in physics, not maths. A mathematical truth such as the fact that the set -1, 0 and +1 is a subset of the set of values between -1 and 1 is not relevant to the issue. The theorem concerns what is measured, and the values measured cannot take just any old real value -- they are restricted to the three (well, not quite true, since in actual experiments there is a fourth possibility, in that you can get both + and - at the same time). Anyway, the point is that the mathematical derivation ought to be as clearly related to the experiments it models as possible. It ought not, therefore, to imply that the apparatus used can give non-integer readings.

Re the quantum correlation page, only the first sentence is actually needed. The rest is context. Perhaps this could be made clearer. Caroline Thompson 20:47, 25 July 2005 (UTC)

I take it my opinion that Bell's theorem comprises two parts -- the local realist inequality and the QM prediction -- has been voted out. We really need an independent opinion on this. Apart from this doubt, though, the introduction is now good. In view of the definition you've assumed, does the QM derivation now deserve to be present?

Incidentally, I note that there is a link to the now re-directed "Bell test loopholes" page. Surely we can say a little more on these than is given in Bell test experiments? The topic does deserve a page of its own.

I revised the quantum correlation page late last night and am not sure I've got it right. I found myself inevitably beginning to transform it into a page on the detection loophole. The point is that the local realist formula can cover null outcomes easily, but the QM one (which I probably should have given as well) is only intended for the case where all outcomes are +1 or -1. The only way of making the QM theory apply to experiments with inefficient detectors is to assume that we can take just the set of coincidences and treat these as if they were the set of emitted pairs. In other words, we are forced to assume "fair sampling". This is why the separate definition of "quantum correlation" is important. When there are no null results, because the mean on each side is (under rotational invariance) zero and because all results have absolute value 1, the definition coincides with the ordinary one. When there are some null values, the difference becomes critical. [I'll put this para in the "quantum correlation" talk page as well.] Caroline Thompson 12:52, 26 July 2005 (UTC)

[edit] Psychology

I'm not sure I agree with this:

The desire for a hidden-variable theory was based on the set of psychological preconceptions about "how the real world works" based on one's contact with the macroscopic

It would be as though we could reduce Kant's transcendental aesthetic to psychology. I'm sure it has been tried, but I don't think this psychological reductionism is a good idea.--CSTAR 13:58, 19 July 2005 (UTC)

I was interrupted while writing that sentence. Change it. I can't find the right word to express the idea of "literalist belief in macroscopic-based aesthetics based on ordinary mental conditioning" that I'm grasping for in this paragraph. linas 01:27, 20 July 2005 (UTC)

is memeplex fits the definition:belief ,based on Ordinary mental conditioning, education/indoctrination/propoganda?. a replicated (by mental conditioning ) belief would be such memeplex.

[edit] Local realism

CSTAR, I'm afraid your present definition is still somewhat misleading. You say:

In order to formulate Bell's theorem, we formalize local realism as follows:

There is a probability space Λ and the observed outcomes by both Alice and Bob result by random sampling of the parameter λ ∈ Λ.

The values observed by Alice or Bob are functions of the local detector settings and the hidden parameter only. Thus

Value observed by Alice with detector setting a is A(a, λ)

Value observed by Bob with detector setting b is B(b, λ)

I think we need to explain that the "natural" interpretation of the above, in which the hidden variable space is entirely associated with the source, might apply to Bell's original inequality but not to those used in practice. The latter employ allow for the fact that there will be factors other than the actual detector settings that are associated with the polarisers and detectors and determine the actual outcomes, hidden variables associated with the source determining only the probability of detection. Though the local factors can be regarded as further components of our hidden variable, they play a logically different role and Bell, in 1971, derived his version of the CHSH inequality on the assumption that, because they were independent on the two sides, they could be averaged out and the derivation of the inequality could proceed by replacing the individual outcomes A and B by their averages over these strictly local components. In 1974 Clauser and Horne produced a derivation that better reflected what is being assumed. They worked directly in terms of probabilities of detection, not individual outcomes.

Anyway, the long and the short of it is that the definition you give is, in practice, too restrictive. If you interpret hidden variable space as including the local components, I don't think your derivation will make sense. You need to replace outcomes by either average outcomes or (as in CH74) probabilities. Caroline Thompson 09:48, 30 July 2005 (UTC)

The structure of the proof as it now exists in the article, follows exactly Bell 1971. As to your comment about hidden variables including local components, this is just a remark in Bell´s paper (and is a remark in the article). I will be happy to put in the mathematical details, which are fairly straightforward.CSTAR.

This matter of including local components is more than just a remark! It is the reason why he proceeded to do the derivation in terms of averages for given detector setting and &lambda:, and the reason why Clauser and Horne worked in terms of probabilities for the same parameters. The definition of local realism as it stands is definitely misleading, as is the fact that you work through the whole derivation as if what is measured in a given trial can take any real value and only later remark that the derivation applies to averages. I haven't looked carefully at the mathematical details. They are probably correct. It's the wording I'm objecting to and the notation.

Incidentally, I used underscores in the CHSH inequality page only because I could find no way of doing overscores. They really ought to be overscores -- the standard notation for averages. Caroline Thompson 09:14, 1 August 2005 (UTC)

The page is steadily improving! What it needs now is clarification of what the local realism assumption implies. How about includingi somewhere (before the second derivation) the following:

Though the important components of the hidden variable λ from the point of view of Bell's logic are the ones associated with the source and shared by Alice and Bob, there are others that are relevant to the separate detectors, the these others being independent. This argument was used by Bell in 1971, and again by Clauser and Horne in 1974, to justify a generalisation of the theorem forced on them by the real experiments, in which detector were never 100% efficient. The derivations were re-worked in terms of the averages of the outcomes over the local detector variables. The formalisation of local realism was thus effectively changed, replacing A and B by averages and retaining the symbol λ but with a slightly different meaning. It was henceforth restricted (in most theoretical work) to mean only those components that were associated with the source.

Caroline Thompson 09:32, 12 August 2005 (UTC)

[edit] Normalised or non-normalised correlation?

CSTAR, I'm afraid there is still a problem here. You are careful to state, correctly, that the correlation C used in Bell test derivations is an "non-normalised" one, but do not mention the fact that the estimated used in practice is normalised. This is a real problem and lies at the heart of the detection loophole. Caroline Thompson

You are using "normalized" in two different senses.--CSTAR 14:19, 14 August 2005 (UTC)

True, which all goes to show that we are not talking about "correlation" but about a rather different statistic, quantum correlation. The way in which this is estimated in practice is not the way you'd do it if you were estimating ordinary (normalised) statistical correlation. The literature often used the term "normalised correlation" but this refers to special kind of normalisation -- division by the total number of coincidences. It's perhaps better to avoid the term and say that the calculation is all done on the post-selected set of data for which coincidences are observed, i.e. selecting those trials for which outcomes on the two sides happen to be simultaneously non-zero. Caroline Thompson 08:36, 15 August 2005 (UTC)

[edit] Did Bell break Quantum Mechanics?

I'm a new user here, so please forgive any breaches of protocol on my part. I started looking into this topic a few days ago. What I have discovered so far is that Bell's Theorem implies at least one of three things:

1) Logic does not apply to the quantum world.

2) There is no intrinsic physical reality in anything. (The existence of objects depends upon our observation of them.)

3) Quantum effects are non-local.

And now you have all sorts of folks parading all over the internet arguing like demented politicians for their candidate for the truth. The truth is with a dilemma, or rather a trilemma in this case, for a conclusion no one knows what the truth is.

I suggest that Bell's theorem is not so profound as it is generally believed to be. EPR was published to prove that quantum mechanics is incomplete. Bell took that suggestion and forced completeness upon it by inclusion of the parameter $λ$ . (In all of this few seem to recall Goedel's proof that no logical system; e.g. quantum mechanics, that obeys Peano's arithmetic can be both complete and self-consistent.) As quantum mechanics is complete with the inclusion of Bell's hidden variable $λ$ it is no longer self-consistent; i.e. it gives nonsense results because because we have exceeded the bounds of the set it describes -- that of observable objects.

--Mr EE 11:43, 2 September 2005 (UTC)

Well, careful there. You have untrained novices with little or no formal education in mathematics parading all over the internet, arguing about quantum. I think the actual academic establishment, i.e. professors, those with PhD's who have worked with QM for decades, these people have a broadly accepted orthodoxy that has not really been "broken" or overturned or challenged in 80 years. There are definitely many extremely interesting things in QM, but the subtle parts are considerably more subtle than what can be reached/understood informally, by the layperson. linas

P.S. the standard orthodox answers are 1) false. 2) its not physics, its philosophy (although see einselection) 3) true. But thinking about locality hinders true understanding. linas 14:46, 2 September 2005 (UTC)

Completeness in the sense of Godel's theorem and in the sense of physics are two entirely different things. --CSTAR 14:34, 2 September 2005 (UTC)

The appeal to authority doesn't fly as far as I'm concerned. I have studied QM myself for years. When originally exposed to Bell's Theorem my reaction to it was one of disbelief and dismisal. My current interest in it stems from a remark I encountered in the course of another discussion to the effect that "Bell's Inequality" is a cracked pot notion. Bell's Inequality as far as I'm concerned is purely a math problem with no necessary recourse to physics. However, its implications for physics if true, i.e. if Bell's Theorem is true, are admittedly bizarre. I agree that 1) is false. If we say that logic is invalid in any space, we kick the legs out from under all reason. While true that 2) is a question of philosophy, you draw a false distinction between philosophy and physics when you say "it's not physics, it's philosophy." Physicists in this sense are a subset of philosophers; if not, then what are you doing here? 3) I would not say that thinking about locality hinders understanding, though I do say that thinking about locality is irrelevant. The wave function is not itself an observable, and thus I will never be able to measure the effect of non-locality upon it. Now as to CSTAR's comment, Bell included

λ

specifically to provide the kind of completeness that EPR had said quantum mechanics lacked by extending the domain of quantum mechanics to include "unobserved observables;" i.e., hidden variables of the kind that EPR, and particularly Einstein, insisted must exist.

Goedel's idea of completeness was that the logic in question, L, be able to definitively prove or definitively disprove any question to which it properly pertains. In this case, $L\equiv QM$ , and that QM answer any question about physics was specifically what Einstein had in mind when he stipulated that QM was incomplete. If you don't think so, read the original EPR paper.--Mr EE 18:15, 2 September 2005 (UTC)

The technical meaning of completeness in Goedel's completeness theorem is that a theory is complete iff a proposition is provable precisely when it is true in every model. Goedel's incompleteness theorem has various versions:model theoretic and proof theoretic, the proof theoretic being the more familiar one. But in any case, completeness in QM DOES NOT mean that it is able to answer every quesion about physics. Completeness of QM has a much more limited meaning, which is, whether properties that in the EPR terminology, are elements of physical reality correspond to elements (such observables) in QM.

Re: Your comment The appeal to authority doesn't fly as far as I'm concerned.

Who's making this appeal? I'm just telling you what I know, you can believe it or not.--CSTAR 18:42, 2 September 2005 (UTC)

Well, as to appeal to authority: most mainstream physicists have been living with and have accepted Bell's results for four decades. QM won, local theories lost. I don't think anyone serious and knowledgable runs around and says "Bell is broken"; QM isn't broken either.

RE: point 2) -- I was stating the current orthodoxy, not my beleifs. Its currently very hard to refine the notions of observer vs. observed in QM (i.e schroedingers cat/ wigners friend). The work on einselection is the *only* serious attempt I know of to work on this question. Hmm, actually, not quite true. There are some fascinating things going on with quantum chaos, but its not currently clear what bearing this will have on the measurement question.

For example: one problem that was solved recently is that of the wave functions of an ideal gas in a box. The wave functions are insanely fractal, and permeate the entire box (even if you've confined all the atoms to on side; the wave functions interfere destructively on the empty side). However, since the functions are fractals, there are all sorts of difficulties regarding support and lesbegue measure and all that. I suspect that these fractal wavefunctions permeating all space help account for einselection, but no one has been able to write these down explicitly.

RE: point 3) -- There are interesting things one can do to attempt to experimentally test locality, and Alain Aspect's experiments in France were one such. I am not aware of any groundbreaking experiments in this area since Aspect's work in the 1980's.

"Well, as to appeal to authority: most mainstream physicists have been living with and have accepted Bell's results for four decades. QM won, local theories lost. I don't think anyone serious and knowledgable runs around and says "Bell is broken"; QM isn't broken either."

I accept Bell's results. What they imply to me however is that QM is a theory about what we observe, and only about what we observe. Bell's theorem proves that QM cannot provide us any information about things we cannot observe. Are there hidden variables? Bell did not prove that there are none. He did prove however that it does not matter if there are any; that was my point. As far as physics goes if you can't measure it, it might as well be figmentary.--Mr EE 00:25, 3 September 2005 (UTC)

You folks seem to have forgotten the other option: that QM is wrong re entanglement. Once you take account of the loopholes in the various Bell tests (and Aspect's were by no means free of these) you find that alternative classical-style theories can explain all that is actually seen. Can I prove these theories are correct and QM wrong? Well, I believe this would become obvious were the experimenters to explore wider ranges of parameters. I think it could be shown that QM does not describe correctly all that we observe.

For those tests that are open to the detection/fair sampling loophole, all that is needed is to look and see what happens to the results as you vary the "discriminator" level -- the voltage level above which your instruments decide that the electrical pulse represents a "photon". I am currently studying some experiments that have already in fact shown what happens: the visibility of the coincidence curve increases as the discriminator threshold increases. In QM language, increasing the discriminator threshold means decreasing the "quantum efficiency" of the detectors. The observed increase is precisely what Bell is famously quoted as considering to be unlikely, that QM would be less successful at explaining experiments with high efficiency than with low.

The experiments in question are reported in:

S. A. Babichev, J. Appel, and A. I. Lvovsky, “Homodyne Tomography Characterization and Nonlocality of a Dual-Mode Optical Qubit”, PRL 92, 193601 (2004)

Have a look at the graph, fig. 4b. Unfortunately, the experimenters concerned currently think the observations do agree with the QM prediction, but they don't seem to be using the standard assumptions about singlet states. What we need now is a similar investigation but based on one of the already-published Bell test experiments in which the QM prediction is already specified. The usual prediction definitely does not agree with what was seen. [For more on the loopholes see my user page.] Caroline Thompson 09:15, 3 September 2005 (UTC)

This is becoming rediculous with the monotone sequence of indentation to indicate who is speaking. Because of CSTAR's objection (I believe it was CSTAR. You all will have to correct me if I'm wrong.) I read Gödel's paper: On Formally Undecidable Propositions. Having read it, I am now firmly conviced that my assessment that Bell stuck Quantum Mechanics on the horns of Gödel's dilemma is correct. The rub comes because if that is true then this entire debate about locality vs. non-locality is interminable because the question of locality itself is an exemplar of an undecidable proposition under quantum mechanics.--Mr EE 14:39, 3 September 2005 (UTC)

Reply: Yes I was the source of the comment that you responded to. Thank you for your response. However I disagree with your conclusion that the Gödel incompleteness theorem is the reason for endless and unresolved debates here between local realists and mainstream physicists. Just to make sure that we are talking about the same things, and to clarify my notation, let me go over briefly what Gödel accomplished in his paper. Please forgive me if I'm being redundant and are going over things you know.

First Gödel addresses a question about formal systems, that is systems given by a formal language together with axioms and rules of inference for formulas in that language. As you point out Gödel was addressing the question of whether "these axioms and rules of inference are also sufficient to decide all mathematical questions which can in any way at all be expressed formally in the systems concerned".

Now quantum mechanics is not ordinarily thought of as a formal theory, but in fact it is possible to provide a reasonable system for quantum mechanics. Call this theory QM. To get an idea how this formalization can be done, see for instance

Gerard Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley Interscience, 1972
Varadarajan, Geometry of Quantum Theory, Springer-Verlag, 1985.

These formal theories are sufficiently rich so that Gödel's theorem applies, so indeed there are "formally undecidable propositions" in this theory QM (as you correctly point out). The question that is being discussed, however, is whether the property of local realism can be settled within QM. To to do this, we need to formulate the property of local realism as a formula that can be written down within the language of QM. Again, this can be done; call the formula LR. However, it can be shown that within the formal system QM LR is false.

Now this does not disprove local realism, because what we have actually shown is an implication

QM implies not LR

But whether QM is actually true or not is an empirically determined fact. And local realists will argue that QM is not empirically verified (which of course I happen to think is absurd..there is abundant empirical support for QM).

It can be argued that both notions of "incompleteness" established a leitmotif for much of the intellectual development in the the latter half of the 20th century. In that sense, there is a cerain eerie similarity between the results. But my claim is that they are fundamentally different. --00:11, 5 September 2005 (UTC)

I agree. They are fundamentally different.

Incidentally, surely one should be able to ditch the part of QM that deals with entanglement without throwing away the whole thing? Personally, I think QM embodies several fundamental mistakes, invalidating a lot of the formalism. The whole idea of a theory that deals only with "observables" is bound to lead to paradoxes. One that bugs almost all of the "quantum optics" experiments I've studied is the interpretation of an interference pattern. When a quantum theorist "observes" no interference pattern, he deduces his beams were incoherent. But his theory does not, it seems, allow him to think about the other possibility: that the beams were in fact 50-50 mixtures, half with one phase difference and half differing by 180 deg. Just this one tiny "hidden" variable -- the actual relative phase of each beam -- makes all the difference, doing away with any need for magic.

Such mistakes are now deeply embedded in the theory, yet often it contains clues about what really happens. It has, as people do not tire of telling us, produced many valid predictions. We just need to look again at its successes, reject its false claims (e.g. that of entanglement) and build a new theory that is not constrained by the strictly observable. Caroline Thompson 08:58, 5 September 2005 (UTC)

CSTAR,

First, I am a total pragmatist when it comes to this stuff. QM is experimentally valid and on that basis it is foolish to discount the theory as hokum. However, as you pointed out QM can be (and indeed is) formalized in the sense of Gödel. Since this is the case, QM is either incomplete or inconsistent. Completeness formally defined according to Gödel is the property that any proposition belonging to the domain of a given logic is provably true or provably false under the axioms of said logic. This was exactly Einstein's lament with regard to QM: That the HUP left propositions belonging to QM in an indeterminant condition. Bell came along and supplied $λ$ , providing an element that completed quantum mechanics -- he stipulated what was otherwise a formally undicidable proposition. By Gödel's result this meant that QM as a logical system is inconsistent. If QM is inconsistent (with the inclusion of Bell's theorem) it is impossible to know that LR is false; likewise, it is impossible to know that it is true. Rather than cutting my own throat with Occam's razor by saying that "within the formal system of QM, LR is false," I think it more prudent to say the existence of hidden variables shows every evidence of being formally undecidable.--Mr EE 17:52, 5 September 2005 (UTC)

Mr. EE,

All meaningful logical questions should be formally decidable. As Wittgenstein said: 'Where there is a question, there is an answer'. If you can't formally get an answer, then you are simply asking logically meaningless questions. As a matter of fact, as I have shown on my page http://www.physicsmyths.org.uk/bell.htm , Bell test experiments can well be explained in terms of classical physics, so QM does not enter into the interpretation of these at all.

Thomas

[edit] The true explanation of Aspect's results

Hi Thomas, I agree with your conclusion -- that QM does not enter into the interpretation of the actual Bell test experiments -- but not, I'm afraid, with your ideas as to the true explanation of the observations. If you study the actual experimental reports and consider the likely behaviour of real photodetectors etc., you find that the exact time of detection is rarely, if ever, critical. The evidence is that the various sources used all produce short pulses of light. There is no need to assume that each necessarily comes from one individual atom. Bell-type hidden variable ideas work just as well if we substitute "light pulse from complete source region" for "photon".

The main component of the hidden variable in Aspect's experiments and other early ones would have been the direction of polarisation of the individual pulse -- something that, under QM, is not supposed to exist until the moment of detection, when it changes from a superposition of states to one particular one. See local hidden variable theory for a general picture of how this works. The basic model does not automatically reproduce the QM correlations, but there are two ways in which allowance for actual conditions improves matters:

The response of the detector to a signal of given intensity would not have been strictly a matter of proportionality. Aspect's apparatus involved "discriminators" that cut out all output voltages below a chosen threshold. Quantum theory says that the variations in voltage would have been random, but classical theory strongly suggests otherwise -- that though there would be random elements, the general trend would be towards higher voltages for stronger input signals. A recent experiment seems, to my view, to have unwittingly confirmed this to be the case. See:

S. A. Babichev, J. Appel, and A. I. Lvovsky, “Homodyne Tomography Characterization and Nonlocality of a Dual-Mode Optical Qubit”, PRL 92, 193601 (2004).

Aspect adjusted his data by subtracting "accidentals" before analysis. It can readily be shown (see my 1999 paper) that this adjustement makes a huge difference, changing results that agree (too well?) with the basic hidden variable model into ones that rule the model out. The matter of whether or not the subtraction can be justified all depends on your model of how the source works and whether or not the many atoms present there at any given time act independently or, being simultaneously illuminated by the same coherent laser beams, tend to all act together. This question has almost been ignored, probably because so few have been aware of its importance.

Until both of these points (and a few others) have been thoroughly investigated and debated, the question of the true explanation remains open. Caroline Thompson 09:04, 20 September 2005 (UTC)

Caroline,

Obviously there isn't a perfect correlation between the photoelectron emissions in both detectors as otherwise the coincidence rate should be identical to the individual count rates of the detectors, whereas in fact the former is about 2-3 orders of magnitudes less than the latter, i.e. the correlation is actually less than 1%. This is apparently because a) the only thing that is correlated between the light pulses in both channels is the arrival time of the front of the light pulses (whereas their frequencies and lengths are not) and b) there is likely to be a further de-correlation in the detectors due to the circumstance that the photoionization process is merely stochastic for the low light intensities involved (as outlined on my page regarding the Photoelectric Effect). However, by the very circumstance that a coincidence stage is being employed, all the uncorrelated events are obviously being filtered out, so one is just left with the small amount of correlated events. Because one is only interested in the relative variation of the latter, one might therefore as well assume that the light pulses in both channels are perfectly identical in the first place and examine the dependence of the coincidence rate on the polarizer orientation under this assumption (as done on my page regarding the Classical Interpretation of Bell Test Experiments).

Thomas

[edit] Important faults in the page

Hi Thomas

I don't think here is the right place to debate the issue of the particular LR model that applies to Aspect's experiments. I agree with you that there is one, but let's leave it at that for now.

There are other important faults in the page, rendering it still substandard, and these are what we should be concentrating on. For instance, the diagrams in the present version are both misleading, the second revealing ignorance of what a two-channel polariser typically does: it outputs two signals at right angles, and the device is a cube, not (as shown) merely a cuboid. Is reasonable? Why was this diagram used rather than the one currently in Bell test experiments, namely ? Caroline Thompson 21:06, 27 September 2005 (UTC)

[edit] Dr Chinese' revert games

I'll leave you to it! You're being petty. Why fuss about this particular reference to the loopholes? Why act as if you had never heard of them and did not take them seriously? I seem to remember you telling a different story a year or so ago and, indeed, you have been known to hedge your bets, admitting that local realism could, after all, be right. Caroline Thompson 21:06, 27 September 2005 (UTC)

For the uninitiated: Caroline Thompson denies the existence of photons, a fundamental element of modern physics. I am doing my best to remove her non-standard POV from Wikipedia pages related to Bell, EPR, and quantum mechanics in general. She also attempts to use Wikipedia to reference her own site in an attempt to gain search index rankings and generally to use Wikipedia as a forum for her ideas.-DrChinese 01:40, 29 September 2005 (UTC)

Re: hedge your bets, admitting that local realism could, after all, be right.

Well yes it could be "right", but it isn't.--CSTAR 00:48, 30 September 2005 (UTC)

How can the photoelectric effect be explained without photons? GangofOne 03:19, 30 September 2005 (UTC)

Dr. Chinese, you are being disruptive and rude. Please stop. While I personally beleive that in the end, QM will be upheld, it is none-the-less true that there are loopholes in the current set of experiments. Caroline is making a concerted effort to try to understand these in her own way. In general, it is vital that those who are interested in this topic understand the loopholes, as this should lead to beter experiments that can close them. Do remember that the michelson-morley experiment and the photoelectric effect were but tiny warts on the edifice of physics; if Caroline thinks she's found another wart, let her investigate. It is perhaps unfortunate that she does not have a stronger understanding in QM, but judging from your resume, you have no formal credentials in this either, and it may well be that she understands this topic better than you.

Caroline, please do continue your studies. You should probably be more conservative with your edits. I think we've got plenty enough pointers saying there are loopholes. A more comprehensive coverage of what those loopholes are would be a good thing to have, but we don't need 101 links interpenetrating all theese articles.

Among other things, it is vital that you cultivate CSTAR for his knowledge and to approach him as a freind and not an enemy. (and CSTAR, please, the same). He really does understand the math behind QM, and so I think its critical that you work collaboratively so that he gets comfortable with what you are trying to do. Be prepared to discuss, not argue, and be clear when you think there's something you don't understand, and ready to admit the same. If he says that something is this certain way, he's probably right.

In particular, I found the comment about the diagram above quite interesting. The beam splitters do indeed work at right angles, and so the black-and-white diagram is "more right" than the color one. Now, I can't imagine why this would make a difference (nor could many/most physicists), but, as they say, "the devil is in the details", and physics is founded on many subtle and supple confusions. linas 22:03, 30 September 2005 (UTC)

Sorry, linas, that ain't gonna happen. Loopholes relate to experiments, not the Theorem. CT can continue her studies in the proper forum, and that isn't here. This is for established science, and that is the beginning and end of it. And if there are loopholes in Bell tests, there are equal loopholes in every scientific experiment that exists. But that's another topic. I will be continuing the enhancement of the Bell page working with CSTAR as appropriate. He has put a lot of time into this. I plan to help polish a few rough edges which may make it more readable to the average reader. After all, that is the audience.-DrChinese 00:35, 1 October 2005 (UTC)

linas is trying to be a good citizen and he is to be commended for trying to mend fences. Although DrChinese could have been more "polite", his intervention here had no ad-hominem aspects to it and I think he is legitimately acting to restore the page to a status approved by a consensus reached long ago. I also note that CT has had standing requests on her webpage urging readers to this page to support her position. I'm not sure what WP policy is on this (and I don't intend to act as a WP policeperson) but this smacks of rabble-rousing to me.

As to the diagram, it's just a diagram, which means it's not to scale nor is it a "conformal representation" of the setup. Isn't that perfectly legitimate for a diagram?

Linas could you please help me in rewriting quantum correlation? It's really awful.--CSTAR

linas, CSTAR: We all need to work to make this group of pages better. The only person I am asking to cease and desist is CT, whose biased agenda is well documented. There is no point to trying to compromise with her, and believe me I have tried - including the private communications which she is now using to mis-portray my stance. I too want everyone to play nice and work towards the common Wikipedia goals. linas, I hope you can assist CSTAR if you have the time. My focus is trying to make sure the novice reader who comes to these pages walks away with a reasonable understanding of the subject; and that the more knowledgeable reader gets a fairly up-to-date version of where things are at. After all, there have been a lot of important new experiments just in the past 10 years. (Aspect is approaching its 25th birthday!) I do not plan to debate the scientific merits of EPR/Bell/Aspect/et al in these talk pages; this should really be done elsewhere as the science is well accepted. As to which diagram to use, they both look pretty decent to my eyes.-DrChinese 14:19, 1 October 2005 (UTC)

"My focus is trying to make sure the novice reader who comes to these pages walks away with a reasonable understanding of the subject", you (Dr Chinese) say! You will not, I think, be too surprised to find that my aim is the same. The difference is that I do not wish to see students unnecessarily misled into thinking the experiments have been more conclusive than they actually have been.

The issue is of vital importance! Suppose, after all, QM is wrong here ... it scarcely bears thinking about ...

See my comments in the Bell test experiments talk page, justifying my reversion. I fear you are suffering from major illusion regarding a matter of logic. It is in the nature of "loopholes" that every single one must be blocked at the same time in order to count.

You have been behaving as if your victory in getting my original loopholes page deleted gives you carte blanche to curtail all references to the subject. This has never been the case. It is possibly fair enough, in the current climate, to say that wikipedia does not need a separate page on the subject, but that is quite a different matter from spreading the false impression that they don't matter.

Linas, your more balanced outlook is much appreciated, as is CSTAR's, though quite why he thinks local realism "isn't right" defeats me!

Caroline Thompson 22:30, 6 October 2005 (UTC)

Caroline, note that QM will never be "wrong", although some day there may be corrections to it. By analogy, Newton's theory of gravity didn't become "wrong" just because Einstein showed up. And, in a certain sense, we already know that QM is wrong, and that quantum field theory is the more correct explanation for reality. The reasons CSTAR (and myself) don't believe in local realism is because there are these HUGE branches of inter-related, inter-twined and very beautiful mathematics, that happen to (by accident? on God's purpose?) share a lot in common with the math used in QM. I am thinking of topics ranging from the ergodic hypothesis and chaos theory where things like the transfer operator is a crude example of something from a C* algebra, which is something that occurs in functional analysis. Never mind the rotation group and its representation by SU(2) and SO(3) and the Spin algebras. The stuff fits together so marvelously, so perfectly, that it makes much more sense than local realism offers.

However, as a careful physicist, I think its important to identify and close all the "loopholes" in the EPR-type experiments. For one, its important to be able to say "now we are finally done", and for two, one may get lucky and find something new. Personally, I wouldn't bet on it, but "shit happens", such as e.g. the photoelectric effect, which was this absurd little tiny problem in the classical theory that ushered in the era of QM. linas 23:31, 7 October 2005 (UTC)

Hi Linas: I've just seen what Dr Chinese has done to the Bell test experiments page. He has reverted again, with the result that he has eliminated the standard reference (namely to Pearle, P, “Hidden-Variable Example Based upon Data Rejection”, Physical Review D, 2, 1418-25 (1970)) on the one loophole he now condescends to mention. He has totally ignored my discussion of the fact that the Rowe et al experiment (which did indeed block the detection loophole) had other serious loopholes and hence is irrelevant to the discussion. He has ignored the basic fact that all loopholes must be blocked at once if you are to claim clear success for quantum entanglement.

Is such arrogant behaviour consistent with wikipedia policy? Doesn't logic matter? Doesn't giving the best possible refs matter? Caroline Thompson 09:04, 8 October 2005 (UTC)

[edit] Mathematical models and "reality"

But Linas, physics and maths are two separate things! Your above appeal to all this "inter-related, intertwined and very beautiful mathematics" is, I fear, totally irrelevant. When we talk of local realism we necessarily mean the real physics of the real world, not a mere mathematical model that happens to fit the real world so far as certain phenomona are concerned.

I'm afraid what you wrote is such a wonderful example of something I was reading yesterday I just had to smile!

"In terms of the power it wields, Quantum Theory is today the Pentagon, if Washington DC were the world of physics. It is a formidable place that you dare not criticize. If you do, they will throw so much mathematical mumbo jumbo at you that you will forget your mother’s maiden name by the time they are done with you." [From http://www.geocities.com/bibhasde/quantum.html]

It's not as if this was news to me. I just happens that I realised 10 years ago the full implications of what I'd been taught in my maths degree back in 1965: that mathematics is no better than the assumptions that lie behind it. Only if every single assumption involved in a mathematical model agrees with something that is physically plausible am I going to even consider the possibility that it will make correct predictions of anything physical. Failing that, it is just part of a fantasy world. Caroline Thompson 08:52, 8 October 2005 (UTC)

Yeah, well, what can I say? It is almost certain that "local realism" is a part of a fantasy world, and that QM is not. As to the analogy, QM is not so much the Pentagon as it is Mount Everest. Those few who ascend come back with tales of tremendous vision. The search for local realism is like a search for a vast cave inside of Mount Everest: it may be there, and it may not. You must excuse those who might think Everest is not hollow, and even if there does prove to be a cave here, its bulk cannot be demolished and is grandeur is not diminished. It is what it is. linas 22:48, 14 October 2005 (UTC)

The pentagon? Geesh, if that analogy's true, local realists should be rubbing their hands in anticipation.--CSTAR 00:57, 15 October 2005 (UTC)

Ah well, each to his own opinion, but as to it's being "almost certain" that local realism is a fantasy, I beg to differ. I don't think you can reconcile the quantum world with the kind of model Newton might have devised, made of solid particles obeying laws similar to his gravitational one. You need something very much more subtle, in which there are probably no "solid particles" there at all, only waves, acting in ways that no waves on the everyday scale can quite match. [See my own pet "Phi-Wave Aether" idea, in which there are semi-permanent "wave centres" that play the part of particles. There are a couple of essays on it on my web site.]

Anyway, the point is that these waves or whatever are real and local, regardless of any mathematical model that says they have to be nonlocal. There is (in view of the various loopholes) no conclusive evidence that any nonlocal effects ever happen. Yes, quantum theory may be Everest, but it is a structure built effectively by a committee.

I've been looking back at the history, and everyone who was anyone would have been to one of Bohr's conferences or (more recently) had a spell working with Anton Zeilinger. A completely different group of people who had never even heard of QT might be able to build not just Everest but the whole universe! Caroline Thompson 09:22, 15 October 2005 (UTC)

Caroline, I am starting to suspect that you have never studied the mathematics of group theory, and in particular, the group representations of the rotation group SO(3) and SU(2). These are not terribly complex objects: SO(3) is a certain collection of 3 by 3 matrices, and can be readily comprehended with a bit of study and practice. I think its also critical that you learn how to add together spins, using either Clebsch-Gordon coefficients, or possibly some more modern mechanism. If you get a good book on this topic, you will find that it is not at all hard or ethereal or abstract, its pretty darned concrete as math topics go. linas 00:31, 16 October 2005 (UTC)

Linas: I do have a degree in mathematics and at one point considered a career in the subject! It's not that I couldn't do the maths if I thought it relevant but, at least in the case of light, I'm quite certain it is such a crude approximation as to be useless. If you want the "real" matrices that are appropriate for dealing with light, go back to the pre-quantum text books. Read:

Ernst Mach (John S Anderson and A F A Young trans.), “The Principles of Physical Optics”, E P Dutton and Co., Publishers, New York, 1926 (recently reprinted)

for hints of the true complexity of how light gets refracted by solids. Read:

Shurcliff, W A and Ballard, S S, "Polarized Light", Van Nostrand 1964

for the matrices and more recent interesting facts.

You could even look at papers such as:

Krasa, J and Jiricka, J and Lokajicek, M, “Transmittance of a laser beam through a pair of crossed polarizers”, Physics Letters A 186, 279-281 (1994)

Tell my how your mathematical models apply to that! Caroline Thompson 09:20, 16 October 2005 (UTC)

[edit] Web links.

I have removed the links in the following references as they were 404 erroring.

A. Aspect et al., Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities, Phys. Rev. Lett. 49, 91 (1982), available at http://fangio.magnet.fsu.edu/~vlad/pr100/
A. Aspect et al., Experimental Test of Bell's Inequalities Using Time-Varying Analyzers, Phys. Rev. Lett. 49, 1804 (1982), available at http://fangio.magnet.fsu.edu/~vlad/pr100/
J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Proposed experiment to test local hidden-variable theories, Physical Review Letters 23, 880-884 (1969), available at http://fangio.magnet.fsu.edu/~vlad/pr100/

Of curse they can be re-inserted if they come back. Rich Farmbrough 10:18, 10 November 2005 (UTC)

They seem to have gone for good -- a pity, as they were free. You can buy individual articles from http://publish.aps.org/ but that's not quite the same thing. Caroline Thompson 09:53, 11 November 2005 (UTC)

[edit] Simply connected spacetime

The following was recently removed from the article:

No physical theory of local hidden variables (on a simply connected spacetime) can ever reproduce all of the predictions of quantum mechanics.

While I agree with the removal ... it does bring up a very interesting point that I suppose should be discussed somewhere. Suppose one modelled Planck-scale spacetime as a filigree of wormholes and what-not. What form would Bell's theorem take on such a manifold? The point being that geodesics have highly ergodic trajectories on surfaces of negative curvature, so one would expect to get a giant mess of random behaviour. I think this could make for an interesting article (even if this article is not the place for that). linas 02:24, 15 November 2005 (UTC)

If finite propagation speed fails, Bell's theorem fails.--CSTAR 03:05, 15 November 2005 (UTC)

I don't understand what simple connectivity has to do with Bell's theorem at all, other than that you need a suitable spacetime (i.e. need a causal structure, which maybe requires a noncompact manifold with a global timelike vector, or some such topological restriction. Whatever the restriction, I'm sure there are non simply connected spacetimes with the appropriate causal structures.) Is there some relationship? Is the point that on multiply connected spacetimes, local hidden variable theories can reproduce quantum mechanics? I have trouble believing that. -Lethe | [[User talk:Lethe|Talk]] 03:13, 15 November 2005 (UTC)

As far as I know, nothing. But that's beyond the limits of what I know.--CSTAR 03:21, 15 November 2005 (UTC)

Yes, well, I guess its too late to retract my remarks. I convinced myself during a walk around the block that this will lead to nowhere. Maybe the point was that with appropriate hand-waving, there are still places such as this were "Bell-test loopholes" can be imagined. linas 23:44, 15 November 2005 (UTC)

[edit] "Before"?

Commenting on this quote:

It was a conclusion of EPR, that once Alice measured spin in the x direction, Bob's measurement in the x direction was determined with certainty, whereas immediately before Alice's measurement Bob's outcome was only statistically determined. Thus either spin in the x direction is not an element of physical reality or effects travel from Alice to Bob instantly.

But, at least in case of photons, not only the two measurements, but any two (space-time) points on the "trajectories" of the two particles are separated by a space-like interval. Hence, they can't be said to be "before" or "after" one another. Each measurement can be said to be after photons were emitted, but nothing more in terms of temporal sequence is defined. No point on the trajectory of Alice's photon is definitely before Bob's measurement, and no point on the trajectory of Bob's photon is definitely before Alice's measurement.

Sorry for some repetitiveness, but isn't it clear enough that the dilemma in the above quote is a false one?

If I'm not mistaken in this, quantum-mechanical nonlocality and relativistic blurring of synchronicity are so intricately intertwined here that one is tempted to think that they are but two sides of the same coin.

- M (Dmanin 06:43, 19 November 2005 (UTC))

Of course you're right. The article should say something like "so that the measurements are causally disconnected"; --CSTAR 07:18, 19 November 2005 (UTC)

[edit] Implications of violation of Bell's inequality

I'd feel a lot better about the section "Implications of violation of Bell's inequality" if violation of the reality assumption (called here "counterfactual definiteness") were put on an equal footing with violation of locality. It's really pretty silly to give up locality, since it's a basic assumption of all mainstream physics. By comparison, I've always felt it's easier to give up statements about (some) counterfactual observations. I don't think denying the reality assumption necessarily entails the many-worlds interpretation, but I'm happy to be corrected on this point. Dave Kielpinski 05:37, 14 December 2005 (UTC)

PS. If no one objects in the next few days, I may edit the relevant paragraph (in a minimally intrusive way) to accomodate my view. Dave Kielpinski 05:38, 14 December 2005 (UTC)

I'm not quite sure of what you're refering to. Can you post the suggested edits here first? "Local" is a tricky word in QM, since one must first state "local with respect to what topology in which space". Clearly, the correlation of spins in a singlet state is non-local in Euclidean space ... linas 19:42, 14 December 2005 (UTC)

In fact, it's not at all clear that QM is nonlocal. Certainly quantum field theory is local in the usual sense of the word, and attempts to extend nonlocal Bohmian mechanics to the relativistic domain have so far been unsuccessful, creating a strong presumption that QM is local. Bell inequalities for local realistic theories can be falsified by 1) giving up locality or 2) giving up realism, i.e. "counterfactual definiteness." In the article, these two options are not treated on an equal footing, and I propose to remedy that.

I realize that all sorts of crackpots are attracted to this subject - a glance at my publication record will show that I am not in that category. Dave Kielpinski 06:54, 15 December 2005 (UTC)

Added publication record to my user page. Dave Kielpinski 07:20, 15 December 2005 (UTC)

Very good, then, glad to have you here, and quite correct about the observation about crackpots. We need the help :)

Funny you mention QFT: in a typical Largrangian, the interactions are "local" in the sense that interactions are at a point or involve no more than second-order derivatives: e.g. $\overline{\psi}(x)\psi(x)\phi(x)$ is local because everything happens at point x. However, one then promptly integrates over all space-time to get the action, and then over all field values to get the functional, and so in that sense QFT is highly non-local. So, for example, any given Feymann diagram (part of a scattering matrix element) involves one or more integrals over all space-time. More simply put, Green's functions are "nonlocal", and Green's functions are "physical" in the sense that they get measured in the lab. So I still maintain that "locality" is a tricky word to use correctly in QM.

I suppose I should encourage you to edit the article, and if I don't like what I'll see, I'll scream. I'm not sure which sections you are even referring to; they may be left-over cruft from a earlier edit battle. I'm not convinced that the various articles we have in Category:Quantum measurement or even Nonlocality, Principle of locality, Action at a distance (physics), Quantum entanglement etc. are consistent, or are free of murky, wacky statements, etc. And finally, I'll admit that I'm not sure I know how to distinguish locality from realism; I've happily thrown both to the wind. I'm not even sure there is a clear definition of these terms... linas 23:24, 16 December 2005 (UTC)

I understand the distinction you are making between different uses of the word "locality" - it is a little ambiguous. I believe the standard meaning of "locality" in QFT is the first sense that you mention, i.e. interactions must be written in the form c \overline{\psi}(x) \psi{x}, while interactions like \overline{\psi}(x - x_0) \psi{x} are forbidden. Without this type of locality, the whole notion of causality is in question and QFT falls to the ground. This is also the sort of "locality" referenced in Bell's theorem. I have never encountered your second definition of "locality" in discussion or in the literature. Incidentally, your first definition seems perfectly clear to me, as all closed classical and quantum systems are in principle describable in the Hamiltonian formalism. I guess I could have edited the article by now... Dave Kielpinski 02:23, 17 December 2005 (UTC)

Definitions of locality are problematic when talking about Bell. I have taken to talking about Bell locality and Bell reality in many discussions because of the confusion. I then map those to the specific assumptions Bell made about each in his original paper. That allows you to use "local" to refer to a theory in which causes cannot propagate faster than c.--DrChinese 19:03, 3 March 2006 (UTC)

[edit] Consistent QM??

Griffiths and Omnes apparently propose some kind of "middle ground" concerning Bell's theorem, but I don't understand it and the article doesn't even mention it (except from an uncommented reference to Griffith). They propose a reformulation of the "Copenhagen" interpretation. As Griffith formulates it, "[Consistent Histories] provides a realistic picture of the atomic realm [...]. the CH appraoach removes any need to look for alternatives to standard quantum theory"

I don't understand the essence of it, but it sounds relevant for this article as well as all those that depend on this article -- can someone summarise their ideas and motivate why they are not included, or why instead they should be included?

Thanks, Harald88 22:04, 17 December 2005 (UTC)

PS I now see that there is a consistent histories page and I'll read it -- but it is currently not linked... Harald88 22:22, 17 December 2005 (UTC)

[edit] Misunderstanding of Heisenberg?

"since the act of taking the measurement changes the state." Isn't this a common misinterpretation? —The preceding unsigned comment was added by 68.183.123.151 (talk • contribs) 2006-04-03 00:35:16 (UTC)

In quantum mechanics, measurement operators do change the system state. See quantum operation.--CSTAR 01:38, 3 April 2006 (UTC)

(Unless the system state was already an eigenstate of that measurement operator. So a measurement doesn't ALWAYS change the state...) --GangofOne 03:04, 3 April 2006 (UTC)

[edit] Accessibility problems

As this is an encyclopaedia entry, I think it is only fair on the casual reader to define all variables used in the article. Articles like this should aim to educate those who have no experience of the topic, rather than those who understand it before they even started reading.

I have the same feeling as expressed above. In particular, the meaning of a' and b' is not explained in the article. I also believe that one should be careful in using the word "system". Does it refer to the whole system {A+B} or only to one of the two particles (either A or B) ? In fact, the article would become clearer if the section on "Bell's thought experiment" was rewritten to describe exactly the way it has been tested by Aspect (two photons, each travelling in its own direction and two polarizers measuring their spin in two different basis,...). Not precising the physical quantities measured tries to show the generality of Bell's theorm, but it makes the presentation confusing.--82.66.238.66 18:28, 15 April 2006 (UTC)

[edit] warning!

Bell Theorem is Religious Indoctrination(it may be called "atheistic",religion doesnt imply anything,just faith),it denies all theories that may arises in the future and denies any future science frameworks chance to break free because earlier theory and framework restricts it.Its a statement of orthodoxy to restrict science,making it more mainstream and conforming. You can argue that it true today,prfectly logical or explained by evidence but its out current understanding of events and it MAY CHANGE IN THE FUTURE. If you accept such dogma,you accept a non-theistic religion based on faith in Quantum Mechanics.Its a logical consequence of this theory.—The preceding unsigned comment was added by 84.94.153.185 (talk • contribs).

All your base are belong to us.--CSTAR 22:21, 4 May 2006 (UTC)

You have no chance to survive make your time. Dave Kielpinski 14:19, 6 May 2006 (UTC)

My dear 84.94.153.185, that's what makes Bell's Theorem so brilliant. Byrgenwulf 12:31, 28 July 2006 (UTC)

[edit] MWI counter claim

The statement:

Hence many worlds can adhere to both the properties of philosophical realism and the principle of locality and not violate Bell's conditions -- the only interpretation that can do this.

had the final clause deleted with claim that it is false. If true I would like to see a source cited, specifying which other interpretations of QM satisify these requirements. --Michael C. Price ^talk 12:19, 28 July 2006 (UTC)

"MWI is the only interpretation which can hold to philosophical realism and the principle of locality".

A few things here:

That's POV, and possibly even OR.
Where's the citation for that statement?
Relational Quantum Mechanics similarly holds to realism, inasmuch as the moon is there when we aren't looking, and locality, inasmuch as the influence of objects is restricted to their lightcone.
It accounts for EPR/Bell's Theorem very similarly to the relative state formulation...because we have to specify relative to which observer a given quantum mechanical description holds, and because observers need to interact (presumably they move at speed < c) in order to compare their results, there is no non-locality but all participants, equipment, photons/electrons etc. are real (they will have a "state" relative to some observer).
There are two references in the article in my sandbox: Rovelli (1996) and Rovelli (2006). I would cite 'em as footnotes or inline, but that would seem odd, because I am not citing a statement but a lack of one! So should I just add them to the bibliography?
Once the RQM article is done, I shall include a brief paragraph here about how it relates to Bell's Theorem.

Byrgenwulf 12:31, 28 July 2006 (UTC)

The claims for RQM I leave in your capable hands, but they will be subject to the same requirements as assertions about other interpretations. The references for the MWI claims are at Counterfactual definiteness -- they should probably appear on this article's page as well. Do you accept that MWI violates CFD? --Michael C. Price ^talk 14:24, 28 July 2006 (UTC)

This article has a very long history, some of it very bitter. One of the original editors for this page was User:Caroline Thompson a local realist who vigorously claimed QM was flawed and in fact, Bell test experiments had not disproved local realism. Dealing with her required a great deal of compromise. Please see the talk page history (and its earlier archives). She died earlier this year.--CSTAR 15:06, 28 July 2006 (UTC)

Hmmm, the issue is a subtle one; I suppose the most simple answer is that MWI violates CFD precisely because there are no counterfactuals...every possibility is actualised, so it is meaningless to contemplate what would have happened if the electron had spin up instead of down, say, because it does, just maybe not "here". I don't, however, see counterfactual definiteness as having any special value or meaning though.

The EPR/Bell section is next up in the RQM article, and obviously any claims made here will be both referenced and sound (after all, I am quite pedantic about that). Specifically this paper deals with the phenomenon, but the results follow quite simply from the original RQM formulation...it's a matter of straightforward application.

So, can we take that last clause out now? :P

CSTAR, I am not quite sure what relevance the history of this article has to with my quibble over this 7 word clause...could you perhaps explain?!? Neither of us are disputing Bell's Theorem or QM here. Is it to do with my comment above? I'm very confused... Byrgenwulf 15:32, 28 July 2006 (UTC)

This soup was concocted by chefs who had to negotiate and argue for what ingredients to put in. Not only that but ingredients kept getting taken in and out. After a while, what exactly was in the soup was never very clear. The 7 word clause was hers.

Re: Is this Thompson the anon IP address to whom I left that flippant message? I doubt it. --CSTAR 15:42, 28 July 2006 (UTC)

I see, thank you; but I really do think it should go. I just checked the unfortunate lady's userpage, and she apparently passed away in February, which means that since the message was left in May, if it was left by her we have rather more spooky action at a distance than any interpretation of QM can handle. Byrgenwulf 15:51, 28 July 2006 (UTC)

[edit] Notable quotes

The quotation from Heinz Pagels basically consists of a string of inflammatory pejoratives ("rubbish," the ad-hominem "wish-fulfilling fantasy," "really weird," and even the really weird term "beast-like") with no mention of argument or evidence. It therefore conflicts with the Wikipedian requirement of NPOV, so I propose to delete it. Since it's the only quotation listed, I propose to delete the whole "Notable quotes" section. Of course, if anyone finds a more neutral quotation, the section can be added again. —Were-Bunny 19:38, 9 October 2006 (UTC)

Since it is a sourced quote then the NPOV rule does not apply; it is not presented as a statement of fact but as a statement of Pagels' opinion. Don't delete it, but do find other quotes that express contrary opinions if you feel the section is unbalanced. --Michael C. Price ^talk 00:08, 10 October 2006 (UTC)

I'm not a physicist, so I'm loathe to edit the original article. Based on my slow reading of Gribbin (Schrodinger's Kittens, 1994), however, this comes across as a particularly messy article.

For example, the article refers to von Neumann's proof against local variables, but Gribbin claims that proof was demolished by Bell. If that is true, it should not be mentioned here as of its only historic significance.

I'll paraphrase below how Gribbin describes Bell's Theorem and its modern consequences. If this makes sense I suggest it be incorporated with a citation to Gribbin (Schrodinger's Kitten). I think I can see pieces of Gribbin's lucid summary in the article, but the message fragmented and expressed in unnecessarily formal language.

Bell's Theorem showed that if non-locality were found to occur, irregardless of any interpretation of quantum mechanics, then physics had to abandon one of two cherished beliefs:

1. That the world exists independently of our observations of it. 2. That there is no communication faster than the speed of light.

Subsequently non-locality has been shown, several times, to occur. That means we have to give up on either the "persistent world" or faster than light communications. Not surprisingly, physicists have decided the lesser evil is to accept a faster than light communication -- as long as that communication carries no "meaning". In other words, "meaning" cannot travel faster than light.

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