Talk:Quantum entanglement/Archive 5

Indistinguishability and enganglement
I think it is incorrect to write Two particles are entangled when they become fundamentally indistinguishable from each other. - even distinguishable particles may be entangled and indistinguishable particles may nevertheless be separable. Rather, the proper concept is (as written in the introduction of the whole article) that the properties of two particles cannot be described independently of each other (but only a joint description is possible), i.e. I would replace the first sentence of this section by s.th. like "Two particles are entangled if they cannot be described independently (nor by a statistical mixture of independent particles)." --Qcomp (talk) 16:42, 14 March 2011 (UTC)


 * I agree that as originally written, the statement was deficient. I clarified the text on 3/17, and it now reads:


 * "Particles become entangled if they are caused to be fundamentally indistinguishable from each other regarding some or all of their properties. If entangled, one particle cannot be fully described without considering the other(s). They remain in a quantum superposition and share a single wavefunction until a measurement is made."


 * By the way, in the reference given for the first sentence, Anton Zeilinger describes an experiment involving entanglement and then states:


 * "The fundamental reason that photon A and photon X become entangled through the procedure is basically simple. There is no way to tell which of the photons in an outgoing fiber behind the fiber coupler came from which of the incoming fibers. Thus they lose their individual identity."


 * There are numerous other very respectable sources that indicate indistinguishability regarding properties as essential for entanglement. -- J-Wiki (talk) 02:36, 23 March 2011 (UTC)


 * This indistinguishably is between the photons of the outgoing fibers in this particular experiment, as Zeilinger explains very well. But this is just one method of creating entanglement. It is perfectly possible to create entanglement between distinguishable particles, or between different degrees of freedom of a single particle, were the concept of distinguishability does not even apply. I am removing this from the concept section because it is only causing confusion. If you want to add it to the section "methods of creating entanglement", be my guest. But please expand it and explain it better. Tercer (talk) 14:11, 1 April 2011 (UTC)


 * I plan to do this, but may not have time to do so for a while. J-Wiki (talk) 22:51, 1 April 2011 (UTC)

Various comments
Here are a few comments about this article from a non-Physicist.

1 The lead really gives the impression that Einstein and friends thought entanglement was true. To say something is 'at the heart of' a paper, gives the impression (to those who don't know) that this was what the paper was in favour of. As we know, the paper doesn't use the term and - if they had used it - they would have decried it; as did its inventor, Schrodinger. The explanation later is too late. It suggests to me that the writers of the lead are in favour of entanglement (as most Physicists are, they say) and are trying to enlist the name of Einstein - even though he was against it. I would suggest that EPR be removed from the lead entirely. S should be there.
 * Actually, considering how well-established by experiment entanglement is, to not mention that Einstein considered the concept to be wrong tends could be thought to give him more credit than he should be given. But I agree that it would be good to mention that the originators of the concept considered it to be wrong (if it's done briefly and without obtuseness, for reasons of style).
 * Einstein needs to be given credit for bringing everyone's attention to the subject. He had informally and vaguely complained about the implications of QM for composite systems for many years, and finally stated his concerns in a clear way that caused other physicists to take notice.  Schrodinger needs to be given credit for driving home the concept and for naming it.J-Wiki (talk) 12:27, 25 March 2011 (UTC)


 * I would ask you to refrain talking about "in favour of entanglement" or "against entanglement". This is science, not politics. Einstein considered entanglement to be a feature that showed quantum mechanics was wrong. I know of no such position about Schrödinger. The history section cites a letter about this, but I couldn't find it. Could the author of the edit improve the reference, including where it was published? All I know is that in his scientific papers Schrödinger never said he considered entanglement to be a defect of quantum theory. Tercer (talk) 18:36, 29 March 2011 (UTC)

2 In the History, again the impression is that the EPR paper (by saying eg. 'identified') invented the term. Using the phrase 'concept of' does not help. The 'However' sentence just confuses the issue.
 * I agree that a better word is needed.J-Wiki (talk) 12:27, 25 March 2011 (UTC)

3 You should not use - in the Schrodinger quote - the term in square brackets. Is there no quote by S that actually uses the word?
 * Schrodinger's first use of the word is in the very next sentence:


 * "When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives (or ψ-functions) have become entangled."


 * But the purpose of the quote in the article isn't to show Schrodinger using the word, it's to show that he understood it's importance. To add the next sentence dilutes that, but if it helps to see his actual use of the word, then OK.

4 There should be a secondary source that says what Bell 'demonstrates precisely' - otherwise it is the writer's opinion.
 * The next sentence of the article explains this, and a link to Bell's theorem.J-Wiki (talk) 12:27, 25 March 2011 (UTC)

5 In the Concept, the first sentence is opaque. There is a confusion with which 'particles' we are reading about. Is there a quote to make it clear?
 * I've made the word link to subatomic particle.J-Wiki (talk) 12:27, 25 March 2011 (UTC)

6 As in so many of these articles, there are very few citations in this section. It all reads like OR. Again, the whole section is confusing.
 * I agree that the first paragraph needs citations. I also think that the majority of the rest of the section should be re-written.  It's not really OR, but an unencyclopedic narrative example of the concept.J-Wiki (talk) 12:27, 25 March 2011 (UTC)

7 The rest of the article has a warning for non-Physicists not to read it. Again, there seem to be few citations. Is it all OR?
 * I agree that these sections need major copyediting at the least. Much seems redundant, and everthing should be made more accessible by better explanations of what is being presented.J-Wiki (talk) 12:27, 25 March 2011 (UTC)

I shall have a go at improving this. But what I put in needs to be checked. Myrvin (talk) 09:46, 25 March 2011 (UTC)

I've now numbered my comments, so as to keep things clear. More later. Myrvin (talk) 14:57, 25 March 2011 (UTC)

1 Perhaps Schrodinger first and mention he was commenting on the EPR paper.

2 I'll think about this.

3 We should really have the first use of 'quantum entanglement', meaning what the article says it means. Obviously S contributed.

4 Referring to Bell's paper won't be good enough to say it 'demonstrates perfectly', Someone else has to say that.

5 The text should say 'subatomic particle' not wikilink to it. I still think the para will be unclear.

6 I agree with you.

7 Wish I could help on that. Myrvin (talk) 19:58, 25 March 2011 (UTC)


 * Re:2 I changed the word to "introduced".
 * Re:5 I changed the word to "physical objects" since the entanglement isn't limited to subatomic particles. This is consistent with the lead.
 * Re:6 I added citations for the first paragraph.
 * J-Wiki (talk) 18:55, 26 March 2011 (UTC)

Re 1 I had a go at the lead. Myrvin (talk) 11:23, 28 March 2011 (UTC) Re 2 And this. Bell stuff could still be clearer. Myrvin (talk) 13:45, 28 March 2011 (UTC)

Latest edits
The edits by User:Tercer are rather gung-ho for the pro-entanglers.
 * Describing EPR's reasoning as 'just plain wrong' is too strong.
 * Bell did not discover a flaw, he showed how the problem could be resolved.
 * I do not understand the words: "the predictions of quantum mechanics are independent of interpretation. otherwisely, they would be different theories, not different interpretations of a theory". At the time of EPR there were two versions of quantum theory: Einstein et al and the Copenhagen one. The article should say so. There is real history here.
 * We presumably need a citation to resolve the BB84 problem. Myrvin (talk) 07:50, 30 March 2011 (UTC)


 * Do you really believe that the predictions of quantum mechanics depend of interpretation? If so, could you give as an example, an experiment in which different interpretations give different predictions? (I mean, different predictions for observables, not for some theoretical entities behind empirical facts.) --Boris Tsirelson (talk) 09:05, 30 March 2011 (UTC)


 * There isn't such a thing as "pro-entanglers". This is science, not politics. By your use of this terminology, I presume you are "against entanglement". Exactly what this means? You think that the use of entanglement should be forbidden? Or you think the mathematical concept of entanglement is inconsistent? Or that it does not model the real world correctly? And what about the experiments? They are just lying, or do you believe in the loopholes? Please note that they test non-locality, not entanglement. As far as I know, no one did an experiment to directly test entanglement, and it is kinda hard to imagine one. About your comments:
 * 1 - They were wrong. If you don't like saying that Einstein and co. was wrong, well, unlucky you. They can't unwrite that paper (not that I think it shouldn't have been written).


 * 2 - Read Bell's paper. In section II, he reproduces EPR's argument in a simplified form, puts it in mathematical form, and says: "But it will be shown that it is not possible". The proof comes next. The issue is that EPR thought that by measuring the spin of one particle of a entangled pair in one direction, and then measuring the spin of the other particle in another direction, they knew the spin of one particle in both directions. And this is just plain wrong.


 * 3 - I couldn't say it better than Tsirelson.


 * 4 - Which BB84 problem? Tercer (talk) 13:46, 30 March 2011 (UTC)

Come-come people, let us assume WP:Good Faith. This is getting to be like one of the debates on the religious pages I edit.

Tsirelson: The words that combined "predictions" and "interpretation" were not mine. I said I didn't understand them. I used the term Copenhagen interpretation in the text. This use is surely not contentious.

Tiercer: This section is actually about history. The pro-entanglers were Bohr et al and the anti were Einstein and his lot. What I believe has nothing to do with it. I am sceptical of both sides. All you accuse me of (at length) was true of Einstein and Schrodinger.

Even if Bell did attempt to show that EPR was 'just plain wrong', that doesn't mean that Bell was 'just plain right'. The real tests came much later. BTW, if he says what you say he said, then he was wrong to think that EPR was about particle spin - it was more about position and momentum.

BB84: You removed words you said: "merely is POV; and the existence of a proof of security is the whole point of a cryptographic protocol". It may be that some reference uses the word "merely", which you removed. If not, then so be it. Myrvin (talk) 15:16, 30 March 2011 (UTC)


 * Ok, let's assume good faith. There weren't two versions of quantum mechanics. Everybody agreed about the experimental predictions of quantum mechanics. This is the theory. What they disagreed was about the interpretation of the theory; there was the Copenhagen interpretation, that was established in the Solvay conferences. Einstein (and others) thought that this interpretation was too much dogmatic. They didn't have their own, however. Nowadays there are many more interpretations, but they are just this: interpretations, not new theories. They all say the same thing about entanglement, for example. Now let's be honest: if you don't know what interpretations are, should you really be editing an article about them? That's why I wasn't assuming good faith.


 * Einstein and Schrödinger were not against entanglement. Einstein thought quantum theory itself was wrong (he didn't like the random bit) and should be supplemented by a more advanced theory. He just used entanglement to illustrate what he thought was a defect of quantum theory. Schrödinger knew that quantum theory was wrong (because of its incompatibility with relativity), but as far as I know he was comfortable with its other aspects.
 * Bell's result was just a mathematical theorem. His theorem showed that EPR's reasoning was wrong. The experimental tests showed that nature agreed with quantum mechanics instead of Einstein's philosophy. But the result of Bell was to separate EPR's philosophy from quantum mechanics, and this result is valid irrespective of experiments. The words about spin were mine, not his. They are about Bohm's simplification of EPR's gedankenexperiment. Of course Bell knew that EPR's paper was about position and momentum. To think otherwise is to insult his intelligence.
 * I had originally wrote that paragraph. Someone added the world merely. The only reference is Arthur's paper, reference 14. It does not use the world merely. Tercer (talk) 17:11, 30 March 2011 (UTC)
 * It's my understanding that EPR tried to show that the Uncertainty theory and therefore QM was incomplete. EPR wanted QM to be enhanced to become complete, the Copenhagens did not. That sounds like two versions to me. It is a moot point whether a new interpretation of a theory is a new theory. You are being insulting again. I think you should learn to moderate your language,
 * Not just a math theorem surely. All I have read says that his reasoning opened the wat for experiments that could say which of the theories (or interpretations if you will) were wrong. (He showed that both could not be correct) He wouldn't really need to do that if he had proved EPR wrong. Maybe others have a view on this. I looked at the article too - so I spotted that it was about Bohm's version of the problem. It was you who said "that EPR thought that by measuring the spin of one particle of a entangled pair in one direction ...".
 * You seem to be suggesting that E & S could think that QM was wrong but that entanglement could be right. I don't think you meant to use the word know about Schrodinger. He did propose his cat idea of course, which sounds like he was worried about other aspects of QM as well.Myrvin (talk) 19:27, 30 March 2011 (UTC)
 * Everyone wanted QM to be complete =) The difference is that most people thought that this was impossible and never tried, while Einstein actively sought holes in the theory. But he never did develop a version of quantum mechanics, not even an interpretation. That's why I say there weren't two versions. I think the first alternative interpretation was Bohmian mechanics in the fifties.


 * It is not a moot point whether an interpretation is a theory. It is the whole point. An interpretation is just the philosophical baggage that comes with the theory. Two different interpretations of a theory must say the same things about the results of the experiments you can make. Two different theories have no such requirement.


 * The point about Bell is that until his theorem, no one knew that Einstein's philosophy and quantum mechanics were incompatible. They tried to accept both, because both were very compelling. But his theorem is that a particular experiment would give different results, were Einstein's philosophy or quantum mechanics were true. Of course, being a math theorem, he couldn't predict which one would be right, hence the need for an experiment. But he proved Einstein's wrong in that Einstein believed his philosophy was compatible with quantum mechanics.


 * Yes, I just said that it is about Bohm's version and that the words were mine. Look in the previous response: "The words about spin were mine, not his. They are about Bohm's simplification of EPR's gedankenexperiment."


 * Yes I meant to use the word "know". Since Schrödinger published his original paper he knew that his QM was incompatible with special relativity. Everybody knew this, it is a basic fact which is easy to check. It was Dirac who corrected it. See here. The point of his cat was to show the absurdity of the Copenhagen interpretation. It wasn't about showing QM wrong. Let me drive the point further: every physicist knows QM is wrong. That's why we have quantum field theory. But there are situations that QM is approximately right, just like newtonian mechanics. And in these situations it is much easier to deal with QM rather than quantum field theory. The phenomenon of entanglement is such a situation. Tercer (talk) 20:52, 30 March 2011 (UTC)

I stopped responding here because you had been rude to me. I find your arguments increasingly erratic. You treat this article as if you owned it. I don't think you know as much about all this as you pretend. As far as I'm concerned my original reversions were fine. I want them back. Myrvin (talk) 15:25, 1 April 2011 (UTC)
 * I have a degree in physics and my area of research is quantum entanglement and nonlocality. I'm patiently trying to explain the basic aspects of the area to you. By your own admission you do not know quantum mechanics. Was my suggestion that you should not edit things you don't understand that you found rude? Tercer (talk) 16:09, 1 April 2011 (UTC)

Yes. And how about "If you don't like saying that Einstein and co. was wrong, well, unlucky you." and "I presume you are "against entanglement". ... You think that the use of entanglement should be forbidden? Or you think the mathematical concept of entanglement is inconsistent? Or that it does not model the real world correctly? And what about the experiments? They are just lying, or do you believe in the loopholes?" - A tirade against my suggestion that you were being too hard on EPR and too 'gung-ho' about Bohr et al.

You are not the least patient. You treat the subject as Faith versus Heresy, and your viewpoint on the history (which is what I was altering) does not agree with my other reading. The point is to make the article as understandable as possible to people like me.

But that's enough! Do what you like with it! Myrvin (talk) 17:57, 1 April 2011 (UTC)

Writing issues
Some of the issues raised in the section immediately above may be due to fuzziness in the writing. If not, fixing the problems would at least be a service to the general reader.

"In this, they formulated the EPR paradox, a thought experiment which demonstrated an apparent inconsistency in quantum mechanical theory." It did not show an inconsistency. It attempted to show that quantum mechanics is an incomplete description. (Greene, Elegant Universe, p. 99.) Einstein et al. thought that there must be hidden variables that determined the results, otherwise we would have a situation in which cause and effect were instantaneous over great distances. A complete theory would describe the factors that determine how one twin turns out one way and its entangled twin turns out the other way. Lacking a predetermination, there must be some communication of information from remote points. Put those points far enough apart and the communication would have to occur at superluminal speed to get there in time to make things turn out as they do. So the later reference in the article to a violation of the theory of relativity is indirectly saying that information about one entangled particle, once it has been measured, must travel to its entangled "twin" at a speed greater than c to account for the fact that a measurement of that twin soon after the measurement of the first one will be determined by what was measured regarding the first one. Einstein saw the possibility of such a result as a theoretical result of quantum mechanics and dubbed this determination of the state of the second twin as "spooky action at a distance."


 * This is a minor technical point. In their paper, they used the terminology "incomplete", because they (tried to) showed there were elements of reality unaccounted for in quantum mechanics, thus the theory is incomplete. But this also amounts to an inconsistency, because quantum mechanics say that incompatible observables can't be measured simultaneously, and the element of reality they found was precisely the simultaneous value of two incompatible observables. It doesn't matter which term you use, as long as we know what we are talking about. I prefer "inconsistency", because it makes it easier to a modern audience to understand what is going on. But if you prefer to be faithful to the letter of their paper, use "incompleteness". Tercer (talk) 20:08, 30 March 2011 (UTC)

"However, with quantum entanglement, if Alice and Bob measure the spin of their particles in directions other than just up or down, with the directions chosen to correctly form a Bell's inequality, they can now observe a correlation that is fundamentally stronger than anything that is achievable in classical physics. However, now the classical analogy of entanglement breaks down―there are no 'directions' other than heads or tails to be measured."

To the average well-informed reader, this paragraph becomes meaningless in the last sentence. The idea that "now" that a Bell's inequality having been formed "there are no 'directions' other than heads or tails to be measured," is incomprehensible. To me it appears that the writer had something else in mind, but the correct meaning is not coming through.


 * Someone, somewhen, removed a key "simulated", and the writing wasn't very good anyway. I hope now it's understandable. Tercer (talk) 20:18, 30 March 2011 (UTC)

"One might imagine that using a die instead of a coin could solve the problem, but the fundamental issue about measuring spin in different directions is that these measurements can't have definite values at the same time―they are incompatible. A quantum die would not have a definite value on any face until measured and, in accordance with Heisenberg's uncertainty principle, would have only one definite value when measured. In classical physics this does not make sense, since any number of properties can be measured simultaneously with arbitrary accuracy. Bell's theorem implies, and it has been proven, that compatible measurements can't show Bell-like correlations,[11] and thus entanglement is a fundamentally non-classical phenomenon." This passage is also confusing. A die does not have spin -- unless you mean physically spinning it on one corner or one face. I think that what the writer was trying to say is that a die has a determinate value on each of its faces, but that quantum values cannot be definite in the same way. If I understand the analogy, it seems to be saying that tossing a die results in a side with some value would come up, and that fact is analogous to the measurement of one quantum state. But a "quantum die" would not have definite values on its other faces. The part about "compatible measurements" is also "indeterminate" as far as I am concerned, i.e., indeterminate in what it is supposed to mean in plain English. Compatible to what? The reader is left to guess about what was on the mind of the writer when this passage was produced.P0M (talk) 16:06, 30 March 2011 (UTC)


 * The part about the quantum die is pure nonsense. I was going to remove it, but I thought it could be useful to someone's understanding. Compatible measurements is a technical term used in quantum mechanics. It's meaning is the same as the incompatible above, but I thought it would be useless to repeat the link. I've changed the page. Tercer (talk) 19:58, 30 March 2011 (UTC)


 * I've had a go at your first point. There's even a Wiki article on Incompleteness of quantum physics to link to. As you can tell by what I said earlier on, I find much of the article confusing too. As with some other physics articles, it reads like an undergraduate essay, minus the citations. If you understand these things (I do not), perhaps you could have a try at clarifying it. Myrvin (talk) 16:59, 30 March 2011 (UTC)
 * Good tweaks. Myrvin (talk) 19:38, 30 March 2011 (UTC)
 * (Edit conflict, so what I wrote below was roughly simultaneous with what you wrote.


 * I think your change works well. I've started to make changes -- but sometimes I'll have to guess which way the original writer was thinking about things. It would be better if the writer himself/herself made things less ambiguous. But I guess somebody will scream if I guess wrong.


 * I am stopping at this point simply because I have found a fundamental question about what Bell established. Either Brian Greene is right or the article is right... More later.P0M (talk) 19:54, 30 March 2011 (UTC)

Schrödinger's position
I have called for references about this upwards, but it seem to have gone unnoticed. The particular phrase that annoys me is "As with Einstein, Schrödinger considered the concept to reveal a deficiency of quantum mechanics, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity". The reference is "Letter from Schrödinger to Einstein, 7 June 1935". However, this reference is useless. I need to know where this letter was published to be able to check it.

And it seems very odd to me that Schrödinger thought entanglement was a deficiency of quantum mechanics. He invented the word, the concept, and developed it mathematically. Nothing in his published research suggests that he didn't take it seriously.

Also, entanglement has nothing to do with violating the speed limit of transmission of information. It is a simple theorem to prove that entanglement can't be used to transmit information faster than the speed of light. I don't know when it was proved, or if Schrödinger knew about it, though. Tercer (talk) 21:06, 30 March 2011 (UTC)


 * It appears on page xv in the introduction to the book, Philosophy of Quantum Information and Entanglement, by Bockulich and Jaeger.


 * You can see it if you search at http://books.google.com/books for the phrase "The point of my foregoing discussion is this: we do not have a quantum mechanics"


 * Quote from the letter:


 * "I was very happy that, in your work that recently appeared in Phys. Rev., you have publicly caught the dogmatic quantum mechanics by the collar, regarding that which we had already discussed so much in Berlin... The point of my foregoing discussion is this: we do not have a quantum mechanics that takes into account relativity theory, that is, among other things, that respects the finite speed of propagation of all effects."
 * J-Wiki (talk) 00:20, 31 March 2011 (UTC)


 * Thanks! It turned out I was wrong. But the reference then is the book, not the letter, since the letter does not appear in full. I changed it, and the wording to conform to the book. Tercer (talk) 04:46, 31 March 2011 (UTC)


 * You're welcome. I agree.  I hadn't realized that the letter appears not to have been published anywhere else. J-Wiki (talk) 11:15, 31 March 2011 (UTC)
 * Nice one J. Myrvin (talk) 07:26, 1 April 2011 (UTC)

A question of fact
The text currently states:

"Specifically, he theorised an upper limit, known as Bell's inequality, on the strength of correlations, for any theory obeying local realism; and he showed that entangled systems violate this limit."

What is "an upper limit for a theory"?


 * The upper limit is for the strength of the correlations. Clarified now. Tercer (talk) 04:55, 31 March 2011 (UTC)

Here is the way Brian Greene explains things on p. 111 of Elegant Universe. To me, his explanation is clear and meaningful. (He restricts description of a setup, "for simplicity's sake" that measures only three axes.):

"If EPR are correct and each electron actually has a definite spin value about all three axes -- if each electron provides a 'program' that definitively determines the result of any of the three possible spin measurements -- then we can make the following prediction. Scrutiny of data gathered from many runs of the experiment -- runs in which the axis for each detector is randomly and independently selected -- will show that more than half the time, the two electron spins agree, both being clockwise or both counterclockwise. If the electron spins do not agree more than half the time, then Einstein, Podolsky, and Rosen are wrong."

The fundamental observation on which Greene's explanation seems to rest is that if there are hidden variables that account for the apparent "spooky action at a distance" then there will be more matches than if there are only quantum superpositions and a 50-50 chance of a match.

If Greene's account is essentially correct then I think the Wikipedia article should reflect this state of affairs.P0M (talk) 04:03, 31 March 2011 (UTC)


 * I fail to understand where you see a contradiction. Also, please note that this article is about entanglement; EPR is only of historical interest. Detailed experimental setups should be in the EPR paradox article or in the Bell's inequality article. Tercer (talk) 04:55, 31 March 2011 (UTC)


 * You have changed the passage to:

Specifically, he demonstrated an upper limit, known as Bell's inequality, on the strength of correlations that can be produced in any theory obeying local realism; and he showed that entangled systems violate this limit.


 * This passage appears to be saying that theories obeying local realism can predict/produce correlations up to some limit, X%, and that entangled systems produce correlations > X%. Am I mis-reading this passage?P0M (talk) 14:57, 31 March 2011 (UTC)
 * Kumar (Quantum, 2009) says that Bell said that the correlations (of the Bohm experiment) are such that it "would lead to spin correlations that generated numbers, called the correlation coefficients between -2 and +2. However, for certain orientations of the spin detectors, quantum mechanics predicted correlation coefficients that lay outside the range known as 'Bell's inequality' that ran from -2 to +2." So, presumably < -2 or > +2. These are not the correlation coefficients I know from statistics (ie -1 to +1) - I think because they are not normalized. The articles on Bell's inequalities and quantum correlation are not clear on this to me. Myrvin (talk) 19:10, 31 March 2011 (UTC)

No, you've read it correctly. Although it is not percentage that is used. Also, the book that Myrvin quotes is wrong. It is not a correlation coefficient. And the values that it quotes are only valid for the CHSH inequality, that is based on the Bohm experiment, but not the same thing. To be more precise, the inequality says that the sum of certain four expected values has to be between -2 and 2 for classical mechanics (and Einsten's philosophy), while for quantum mechanics the sum can be smaller than -2 or greater than 2 (actually it is bounded between -2√2 and 2√2, this is Tsirelson's bound). The thing is that this sum of expected values can be interpreted as a measure of correlation. Tercer (talk) 22:51, 31 March 2011 (UTC)
 * It looks like Greene's analogy may depart pretty far from the actual mathematics. P0M (talk) 03:26, 1 April 2011 (UTC)
 * It is my view that he complicates too much out of fear of exposing his reader to mathematics. But his description is probably correct (I'd have to read more about his experimental setup to be able to judge). Tercer (talk) 03:54, 1 April 2011 (UTC)


 * It may not matter what it's called, but the term correlation coefficient is used in the Bell's theorem article - under CHSH it's true. That's where I got the un-normalized idea from. I'm sure I've seen it elsewhere too. Myrvin (talk) 06:49, 1 April 2011 (UTC)

entanglement and quantum nonlocality
This article confuses the two concepts thoroughly. And they're not the same. See quantum nonlocality. It particularly bothers me the part in the lead that says that Clauser's experiment was about verifying entanglement. It was about verifying nonlocality. Entanglement is a algebraic concept, that as far as I know has never been tested directly. And I doubt it is possible to test it directly. I'll make some changes accordingly. Tercer (talk) 13:56, 1 April 2011 (UTC)
 * And you put back all the stuff we were arguing about in the first place! Nobody messes with your article then. Myrvin (talk) 14:39, 1 April 2011 (UTC)
 * You stopped responding. I assumed you had agreed with me. Please discuss it in the proper section, not here. Tercer (talk) 14:55, 1 April 2011 (UTC)
 * yes sir! Myrvin (talk) 15:21, 1 April 2011 (UTC)

Testing quantum entanglement experimentally?
Tercer said that, "Entanglement is a algebraic concept, that as far as I know has never been tested directly. And I doubt it is possible to test it directly."

An algebraic concept would be a member of the set of concepts, or abstract entities, that can be consistently produced using formal devices established in number theory. The only way to test an algebraic concept would be to establish its consistency on a logical/mathematical basis. How would somebody "test directly" the concept called "equation"?

A geometric concept can be an axiom. Many geometries can be created by using different sets of axioms. A proposed geometry can be tested, but only insofar as its logical consistency can be challenged.

Whether it is algebra or geometry, there is another kind of testing -- whether the descriptions that can be formed thereby have a good fit to the Universe in which we find ourselves. It is possible that on a large enough scale the angles of a triangle would not add up to 180°. In that case, Euclidean geometry would fail its test. In other words, we would say that it is a nice axiomatic system, but that it does not suit the real world except as an approximation within certain size limits.

I have never heard of entanglement being described as an algebraic concept before. Be that as it may, entanglement was originally portrayed as a physical consequence that was to be expected if quantum mechanical explanations were true. In operational terms, that amounted to saying that if one creates two particles by means of one physical operation then measurement of some feature of the state of one of those two particles would determine the state measured for the other particle even though that particle was not in proximity to the first (and even might be far enough away that a signal from the site of the first measurement could not reach the site of the second measurement before that measurement was taken). Such correspondences have been found, and nobody seems to have challenged the accuracy of the measurements on which those correspondences have been predicated. Instead, the argument has centered around whether the conceded physical facts can be explained by supplementing quantum mechanics with additional variables. It was argued that if these "hidden" variables were supplied, then causality and locality ideas could remain as they had been before.

A definitive scientific test of the idea of entanglement would be accomplished only by finding some experiment that demonstrates that entanglement and/or the expected results of that state fail in some experimental setting to appear as and when theory states they should. So far (although there are loopholes remaining to be closed) it is the hidden variables theory that appears to fail in the lab. On the other hand, as far as "evidence tending to confirm" entanglement goes, there appears to be plenty of that. The general drift of what I have read is that anybody with an adequate lab could repeat experiments and expect to get results on spin, polarization, etc. in accord with what others have found, and that the only problem with those findings is that they might be explainable by the alternative, hidden variable, approach. Therefore the current experimental goal is to find experiments that these these alternative theories conclusively, i.e., with no loopholes.P0M (talk) 07:57, 2 April 2011 (UTC)


 * My point is: these Bell inequalities experiments test nonlocality, not entanglement. Nonlocality is a consequence of entanglement, but not the same thing; hence the section I added. Entanglement is a very basic property of the way we describe states in QM; if you accept superpositions and the tensor product rule for combining quantum systems, you already have entanglement. To test it would be then to test the basic formalism we use to describe quantum states. For that, I don't know, maybe quantum tomography? Tercer (talk) 01:24, 11 April 2011 (UTC)


 * Theory states that if "twinned" particles are prepared in a certain way, then measuring one of them will give determinate information about the other particle. Any experiment that consistently demonstrated that particles supposedly entangled did not show correlation between relevant measurements of them would falsify the theory that predicted correlation.P0M (talk) 11:52, 11 April 2011 (UTC)


 * A way of testing for one form of entanglement is described nicely by Anton Zeilinger in Dance of the Photons:


 * "If we send two photons into a beam splitter, they usually ... end up in either of the outgoing beams. But [if] the two photons are entangled such that they are always different in polarization [then] In that case they ... always end up in separate outgoing beams. This has enormous experimental consequences.  Just take a beam splitter and send two photons in, one from each side...  If they come out in separate beams at exactly the same time, you definitely know that the two photons were entangled in the specific way we just discussed.  So this provides us with a simple procedure for identifying one kind of entanglement uniquely."


 * This probably should be mentioned in the article, perhaps by expanding the section on methods to be ==Methods of creating and testing for entanglement== However, Zeilinger doesn't give a peer-reviewed reference for this, unfortunately.J-Wiki (talk) 01:04, 12 April 2011 (UTC)


 * If such trivial tests satisfies you, entanglement is tested everyday in many labs around the world. The scheme suggested by P0M can not differentiate between the entangled state $$|01\rangle + |10\rangle$$ and the separable, classically correlated state $$|01\rangle\langle 01| + |10\rangle \langle 10|$$. To see the difference you have to measure it in different bases as well, effectively making a quantum state tomography. The scheme by Zeilinger is for the particular case of quantum optics, and he is probably talking about differentiating between Bell states (I couldn't find it in my library and the one in google books isn't searchable). But yes, he is testing entanglement indeed. Maybe I wasn't clear. I think entanglement is too fundamental; it is hard to design an experiment to test it without also assuming (for the functioning of the apparatus) that entanglement exists. What we can say for sure is that entanglement is consistent with all the experiments we do, and it is so fundamental that as far as I know no one has never even dreamt of making a version of QM that does not have entanglement. Tercer (talk) 13:58, 12 April 2011 (UTC)
 * Very nicely stated. It's remarkable to see how such unexpected revelations can come right out of the math. The math minds of people like Einstein and Born are unbelievable to me. They seem to see the "outrageous" consequences almost immediately once the basic theory gets established. The article should make it clear that entanglement is not some exotic derivative of quantum mechanics built on theoretical stilts and perhaps resembling a metaphysical sandcastle, but something that is integral to quantum mechanics and just waiting there to be noticed.P0M (talk) 02:01, 13 April 2011 (UTC)
 * This distinguishes two types of entanglement: Schrodinger ent and Scully ent (sadly not Mulder's partner but Marlan O. Scully). Perhaps a step too far. Myrvin (talk) 10:03, 13 April 2011 (UTC)

New EPR quote
I (User:Myrvin) added a quote from the EPR paper. Elsewhere, User:Dmcq wrote:

I just read your last edit and yes the quote you gave "We are thus forced to conclude that the quantum-mechanical description of the physical reality given by wave functions is not complete" is correct - but the paper qualifies what it means by reality and gave a very important bit in the next paragraph "Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted." Physical reality in the paper is a hypothesis as they say "we left open the question of whether or not such a description exists". So overall even though I was expecting them to plant a flag in the ground as it were they did not and were much more careful about what they had actually established than I'd ever have been.
 * Should we add all of those words? I tried to give what they thought they had concluded, but maybe it was too gung-ho.Myrvin (talk) 13:02, 8 April 2011 (UTC)


 * There is a problem in the way Heisenberg, and also Wikipedia writers, use the term "simultaneous measures." The details are in print, but I have not dug them out again as far as Heisenberg goes. The problem is clearly discussed in Schrödinger's "cat" paper. The idea of "a measurement" is idealized in general discussions. General discussions, popularizations, talk as though one makes a single measurement of, e.g., and electron's speed, and writes it down in indelible ink before going on to make some other measure. But the fact in the laboratory is that any single reading might get messed up and be totally misleading. So what is necessary in the real world is to make the same experiment over and over again. The experiment can even be run on different kinds of apparatus, but the electron (or whatever) must be "prepared" in exactly the same way. Doing the experiment a large number of times helps to screen out instances that have been messed up somehow. However, this discussion only sets the stage for the major qualification that needs to be made:


 * The real problem with "simultaneous" measures of things like position and momentum is that they cannot be made at the same time. The actual procedure would be to measure one of the two first and quickly measure the other one. The problem is that measuring one, e.g., position, will impart a momentum change on the measured particle and so measuring its momentum will give a result that contains a factor derived from measuring its position. So not only are the measurements not truly simultaneous, but they also involve indeterminacy.


 * The EPR group does not want to admit to indeterminacy, believing that "God does not play dice." But adding "hidden variables" to account for the apparently indeterminate experimental results did not take care of the problem raised by the experimental needs involved in taking measurements. As far as I know, nobody has figured out a way to take a measurement of momentum and a measurement of position of one particle at the same time. If it is true that "two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted," and there seems to be no way around this conclusion, then it would seem that EPR must concede the quantum theoretical conclusions.


 * "While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible."


 * The ending of the EPR paper assumes that "reality" exists, i.e., that before we make a measurement of the momentum or the position of a particle that momentum and that position both exist. It also states a belief that it is possible to give a complete description of that "reality." So what EPR express is their subjective confidence that the macro features of "reality" are preserved at micro levels, and their hope that these features of "reality" can be given a theory that describes them. If anybody could come up with a theory that is valid at the micro level and that provides determinacy with regard to features of this "reality" such as position and momentum, then the confidence of EPR in the "micro reality" would receive some needed grounding. To me, however, their discussion has the psychological quality of proponents of some belief system that start with the desired conclusion and then insist that there must be ample reason for those beliefs -- somewhere and somewhen.P0M (talk) 16:40, 8 April 2011 (UTC)

Yes they were realists. I've added this quote from Popper, another realist to the Uncertainty principle article:"[Heisenberg's] formulae are, beyond all doubt, derivable statistical formulae of the quantum theory. But they have been habitually misinterpreted by those quantum thoeorists who said that these formulae can be interpreted as determining some upper limit to the precision of our measurements.(original emphasis)" Looks like I'd better check the spelling there.Myrvin (talk) 17:42, 8 April 2011 (UTC)
 * Edit clash**


 * I want to go over that paper and its historical context, and then check through the relevant Wikipedia articles again. I think the real deal was that Einstein noticed some consequences that apparently Bohr and Heisenberg hadn't noticed or hadn't quite worked through. Einstein said, in effect, that if things were as theory stated they were, then some remarkable consequences would follow. The QM guys said that quantum states of particles were superimposed as a result of many different kinds of interactions, and that the superpositions were resolved by doing something that made the particle's state resolve as one thing or the other (i.e., when a measurement was made). Einstein thought that there must be something wrong with that part of the theory because it implied that when two particles had their states mutually related the theory said that they shared the same superimposed states (wavefunctions). The consequence of such a sharing would be that resolving a state into, e.g., a positive spin, in a measurement performed on one twin would ensure that the spin of the entangled particle twin would show up as a negative spin. He then argued that the current understanding was that position and momentum could not be determined for one particle. Learning one would smudge (to use Schrödinger's term) the other. But the theory also said that one could learn the position by measuring one twin and learn the momentum by measuring the other. To preserve the basic quantum theoretical idea that the two could not be determined with "certainty," one would have to assume that learning the position of one twin would smudge the momentum of the twin, and that could not conceivably happen if a light speed signal could not travel from one particle to the other before the second particle was subjected to measurement. I believe Einstein died before anybody tested the idea out and discovered that measuring one twinned particle did indeed affect the subsequent measurement of the other twinned particle. But if he had seen convincing experimental evidence that such entanglement actually occurred, he probably would have been open to trying to understand what that would mean should his idea of "hidden variables" be unsupportable.


 * Recently I saw something else, which I again failed to make a note on, that indicated that while particles have finite location, their wavefunctions are of infinite extent. The wavefunctions of the entangled particles would then always be in touch. Or perhaps that is a poor verbal formulation. Perhaps one should say that the entangled particles share a single superimposed wavefunction, infinite in extent. P0M (talk) 00:57, 9 April 2011 (UTC)

Since making that edit, the whole section on Popper's criticism was deleted from Uncertainty principle because: " Popper is great as a philosopher of science, but why should we care (WP:DUE) that someone who was neither physicist nor mathematician misunderstood QM? Lots of people do that.)" I put it back. Myrvin (talk) 07:00, 9 April 2011 (UTC)


 * The contention over Popper is beginning to sound like some of the discussions regarding other articles I've worked on. Originally there is an article to explain X. Then somebody adds a section on critiques of the establishment position on X. Then a fight starts because discussion of the opposing views starts to undermine the coherence of the exposition of the main topic. For instance, in an article on Special Relativity somebody introduced a reference to a multi-chapter (perhaps even multi-CD) collection of challenges to Einstein's ideas. Fortunately nobody has yet tried to bring those arguments into the Special Relativity or General Relativity articles. But I think everyone can see the potential for getting things so confused that nobody can easily understand what the theory under discussion actually is.


 * One way that this kind of situation has been handled is to include a short section on "controversies" that basically just mentions "Paradox one," "Paradox two," etc. and then gives a link to a subordinate article where the disputed matters can be discussed more thoroughly.


 * It seems to me that just getting the idea of "entanglement" explained clearly is almost more than can be done in 32K of text. For one thing, you sort of need more than one thing for any real tangling to occur. (Maybe an octopus would disagree.) It's clear that when people talk about entangled electrons there are two electrons involved, but it is not clear that there are actually two discrete wave functions that are copies of each other and are superpositions of quantum states. Just exploring that issue along would require a few paragraphs, no?P0M (talk) 18:07, 9 April 2011 (UTC)
 * It's now been expanded quite a bit (not by me) with citations I found. Didn't know old P had such an effect on all this. Myrvin (talk) 10:15, 12 April 2011 (UTC)

More comments
At the risk of throwing another Schrodinger's cat amongst the quantum pigeons, I have some more comments to make:
 * 1) The article lead seems to promise details about two or more objects, there's a lot about two but little about more. I don't think I'm referring to ensembles. In real quantum life, particles are interacting all the time: do they all become entangled?
 * 2) When a particle is measured in some way, something (spooky says Einstein) seems to happen to its entangled partner. Does this happen to all the particles it has ever interacted with?
 * 3) When all those particles were created at the Big Bang, were they all entangled with each other? If so, when we measure one of those, does something happen to all the others? Maybe this has to do with the de Broglie–Bohm theory. Myrvin (talk) 07:09, 1 April 2011 (UTC)


 * One way to clarify lots of these issues that has been used by physicists struggling with some of these questions is to look at the idea of decoherence, i.e., the idea that preserving quantum states in superposition is rather difficult because to do so practically demands isolating whatever it is that has states in superposition. Any random interaction will possibly make the particle "show up" as having one spin or another, or resolve whatever else there might be in superposition. I just saw a straightforward statement to the effect that once a measurement has been done on one entangled twin, the entanglement ceases. I don't remember the context very well. Maybe I can find it again.


 * How would one know, except by having observed the creation of "twins" by some process, whether any two particles were entangled?


 * When we make models to deal with things like entanglement, we are coming in during the middle of the program. We make models/theories that can serve as predictive abstractions and generalizations from whatever is going on in the world. It would be a worthwhile hypothesis to say that every fundamental particle from the time of the Big Bang "must have been" entangled. But we would need to test the hypothesis.


 * I think Schrödinger had the idea that the entire experimental apparatus used in an experiment has its own quantum state. If that idea is correct, then the entire Universe may have its own quantum state. It's too late to think about this kind of stuff. P0M (talk) 08:02, 1 April 2011 (UTC)


 * Interesting comments.


 * 1 - Entanglement between more than two particles is called multipartite entanglement. The reason it's not covered in the article is that it's much more complicated. I hope to create a section about it someday. Yes, this is not about ensembles, and yes, all the particles become entangled.
 * 2 - Nothing happens to its entangled partner. If something happened, this could be used to transmit information faster than the speed of light. I'm trying to find a good source about this theorem to add it to the article.
 * I don't understand this part. Entanglement implies that if I measure one twin its wavefunction collapses, it takes on a definite state (positive spin or whatever), and the other twin will, when measured, be found to have the opposite spin. The reason that information, e.g., whether to bet on candidate A or candidate B before the newspapers arrive in your town, cannot be transmitted is that the "transmitter" does not have a choice of whether his particle has one spin or the other, so the other guy measures a spin but doesn't know what that spin is supposed to mean. The transmitter found out that he had a spin positive twin, and sends a radio signal to the recipient saying, "I got a spin positive. What did you get? If you got a spin negative you should bet on Hoover." But the newspaper arrived a little earlier since it was transmitted the moment the vote was certain.
 * "Nothing happens" is correct if, by that locution, you mean that no process mediated by physical interactions (limited by c) has occurred. P0M (talk) 02:45, 13 April 2011 (UTC)
 * No need to bring relativity into the conversation =) The fact that nothing happens is a simple theorem, the no-communication theorem (actually, this article is currently a piece of shit, so I don't think it will help). Its statement is that Alice's reduced state is the same before and after Bob makes his measurement. This means that there's no experiment Alice can do to tell if Bob has made or not his measurement.
 * Now let's return to informal talk, and bring back relativity. Let's say Alice is in Venus and Bob is in Mars, and share an entangled pair, and each one measures his/her particle simultaneously (or, in relativity jargon, with an space-like separation). Say Alice obtains up and Bob obtains down. Now which one collapsed the wave-function and determined the other's state? Well, there's a reference frame in which Alice made the measurement first (Alice's frame, for example), and a reference frame in which Bob made the measurement first (again, Bob's). So the principle of causality prohibits a causal relationship between one's measurement and the other's outcome. We can only say that they are correlated. It's meaningless to talk about when the measurement outcome became certain, because this can't be measured. Tercer (talk) 04:10, 13 April 2011 (UTC)
 * I was confused as to what "it" referred to. It sounded to me as though you meant that no matter what Alice did (say at time t) Bob, at x distance away, would still have a 50% chance of finding spin-up or spin-down when he did his experiment at time t'= t + x/c.P0M (talk) 07:57, 13 April 2011 (UTC)


 * 3 - Actually entanglement is destroyed when you measure one particle of a entangled pair. If it is various particles, not necessarily. Also, it is meaningless to apply this quantum mechanics to the Big Bang. We know for sure that the Big Bang is out of it's domain of validity.


 * If you have a single copy of your particle, it is impossible to tell if it is entangled to others or not. But if you have a large number of copies, you can perform quantum state tomography and tell it it's state is mixed or pure. If it is mixed, then it is a part of a entangled system. If it is pure, it's not.


 * I think you might be thinking about the universal wavefunction. This concept is very problematic. But Schrödinger's idea of assigning a quantum state to the experimental apparatus is very useful to study transmission errors and decoherence. Tercer (talk) 13:45, 1 April 2011 (UTC)

1. So if particles A & B interact, and then B goes off to interact with particle C (before B is measured), and C then interacts with particle D. When A is measured how many particles are affected?
 * I think it's like this: When B interacts with C, that is a "measurement" of B. The history of the development of quantum mechanics made people zoom in on what happened when they measured things. The way they then talked about what goes on created opportunities for a sort of variation of solipsism in which what humans are conscious of becomes the issue, rather than what physical changes have to occur to make something subject to our observation. (Bohr and Heisenberg were clear that consciousness is not what was deciding how Mother Nature makes her probabilistic decisions on where to show her hand.) After interacting, A and B had superposition. When B interacts with C, B has to "decide" whether it is this way or that way. A then "collapses its wavefunction" also. If, after C interacts with particle D, or even after B interacts with C, one were to measure particle A, its state would not be in superposition with any other states except the state of whatever was used to measure particle A. P0M (talk) 12:45, 11 April 2011 (UTC)

2. I thought some people were really happy with the idea that you CAN use entanglement to transmit info faster than c.
 * John G. Cramer ohas some ideas for how one might be able to construct an ansible. See [his website]. People were, and perhaps some still are, happy with the idea that you might be able to transfer information faster than the speed of light. But the kicker has always been that if, for instance, NASA on Earth does something to make the spin of it's twinned electron show up as spin positive or spin negative, it cannot decide which way it will show up. If Earth get a spin up, the remote station on Mars will measure its electron as spin down. But it won't know what that result is supposed to mean. And, supposing that Earth forgets to measure its electron on schedule, when Mars measures its particle it will still get either spin up or spin down, but that result is meaningless. P0M (talk) 12:45, 11 April 2011 (UTC)

3. Didn't know about the Big Bang - I wonder why it's meaningless. (This might be interesting []) How about all the photons coming at us from the sun, are they all entangled - or a lot of them? Myrvin (talk) 13:58, 8 April 2011 (UTC)
 * I have no answer for your question about photons coming from the sun, but I do have an answering question: How would you know whether the photon you were measuring was entangled? P0M (talk) 12:45, 11 April 2011 (UTC)

1. I see that a measurement could include any interaction, but I don't think I find that anywhere. Quantum measurement and the measurement problem don't seem to include anything except measuring machines. I have seen the idea of information being the deciding factor. Does it mean that when B has decided after hitting C, its spin (say) is made invisible again after it interacts with C? Or that it does not become entangled again?
 * See Quantum_information%23Quantum_information_theory
 * I think it's a "dogs and Pekinese" or "white horse is not a horse" situation. Doing something to a photon in flight, even if the "do-er" is a random fleck of dust in interstellar space, will make the photon "show up" somewhere. But that fact won't serve to inform anybody unless somebody is already out there watching that fleck of dust. On the other hand, if somebody wants to "measure" a photon, e.g., find out its position x, y, z, t, then s/he would probably put a detection screen in the "flight path" of the photon. So "measurement" always means "doing something to the photon," but "doing something to the photon" (since only Mother Nature may be observing) does not necessarily provide humans with the basis for making a measurement.P0M (talk) 01:20, 12 April 2011 (UTC)
 * So how does anyone know that a measured entangled particle hasn't hit something after entanglement and before measurement? cf Bell's inequalities and EPR itself. Myrvin (talk) 10:06, 12 April 2011 (UTC)
 * That's the problem for experimenters, no? If it has "hit something," then it has been "measured" already. When the experimenter gets hold of a particle that was promised to be entangled, he is actually measuring a particle that is no longer entangled. And the twin of this particle has already had its superposition resolved by that collision. I suppose the possibility of unintended decohering of quantum states is one of the reasons for doing the same experiment many times. There will be lots of times when the experiment gets "hit" by something.P0M (talk) 02:26, 13 April 2011 (UTC)
 * You might find this interesting. Myrvin (talk) 09:26, 14 April 2011 (UTC)
 * And this Myrvin (talk) 12:55, 14 April 2011 (UTC)
 * The second item should be put into the article either as a footnote or as an extra resource. By the way, you can find the original Schrödinger "cat" article by a web search for "a translation of Schrödinger's cat paradox paper."P0M (talk) 14:10, 14 April 2011 (UTC)

2. I thought there was a big disagreement between locality nad non-locality - one insisting that the phenomena of entanglement couldn't happen at long distances, while the other says they do.
 * Right. I think Einstein's basic comment to Heisenberg amounted to saying, "Have you considered that if you are right then doing something like tickling me in Berlin will make my twin laugh in Java? That's impossible, you know. Anything that appears to be "action at a distance" is in fact mediated by some mediating process, e.g., a radio transmission that reproduces a speech broadcast in London via BBC all around the world. No radio waves, no transmission. Furthermore, the transmission time = distance/c. Yet your idea implies an instantaneous change of state in both entangled particles. This is madness, as you yourself must comprehend." Then, if grounds are provided for believing that measuring entangled electron one and finding that it has positive or negative spin will indeed mean that at any time entangled electron two is measured it will have the opposite spin, they offer the further justification of their belief. They will claim that the electrons were always one way or the other, and that the determining factor is an additional variable or characteristic of the electron(s) that we happen not to know about. P0M (talk) 01:20, 12 April 2011 (UTC)
 * This also determinism v non-determinism? Myrvin (talk) 10:06, 12 April 2011 (UTC)
 * When I was working on the "Race" article, and people were getting into ideas about genetics and determinism, one of the discussants said that every conception is an experiment in quantum mechanics -- meaning that what happens at the level of genes and chromosomes when they are sorting themselves out in sperm and ova and then recombining in a fertilized cell is a matter of quantum probability. I guess it's a "belief," at least until the final arguments about the Bell Inequalities have died down, but that writer clearly believed that what you and I are like was not written down at the time of the Big Bang. If the fission of one atom of uranium is a matter of probability only, if fission is not set off by some outside event and not programmed into each atom ab initio, then one could de-couple one's actions from a preordained path by making a few significant choices based on whether a Geiger counter clicked. What kind of "warranty clock" could be attached to each uranium atom? What determinate process could determine how long that individual atom would have on its warranty card? (I'm thinking of automobiles with 3 year warranties that self-destruct just after the 3 years is up.) To me, possibility comes before actuality (logically speaking of course), and probability is more basic than "certainty." Maybe things are certain only after they have happened. P0M (talk) 02:18, 13 April 2011 (UTC)

3. Good question. Myrvin (talk) 20:53, 11 April 2011 (UTC)
 * I found Isaacson, Walter, Einstein, His Life and Universe, p. 448f online last night. His discussion if very clear.  I didn't read anything except the basic development of the EPR paper, but maybe he has answers about the Big Bang. If entanglement requires superposition, then examination of the practical difficulties of studying entanglement experiments should give you an indication that any initial entanglement(s) would long ago have disappeared (except, possibly, for "two particles lost in space"). The big practical problem for studying entanglement is that after you have gotten things entangled you have to work very hard to keep them from bumping into anything that will cause them to decohere, i.e., anything that will make their wavefunctions collapse. You need to create jails that the prisoner can't bump into, one for each entangled twin.
 * This stuff all comes rolling out of my pack rat mind. I'm not sure that I've remembered it all correctly.P0M (talk)

Schrödinger
An edit has been made to the part of the lead that talks about "these first studies", which removed the words: "with the aim of criticizing quantum mechanics" with the comment: "Schrödinger's paper was a technical study of entangled, not a critique of QM". Yet the article on Schrödinger's cat states: The thought experiment serves to illustrate the bizarreness of quantum mechanics and the mathematics necessary to describe quantum states. Intended as a critique of just the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger cat thought experiment remains a topical touchstone for all interpretations of quantum mechanics.

Now this may not be the same article in question (it was in 1935 though), but it does look as if S was trying to criticize QM or the CI in some way. Perhaps we should try to find citations about this. At least we should say what this S paper was - didn't he do a few in 1935?. The part now reads as if EPR wasn't critical either. Myrvin (talk) 08:51, 13 April 2011 (UTC)

The Stanford site has:"In 1935 and 1936, Schrödinger published a two-part article in the Proceedings of the Cambridge Philosophical Society in which he discussed and extended a remarkable argument by Einstein, Podolsky, and Rosen. The Einstein-Podolsky-Rosen (EPR) argument was, in many ways, the culmination of Einstein's critique of the orthodox Copenhagen interpretation of quantum mechanics, and was designed to show that the theory is incomplete." which reiterates what the article used to say about EPR and the Copenhagen interpretation. Also, it suggests that S was expanding on this criticism. Myrvin (talk)


 * I agree that it's now a little misleading, at least wrt the EPR paper. --Sabri Al-Safi (talk) 09:20, 13 April 2011 (UTC)

This has: Shortly after publication of the EPR paper, Schrödinger wrote to Einstein on 7 June 1935 to congratulate him: “I was very pleased that in the work which just appeared in Phys. Rev. you openly seized dogmatic quantum mechanics by the scruff of the neck, something we had already discussed so much in Berlin” Myrvin (talk) 09:37, 13 April 2011 (UTC)


 * That paper has a lot of juicy stuff in it but so few references! I'd love to get my hands on the reply from Einstein to Schrodinger, though a quick Google isn't coming up with the goods =[ Anyway, it does seem like Schrodinger was also critical of CI --Sabri Al-Safi (talk) 09:55, 13 April 2011 (UTC)


 * More from the Stanford Encyclopedia:


 * "[In the 1935 paper, Schrödinger wrote:]


 * "Attention has recently been called to the obvious but very disconcerting fact that even though we restrict the disentangling measurements to one system, the representative obtained for the other system is by no means independent of the particular choice of observations which we select for that purpose and which by the way are entirely arbitrary. It is rather discomforting that the theory should allow a system to be steered or piloted into one or the other type of state at the experimenter's mercy in spite of his having no access to it."


 * In the second part of the paper, Schrödinger showed that, in general, a sophisticated experimenter can, by a suitable choice of operations carried out on one system, ‘steer’ the second system into any chosen mixture of quantum states. That is, the second system cannot be steered into any particular quantum state at the whim of the experimenter, but the experimenter can constrain the quantum state into which the second system evolves to lie in any chosen set of states, with a probability distribution fixed by the entangled state. He found this conclusion sufficiently unsettling to suggest that the entanglement between two separating systems would persist only for distances small enough that the time taken by light to travel from one system to the other could be neglected, compared with the characteristic time periods associated with other changes in the composite system. He speculated that for longer distances each of the two systems might in fact be in a state associated with a certain mixture, determined by the precise form of the entangled state.


 * Based on this, I've changed the sentence in the article to read:


 * "Although these first studies focused on the counterintuitive properties of entanglement, and suggested that quantum mechanical theory was therefore incomplete, eventually entanglement was verified experimentally, and recognized as a valid, fundamental feature of quantum mechanics..."J-Wiki (talk) 00:24, 14 April 2011 (UTC)

Good stuff J. A small point: I wonder if the word "therefore" is necessary. It looks now as if, because the results were counterintuitive, therefore QM was incomplete. Myrvin (talk) 07:06, 14 April 2011 (UTC)


 * How about Although these first studies posed the counterintuitive properties of entanglement as evidence of the incompleteness of quantum mechanics,... --Sabri Al-Safi (talk) 09:39, 14 April 2011 (UTC)


 * Big improvement. However, I've refined further it as: "Although it was suggested in these first studies that the counterintuitive properties of entanglement implied the possible incompleteness of quantum mechanics,..." and will change the text in the article.J-Wiki (talk) 10:36, 14 April 2011 (UTC)

Do you think we should include some of that text above in a reference so that someone later won't change it because they believe S didn't object? Also, is the "paper later that year" still ambiguous? Myrvin (talk) 12:01, 14 April 2011 (UTC)


 * The text I changed was "Although these first studies focused on the counterintuitive properties of entanglement, with the aim of criticizing quantum mechanics, eventually entanglement was verified experimentally, and recognized as a valid, fundamental feature of quantum mechanics; the focus of the research has now changed to its utilisation as a resource for cryptography and computation.". I removed the part "with the aim of criticizing quantum mechanics", giving the reason that Schrödinger's paper was a technical analysis of entanglement, not a critique of QM.


 * I agree that it should be said the EPR's goal was to use entanglement to criticize QM. But Schrödinger's paper does no such thing. Has anyone here read the paper? The introduction and conclusion are written in plain english, very readable. The paper's focus is the counterintuitive properties of entanglement, as I left the lead saying. It discovers quantum steering, and its objective is to strengthen, instead of resolving, EPR's paradox. But it never says QM is incomplete or should be modified, it merely points out the counterintuitive properties.


 * As a matter of style, I prefer the original lead (before my alteration) to the current version. I find really sad articles that use the words "suggested", "possible", etc. It's as if they don't know what really happened, but feel the obligation to talk about the issue. For me, this is nonsensical. A article should be clear and definite, not vague and undecided.


 * I don't know why someone brought up Schrödinger's cat. It is a critique of the Copenhagen interpretation, and based on superposition, not entanglement. Tercer (talk) 17:27, 14 April 2011 (UTC)

As I said, I think we need to be sure what 1935 paper we are talking about. It seems that he wrote 3 connected papers in 1935. This is a translation of these (So I guess they must have been in German). The intro says: This is a translation of Schrödinger's three-part 1935 paper[1] in Die Naturwissenschaften. Earlier that same year there had appeared the Einstein, Podolsky, Rosen paper[2] (also famous in "paradoxology") which, Schrödinger says, in a footnote, motivated his offering. Along with this article in German, Schrödinger had two closely-related English-language publications.[3] But the German, aside from its one-paragraph presentation of the famous cat, covers additional territory and gives many fascinating insights into Schrödinger's thought. The translator's goal has been to adhere to the logical and physical content of the original, while at the same time trying to convey something of its semi-conversational, at times slightly sardonic flavor. The letter to Einstein's taking "dogmatic" QM by the scruff of the neck states the way he felt about QM at the time. I can't get to read the Cambridge paper, and I don't think we can go by the abstract; and that may be yet another one anyway, being "one of the closely-related English articles". Myrvin (talk) 18:27, 14 April 2011 (UTC)

I like the final paragraph of the translation:"The simple procedure provided for this by the non-relativistic theory is perhaps after all only a convenient calculational trick, but one that today, as we have seen, has attained influence of unprecedented scope over our basic attitude toward nature." Myrvin (talk) 18:39, 14 April 2011 (UTC)

According to this S viewed entanglement as "sinister" and viewed it as a flaw. Myrvin (talk) 18:33, 14 April 2011 (UTC)

Oh! The reference to "sinister" seems to be that very Cambridge paper. Myrvin (talk) 18:35, 14 April 2011 (UTC)
 * I have squeezed this quote from the Cambridge paper: "Its sinister importance is due to its being involved in every measuring process and therefore forming the basis of the quantum theory of measurement, threatening us thereby with at least a regressus in infinitum, since it will be noticed that the procedure itself involves measurement." Myrvin (talk) 18:50, 14 April 2011 (UTC)


 * I thought we had already settled that Schrödinger was in fact dissatisfied with entanglement and QM at that time. See the section "Schrödinger's position" above. What I'm arguing is that this specific Schrödinger's paper is not a critique of QM. The paper I'm talking about is the Cambridge one, which I cited. The paper that the lead is talking about I don't know; who wrote that part is J-Wiki. And it is very hard to decide which one initiated research in entanglement.


 * But you do bring an important point: which one is "the" paper Schrödinger defined entanglement? The Cambridge one was received 14 August and published 28 October; the one in Naturwissenschaften only has the date of publication, 29 November. Can you find out which one he wrote earlier?


 * About the "sinister" quote: it is from the Cambridge paper indeed. But again, he is only pointing out its counterintuitiveness.


 * I now had time to read the preceding arguments carefully. J-Wiki's quote from Stanford Encyclopedia is correct: The second part of Schrödinger's paper (I was not aware of its existence), published in 1936, is a critique of QM and does propose an alteration to it. I apologise for the confusion, and have restored the lead to its former state. I have, nevertheless, added the reference that would have avoided this argument. Tercer (talk) 00:39, 15 April 2011 (UTC)

@Myrvin (see above) Regarding Schrödinger's general stance, I think he totally accepts the mathematics. (After all, he made his own theory and later proved that it could derive or be derived from Heisenberg's work.) However, he does not like the way that Bohr and his group interpret the mathematical models that they have all come to agree upon. According to the way Bohr et al. see things, an electron at one energy state has a certain orbit (or orbital when their picture started taking account of the idea that location could be only problematical). When it gains the energy of a photon it absorbs, it "jumps" to another orbital, and there is no trajectory from one orbit to the next. First it is here and then it is there. According to the way Schrödinger looks at things, regardless of whether you conceptualize it as a wave or as a particle, it has to make its way by some path between the orbitals.

With regard to entanglement, I think he is aware that the possibility that it is a real phenomenon, which Einstein had brought up in a sort of back-handed way. He is not only aware of it, but he is beginning to see implications. The cat idea is presented as a "crazy" idea, I think. He is saying, "Just look at the implications for this idea if we take it seriously." I suspect that he was never very happy with the ideas entailed in his own theory because they seemed to point to things like "cats that are in a state smeared between life and death."

The idea of the "collapse of a wavefront" has to be used to make a quantum theoretical description apply to reality. Yet the collapse is never predicted by the theory. You always have to say something like, "If a photon is fired at the detection screen at some time t, then the result will be such-and-so -- in probabilistic terms. In something like the double-slit experiment you end up saying that "the photon must hit the detection screen," or maybe it can sometimes tunnel through the detection screen. Probably nobody would notice. So then the question is where it will hit. (The time when it will hit is generally to be learned by performing a simple calculation.) It seems to have a superposition of many possible arrival points, and it seems to play an appropriate role in filling out the probability map for the double-slit fringes. But what happens to make it "show up" at one place or another is outside the theory. This part is disturbing. Then there are the situations where an equal chance for one or another thing to happen. Perhaps both 50% probabilities are realized, but in different Universes.

So all of these ideas are actually upsetting, or intriguing, to most or probably all of the people working in the field at that time. And I think that people did not start to settle down until the idea of a sort of inevitable decoherence just from things knocking around the the same universe started to pull people's heads out of the clouds. Schrödinger did not, I think, object to what was being discovered in the lab. How could he? But he was annoyed by some of the ways that others glossed these ideas in ordinary English. It was bad enough to be puzzled and disoriented by the new ideas. P0M (talk) 01:33, 15 April 2011 (UTC)
 * Yes, I wonder if S pronounced "entanglement" with the same curl of the lip that Hoyle must have pronounced "Big Bang". Myrvin (talk) 08:09, 15 April 2011 (UTC)

The biographies seem to mention only the German papers and not the Cambridge. I'll keep looking. In one I also found this interesting:. I think S was quite a wag; and used irony a lot. Myrvin (talk) 08:51, 15 April 2011 (UTC)

This says that in the Summer of 1935 he was in Oxford writing the German essay. He was a busy lad that year, he also spent some time in Madrid. Myrvin (talk) 10:26, 15 April 2011 (UTC)

This gives the most detailed timeline I've found. It refers to the cat idea as "burleske". Myrvin (talk) 13:47, 15 April 2011 (UTC)


 * Thanks for the links. The last one is a little puzzling to me, so I'll have to read it again when I have more time. There are, I think, other places where Schrödinger emphasizes the peculiar situation in which we find ourselves when we try to deal with quantum mechanics and the "things" that it describes. In human experience, we always deal with the photons and other very small entities after they have "shown up." In quantum mechanics we only deal with the photon in flight, before it has "shown up." It seems impossible to determine what makes a photon "decide" to pick one or another location to show up at in a double-slit experiment. Is there something about one irregularity in the surface of the detection screen that is somehow "attractive" to at least one photon? Is there a cosmic machine that keeps scores of the number of hits across the detection screen, notes that fringe 13 us under quota and so directs the next available photon to that band? As far as I know, people just say "wavefunction collapse," and throw up their hands. Back to Schrödinger and his critique (not criticism) of QM -- I think that he is aware (at least subconsciously) that humans will strongly tend to import macro scale ideas to the quantum domain, and that there is really no grounding for that stance. Superpositions are especially problematical for macro human minds because we cannot truly comprehend what it means for the same electron being "spinning" in two contrary ways. Similarly, the theoretical account of psi-functions seems to be that they are infinite in extent. It isn't any basis for an r-squared diminution of effect, just a continuum of varying probabilities. So the idea that two or more entangled photons have one psi-function rather than two discrete psi-functions is truly mind boggling. To some extent these ideas that are compatible with the quantum domain are incompatible with the macro domain. Maybe it takes generations for humans to adapt to a change such as the one quantum mechanics has made. When I was in physics in 1958, the book we used barely mentioned quantum mechanics or relativity theory. Some of the things we were taught in chemistry were entirely by rote, but were already explained in clear and simple quantum terms by Linus Pauling. Think of somebody thousands of years ago who says, "Are you telling me that if you walk away from me in a straight line in that direction you will eventually come up behind me?" I think that Schrödinger was probably being careful not to accept anything without thoroughly understandings its consequences. He was very sensitive to what he called the "unsettling" consequences, and was looking for ways around them. (I read somewhere that Schrödinger did not like cats. Perhaps that accounts in part for the "burleske." But his intent must have been to typify the quantum state in human-understandable terms. What sense can we make of the idea of something that is dead and not-dead at the same time?)P0M (talk) 15:51, 15 April 2011 (UTC)


 * Reading through both articles, I found the relevant parts. The Cambridge one has the definition right in the start:


 * When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between

them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives (or ψ-functions) have become entangled.


 * The one in Naturwissenchaften also has a definition, in section 10:

"That a portion of the knowledge should float in the form of disjunctive conditional statements between the two systems can certainly not happen if we bring up the two from opposite ends of the world and juxtapose them without interaction. For then indeed the two 'know' nothing about each other. A measurement on one cannot possibly furnish any grasp of what is to be expected of the other. Any 'entanglement of predictions' that takes place can obviously only go back to the fact that the two bodies at some earlier time formed in a true sense one system, that is were interacting, and have left behind traces on each other. If two separated bodies, each by itself known maximally, enter a situation in which they influence each other, and separate again, then there occurs regularly that which I have just called entanglement of our knowledge of the two bodies."

I think it's fair to say that both define entanglement and were written around the same time. However, the Cambridge one deals exclusively with entanglement and its consequences, and the one in Naturwissenchaften is a more general paper about QM philosophy that also happens to discuss entanglement. So I propose we leave the article as it is, citing the Cambridge papers as initiating the study of entanglement. Tercer (talk) 16:31, 15 April 2011 (UTC)

Special relativity
So far the article refers to SR and the limitation problems of the speed of light. There are surely other problems too that might affect entanglement. I'm thinking of the case where one of the entangled pair is taken away very quickly. After some time, this one will be seen to be younger than the one left behind. Can entanglement survive the different ages of each pair? Myrvin (talk) 08:45, 18 May 2011 (UTC)


 * Are you talking about a Twin paradox effect, with one of the particles being in a non-inertial frame? It's hard to see if this presents any problems, since standard QM doesn't talk about relativistic effects. QFT might have something to say about that. Certainly entanglement won't be broken just because one of them has experienced a shorter time interval - both particles are affected only by local unitary Hamiltonians, which will preserve the entanglement even if different on each particle. --Sabri Al-Safi (talk) 10:15, 18 May 2011 (UTC)


 * I agree. In principle, only the difference between space-like intervals and time-like intervals is relevant to entanglement. Boris Tsirelson (talk) 15:11, 18 May 2011 (UTC)

Complex language
This article is ridiculously incomprehensible to those not familiar with physics. It could very well do with a plain English introduction with as few technical terms as possible. I came to this page looking for confirmation that I understood the concept of quantum entanglement ok, and from reading this article, I have no idea whether I do or don't. — Preceding unsigned comment added by 81.132.206.45 (talk) 19:30, 1 June 2011 (UTC)
 * I fully agree. The approach is part of the professional malaise that affects lots of writing -- even textbooks intended for freshman. I have been looking at the textbook used to teach physics majors et al. calculus as freshmen. From the standpoint of somebody who has been through a few mills in the last half century it is clear that the authors are writing to impress or at least satisfy their professional colleagues. Under their rules it does not matter particularly whether the neophyte can understand something. It matters only that whatever is said can be defended against the critiques of other professionals. Einstein and Heisenberg could write for a general audience and not snow them with their magic wand waving. Schruodinger was less able than they were, but at least he did not deliberately make things appear to be limited to the professional domain of an elite audience.
 * I fully agree. The approach is part of the professional malaise that affects lots of writing -- even textbooks intended for freshman. I have been looking at the textbook used to teach physics majors et al. calculus as freshmen. From the standpoint of somebody who has been through a few mills in the last half century it is clear that the authors are writing to impress or at least satisfy their professional colleagues. Under their rules it does not matter particularly whether the neophyte can understand something. It matters only that whatever is said can be defended against the critiques of other professionals. Einstein and Heisenberg could write for a general audience and not snow them with their magic wand waving. Schruodinger was less able than they were, but at least he did not deliberately make things appear to be limited to the professional domain of an elite audience.


 * Check out what Brian Greene has to say on the subject. I am sure that it will start with the concrete and only later lead to the abstract. Anybody can probably deal with descriptions of the experiments that demonstrate entanglement. Given those rather incredible facts, people are provided some grounds for expecting and understanding that the theory-grouinded explanation have a basis in fact.P0M (talk) 03:06, 2 June 2011 (UTC)


 * You're being unfair. I've written quite a bit of the article, and made a great effort to make it accessible. I've responded to every question in the talk page and I've rewritten many confusing passages. I can accept the critic of being a bad writer. But to accuse me (and the other authors) of writing to impress my peers and ignoring the lay reader is simply offensive. If I wanted to do so I would only edit the mathematical portion of the article (and oh it does need editing).


 * 81.132.206.45, you should keep in mind that this is an encyclopedic article about an advanced subject; to actually learn it you need textbooks. And if the knowledge you had before coming here came from reading the popular press, it was probably completely wrong. Tercer (talk) 05:40, 2 June 2011 (UTC)
 * I agree to some extent with P0M, but I also think that many Physics articles were written by students - albeit Post-Grads maybe - from their lecture notes. That would account for the lack of citations, the gobbledegook, and the disturbing certitude of much of the text. Tercer seems to be saying that if you don't understand it already, then there's no point in looking at Wikipedia. Myrvin (talk) 09:37, 2 June 2011 (UTC)
 * If you look at the Stanford page: you can see perhaps a better way of approaching the subject for the general reader. I don't think that this is all that good (I don't like the mention of energy and resource so early on), but at least it doesn't immediately mention degrees of freedom, which would mean that the general reader would be lost straightaway. Myrvin (talk) 09:53, 2 June 2011 (UTC)
 * I do not mean to be offensive, especially to individuals. I was remarking on a general tendency seen over hundreds of years. There is a craftsmanship of writing that considers the needs of all readers. Brian Greene will start with the concrete facts, tell the reader what happens in the lab or what is observed in an astronomical observatory, and then go deeper -- and tell the reader that if math and more intense analysis of the phenomenon are unwanted then to go ahead to page such-and-so.
 * The idea of "state" is deeply technical. The word "state," however, has a very vague meaning in everyday English. "When he came home from the prom he was in a terrible state." The writer cannot assume that the average reader will understand "state" in the way that the writer meant it. "Quantum mechanical system" is another one. There are all kinds of "systems" discussed in everyday life, from the "Alexander system" to "a new system for betting at the track." "Degree of freedom" is extremely abstract, and again the average reader can take those words in several ways.
 * If I remember correctly, the objection that Einstein offered to Bohr and his colleagues was as follows: Suppose that we create a situation in which the positions and momentums of two objects are merged. We tether them together somehow, they move together for some time, and then we cause their trajectories to diverge slightly. At some point in the future they will be distant from each other. According to your quantum theoretical ideas, it is impossible to get both the exact position and the exact momentum of some object because measuring either one of them disturbs the measurement of the other. However, if you are right it would mean that measuring the position of object A would mean that a measurement of the momentum of object B would be "smudged" in a quantum mechanical way. If that is true, then doing something to object A in one place in the universe would have a simultaneous effect on object B in a distant place in the universe. But that is spooky action at a distance.
 * I probably haven't got the details right, but the experiment could be written to make the two masses equal and then the whole discussion could be rewritten in terms of "position" and "speed and direction."
 * Once a clear and concrete instance is presented, the general idea can be extended to show how it applies to other pairs of measurements.P0M (talk) 13:35, 2 June 2011 (UTC)
 * I think we should have a go at rewriting the lead at least. It seems to have been written by physicists for physicists - like much of the rest. Myrvin (talk) 13:54, 2 June 2011 (UTC)
 * I don't have a lot of time right now. Does anybody have the citation for the original Einstein challenge I described above?P0M (talk) 14:08, 2 June 2011 (UTC)
 * I've had a go. I wonder how long it will last. P0M, if you mean the EPR paradox it's there already. There were other challenges by Albert to Bohr though. Myrvin (talk) 18:25, 2 June 2011 (UTC)
 * Thanks Mryvin, your efforts are appreciated, the introduction seems understandable to me now, although that might just be that I've read so much about it in the last 24 hours that everything is spontaneously starting to make sense! :-) — Preceding unsigned comment added by 81.152.67.184 (talk) 19:57, 2 June 2011 (UTC)
 * I was looking for the concrete setup used in discussions between Einstein and the Copenhagen group. It is in "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?" PhysRev.47.777, but what I had in mind is slightly different. There may have been an earlier version.
 * The EPR paper mentioned above says that if there are two "systems" that are "together" so that they share a psi function, then later, after they have separated, measuring the position of A can tell you the position of B, so B must have had a real value to be found by this indirect means. On the other hand you could just as easily have measured the momentum of A, and that shows that the momentum of B must have had a real value. So if system B has a real position and a real momentum, then system A cannot have been unique and lacking in a real position and a real momentum. The way of quantum mechanics as explained by the Copenhagen group makes the incredible claim that when you measure the position or momentum of A you do something that makes as though measured the position or momentum of B.
 * I thought I had seen something that suggested using a measurement of the position of A to determine the position of B, and using a measurement of the momentum of B to determine the momentum of A. If you don't believe in spooky action at a distance then you would get a true and determinate value of both position and momentum for both systems, doing an end run around the messing up of the second characteristic of any single system.  But maybe this is something that my mind added in and my memory has grown smudged.P0M (talk) 02:17, 3 June 2011 (UTC)
 * P0M: Have a squint at this: . Myrvin (talk) 13:30, 3 June 2011 (UTC)
 * I found the experiment I had in mind, although a little abbreviated."Einstein’s thought experiments had previously tried to show quantum theory was wrong, but in 1935 he presented a paper arguing quantum theory was incomplete. In this paper Einstein and two colleagues proposed a thought experiment which involved two co-related particles emitted from a source and moving away from the source in opposite directions at the speed of light. Measuring the position of particle1 can give an exact idea of its position, while measuring the exact momentum of particle 2 allows us to know the exact momentum of particle1 due to the co-relation of the two particles. Einstein also argued that the measurement of particle1 could not disturb particle 2 due to the impossibility of faster than light signaling. This means we can know the exact position and momentum of particle 1 contrary to the uncertainty principle." It is at:

http://homepages.paradise.net.nz/rochelle.f/Bohr-v-Einstein.html
 * The 1935 paper is the EPR one that I mentioned before. I think the explanation given immediately above is wrong, but the EPR_paradox article says the same thing.
 * Anyway, to me this kind of concrete situation should be presented first. P0M (talk) 23:35, 3 June 2011 (UTC)
 * Yup, that's the EPR paper OK. Here is the actual paper: The problem with this for Q entanglement is that the concept hadn't been named by Schrödinger at the time of the paper - and (if anything) the paper was against QE. As you say EPR were debunking Heisenberg with their thought experiment. Schrödinger later used the term entanglement, and he didn't like the consequences either. Myrvin (talk) 07:02, 4 June 2011 (UTC)
 * J-Wiki has now made some changes to the lead. Do we think this has clarified it? J is not one for confusing the ordinary reader and I think I could live with it, but he does put back the concepts of "quantum system" and "quantum state" that I was trying to avoid at the top. He wants the idea of a single particle being in an entangled state to be included. I don't understand that - and to be honest J, I don't see it in what you've put in. Myrvin (talk) 12:23, 4 June 2011 (UTC)


 * Some comments.


 * 1 - I don't get your point, P0M. Do you want to include a discussion of the EPR paradox in this article? Or do you want to include a more concrete experiment involving entanglement? If the first, I'm opposed to it. The whole point of the EPR paradox is that it is completely wrong and ignited the investigation into quantum entanglement. Anything more than a brief comment in the history section is a disservice to the reader. Also, interested people can read the EPR paradox article, who develops the subject with the care it deserves. If the second, that is the objective of the "concept" section. If you could help improving it, I'd be glad.


 * Bringing in the EPR paradox would only confuse the reader. I did not have a point, exactly, because I was just looking for a concrete example of entanglement that could be cited. Ideally, it should involve things such as momentum that people experience in everyday life. P0M (talk) 16:22, 4 June 2011 (UTC)




 * 2 - Myrvin, I don't think it is a good idea to remove the terms "quantum system" and "quantum state". They are the most fundamental concepts in quantum theory, and I don't think it is possible to develop any serious discussion without them. What we should do is try to give specific examples of quantum systems; substituting the term for subatomic particles is just wrong; what about whole atoms; can't they be entangled? And what about molecules? Are they quantum systems? And photons? Are they wave or particle? Then they can't be entangled? And Schrödinger's cat; it is obviously not a particle. This is why it can't be entangled?


 * One of the problem with reading things on the WWW as opposed to buying books is that there is no easy way to put exclamation points in the margin and a card between the pages. At some point I found an explanation of something that used the term "quantum state" or maybe it was just "state." It suddenly made things much clearer for me and at the same time made the term itself clearer. Anyway, "quantum state" is a powerful concept, and it would be very useful if we could explain this quantum theoretical entity. The difficulty in doing even a thumbnail sketch of this idea is another reason to make the lead a concrete example, i.e., let the lead tell readers what they would see in the real world that is then to be given a quantum theoretical explanation. The idea of "quantum system" is going to be hard to cover in brief compass because the boundary of any quantum system seems (at least to me) to be elastic. Having a concrete example would enable us to speak of the quantum system pertaining to the entangled entities mentioned in the example, and to speak of the state of that particular quantum system. To that same quantum system we could then attach by reference the measurements that are thought to map to characteristics of the thing(s) in the real world.P0M (talk) 16:22, 4 June 2011 (UTC)


 * Quantum system is really anything that is describable by quantum mechanics. About substituting quantum state for characteristics, I also think it's a bad idea. Which characteristics? The position and momentum? Or only the combination of both that QM allows to exist? Characteristics is a vague term. As for quantum state, you click on the link and read the definition: "A quantum state is a set of mathematical variables that fully describes a quantum system.". I don't think that is too much to ask for someone who is trying to learn QM.


 * The general reader is going to need some help to understand that the state of some things is a set of mathematical variables. That is like saying that the state of health of a certain person is the body temperature reading on a digital thermometer, the lines drawn by an EEG, the lines drawn by an EKG, etc. The problem is due to the fact that what we mean by "state" in the two situations is very different. P0M (talk) 16:22, 4 June 2011 (UTC)


 * Again, it's not our job to teach the concepts of "quantum system" and "quantum state"; that's why we have hyperlinks. But it's nothing complicated: even in classical mechanics, the state of a particle is a set of mathematical variables, e. g., its position and momentum. Tercer (talk) 03:35, 6 June 2011 (UTC)


 * If it is "nothing complicated" we should be able to give the readers enough of a "steer" to help them get through the lead without having to bop over to any other article(s).P0M (talk) 08:02, 8 June 2011 (UTC)


 * 3 - The article now says that "special" interactions are necessary for creating entanglement. This is flat-out wrong; an interaction has to be very special to not create entanglement.


 * This point needs to be carefully pinned down for the reader because we are so certain in everyday life that things that are not in touch in any way (including field effects) cannot affect each other. The idea that if Click and Clack shake hands, go their separate ways, and then later somebody shoves Clack in the subway that will do something to the momentum of Click is just not what our everyday experience has prepared us to believe. It sounds more like voodoo: Make a dummy with a lock of hair retrieved from the barber shop, etc., stick a pin in the dummy, and, because of the original contact of hair with scalp and fingernails with fingers, the person depicted by the dummy gets a stabbing pain.P0M (talk) 16:22, 4 June 2011 (UTC)


 * You're still thinking that entanglement is action at a distance. This was Einstein's mistake. When you shove Clack in the subway you do not do anything to Click's momentum; that would be action at a distance. If their momentum is entangled, you see a very strange correlation when you measure both, and that's it.


 * Measure Clack and you will see a correlation that classical physics would not lead you to expect when somebody measures Click. Is wavefunction collapse an "action"? I think not. P0M (talk) 08:02, 8 June 2011 (UTC)


 * The fact that you do not see entanglement in everyday life is the same reason why you don't see hardly any quantum effect. And that reason is actually difficult to explain, but it's usually quantum decoherence. Tercer (talk) 03:35, 6 June 2011 (UTC)


 * Tercer, what I mean by the use of the word "special" is that there are a limited number of methods used to effectively create entanglement. All of these appear to involve causation of confusion regarding which (related and constrained) properties are possessed by particles.  This doesn't seem typical of most physical processes.  Do you have a good reference for the idea that entanglement happens more often than not?J-Wiki (talk) 18:33, 4 June 2011 (UTC)


 * That's a matter of experimental convenience: the method has to reliably produce always the same state, and to be controllable somehow. And that is hard. Also the experimentalists are usually interested in maximal entanglement, and this one needs a bit more care. The issue of the confusion about which properties are possessed by which particles is not a particularity of entanglement, but superposition: you do need superposition to create entanglement, but almost all interesting quantum states need superposition, and you have superposition precisely when you don't know which photon went through which slit (in the double-slit experiment). So the question reduces to how special is superposition: again, nothing special. You have to forcibly remove it if you want. Again, in the double-slit experiment, you have to mark the photons somehow. Usually they are marked by polarisation (as in the very interesting quantum eraser experiment): the left slit is covered by a horizontal polariser, and the right slit is covered by a vertical polariser; now superposition disappears, and with it the interference pattern.


 * "Disappears" is probably not the best word, as your further discussion below shows.P0M (talk) 08:02, 8 June 2011 (UTC)


 * Actually, a more complete description of the above experiment would say the photon had its position degree of freedom entangled with its polarisation degree of freedom, as in $$|L\rangle |H\rangle + |R\rangle |V\rangle$$; the superposition only disappears if you ignore the polarisation. So you see, entanglement is so common that I've created it without intention.


 * Well, it was your idea to qualify the interactions as "special", so it's you who has to provide a reference. But nevertheless, I'll try to find a book that says they're nothing special. Tercer (talk) 03:35, 6 June 2011 (UTC)


 * Thanks for the explanation. I was trying to clarify what was already in the article, and the article presently does not provide a good explanation of what, precisely, is needed to create entanglement. (Nor have I read a good explanation anywhere else.)  Much of what you have just written should be in the article, with references.  In the “methods” section, it should be explained that these techniques are used primarily for experimental convenience, and to generate maximal entanglement.  Also, you state that superposition is needed to create entanglement -- this should be clearly stated in the article.  If entanglement occurs in most physical processes, to varying degrees, this should also be in the article.  (It sounds like entanglement is in some ways analogous to energy, in that virtually all physical processes involve exchange of energy, yet "generation" of usable energy is accomplished using particular techniques, for efficiency and control.)  In any event, I agree that the word “special” should go, and have removed it.J-Wiki (talk) 02:59, 7 June 2011 (UTC)


 * You're welcome. I think your analogy with energy is quite correct. I agree that the current state of the article leads the reader to think entanglement is somewhat misterious; but I really don't have time to edit it right now. I think that in the end of July I'll give it a go. Tercer (talk) 01:52, 8 June 2011 (UTC)


 * It's not my question to answer, but I may be able to supply a few clues. What do we mean by a quantum mechanical system? An atom has a nucleus and one or more electrons. Is the nucleus a quantum mechanical system? I think so. If its electrons were stripped away and it were subjected to "measurements" or events that cause it to de-cohere, then it would have no further connection with its former electrons. The electrons might be subjected to decoherence that would give them and their former nucleus determinate values (momentum, or whatever). So the nucleus (or even the protons and neutrons involved) might be considered quantum mechanical systems, the electrons might be systems, the atom might be considered a system, the chemical compound that the atom is found in might be considered a system, and so forth. Einstein considered two masses being in contact at three points for a finite length of time enough to make them a single quantum mechanical system.


 * The salient events seem not to be the ones that make things that interact with each other in some way to become a single system. Rather it is the events that make things that were once a spatially and temporally contiguous system and later become separated to cease to be entangled that are the things to watch. Any "measurement" that requires a member of an entangled pair to have one spin or the other, or to take on some other definite value that was previously in superposition with that of another spatially separate "twin," will terminate at least that component of the entanglement. So all the things in the universe are not entangled in a series of connections going back to the beginning of time.


 * For entanglement not to happen would mean for two quantum mechanical systems to interact with each other in some way, yet after their period of contact was over they would end up having exactly the psi functions that they had before their interactions. Perhaps an example of this kind of thing (or an "almost example") would be the passage of a photon through a polarizing crystal. The only thing that happens (unless the photon happens to be absorbed by the crystal) is that the plane of vibration of the photon is changed. Such a change is not negligible because imposing contrary polarizations of photons will prevent them from interfering. (There is a Scientific American article that describes how anybody can do this experiment. Its an article on quantum erasure.) But nothing else is changed, so if the photon can be put through another change of polarizations so that the plane of vibration of each photon is consistent with itself then the photon will still be able to interfere with itself. Graphically that is something like: random polarization angles → ( | and — )(which won't interfere) and then | → (\ and /) and — → (\ and /) but each photon is entirely polarized as \ or as /, i.e., each photon is not crossed to itself. On a macro scale, if one person is running from north to south, the other person is running from east to west, and they both reach x, y, z at t, then we expect their paths from that point on to reflect the history of their collision. In a coffee shop I used to frequent the glass windows were so configured that reflections merged imperceptibly with direct line sightings, and one would occasionally seem to see two people walk right through each other. No matter how many times I saw that effect I never quite got used to it -- I think primarily because I never knew whether I was looking at two "real" people, two "reflected people," or one "real" and one "reflected" person.  Maybe a better example of being at the same space and time coordinates but not being influenced would be what happens when a north moving wave and an east moving wave cross. P0M (talk) 00:49, 5 June 2011 (UTC)


 * P0M, thanks.J-Wiki (talk) 02:59, 7 June 2011 (UTC)


 * 4 - The lead is now contradicting the concept section. It says that the nonclassical feature of quantum entanglement is that when we measure the spin of an electron, the other becomes instantly known. But the concept section says that this behaviour is not at all mysterious, and the same thing happens with the very classical half-coins. Tercer (talk) 13:48, 4 June 2011 (UTC)


 * And this point brings us around to superposition of states. I just saw something recently about an experiment establishing that the nucleus of one atom was simultaneously spinning in both directions. The idea that we have to get across is that, in terms of the above example, if two such nuclei were entangled if one were measured and were shown to be spinning in one direction, then the other would have to have the complementary spin when it got measured. The idea that the quantum state can be such that it contains contradictory or opposed components such as spin is something that people have to be led into. For the purpose of this article I think we can be a bit dogmatic, i.e., we just assert that superposition of states is what nature does. People who want more than that can go to the appropriate linked article. But not everybody who wants to know the basic nature of entanglement can be expected to absorb a whole book such as Introducing Quantum Theory and then come back and read this article. P0M (talk) 16:22, 4 June 2011 (UTC)


 * I didn't have that experiment quite right. Here is the URL and a couple of other things I found interesting:
 * Pairs of atoms entangled:
 * http://news.bbc.co.uk/2/hi/science/nature/8081058.stm
 * http://www.nytimes.com/2005/12/27/science/27eins.html?pagewanted=all


 * Using calcite crystal to identify which slit a photon traveled through (with qualifications):
 * http://www.bbc.co.uk/news/science-environment-13626587
 * http://www.rdmag.com/News/2011/06/General-Sciences-Physics-A-Quantum-Physics-First/


 * My point is that the lead is now wrong. If you think the truth is too complicated to be in the lead, well, don't say anything in the lead. To tell a lie just because it's simpler is just evil. Tercer (talk) 03:35, 6 June 2011 (UTC)


 * Are you saying that I am in favor of lying, and that I am evil? P0M (talk) 08:13, 8 June 2011 (UTC)


 * Myrvin, the wording before my edit implied that entanglement only occurs in systems composed of two or more particles, now it doesn't.J-Wiki (talk) 18:33, 4 June 2011 (UTC)

Complex language - continuation
Numbering was a good idea.

1. EPR IS in the article. I was hoping that the electron example would be concrete enough in the lead.


 * It's a good idea to have a concrete example in the lead. I'll try to reword it. Tercer (talk) 19:12, 6 June 2011 (UTC)
 * How about: "There are these two (very small) chunks of concrete ....". Myrvin (talk) 07:13, 7 June 2011 (UTC)

2. The problem with hyperlinks is that they could easily put off the general reader and they do go on. I did what you said for quantum state and the def is meaningless without further linking to quantum system which redirects to the whole of quantum mechanics. Sorry J, I now think this is too much. I would be happy with a term like physical property. Because a physicist thinks it's "nothing complicated" does not make that true for others.


 * Myrvin, the term “quantum system” is used six times in the article “Quantum mechanics”!  To me this indicates that the article “Quantum system” needs to be written.  It seems to be a nice, concise term that adequately conveys all that's needed.J-Wiki (talk) 03:03, 7 June 2011 (UTC)

Gosh! Myrvin (talk) 14:09, 8 June 2011 (UTC)
 * I changed the redirect to physical system, but that is also inadequate. It should not be hard to write a stub about quantum system. Tercer (talk) 18:57, 7 June 2011 (UTC)

3. I have been here before. Everyone I read says that, if QE happens, then it is action at a distance and that QM people are happy with that. Yet Tercer says it isn't. The article Action at a distance (physics) says: Experiments testing Bell-type inequalities in situations analogous to EPR's thought experiments have been consistent with the predictions of quantum mechanics, suggesting that local hidden variables theories can be ruled out. Whether or not this is interpreted as evidence for nonlocality depends on one's interpretation of quantum mechanics.[5] In the standard interpretation the wave function is still considered a complete description so the nonlocality is generally accepted, but there is still debate over what this means physically. The Stanford page on the subject has: The curious EPR/B correlations strongly suggest the existence of non-local influences between the two measurement events, and indeed orthodox ‘collapse’ quantum mechanics supports this suggestion. According to this theory, before the measurements the particles do not have any definite spin. The particles come to possess a definite spin only with the first spin measurement, and the outcome of this measurement is a matter of chance. If, for example, the first measurement is a z-spin measurement on the L-particle, the L-particle will spin either clockwise or anti-clockwise about the z-axis with equal chance. And the outcome of the L-measurement causes an instantaneous change in the spin properties of the distant R-particle. If the L-particle spins clockwise (anti-clockwise) about the z-axis, the R-particle will instantly spin anti-clockwise (clockwise) about the same axis. (It is common to call spins in opposite directions ‘spin up’ and ‘spin down,’ where by convention a clockwise spinning may be called ‘spin up’ and anti-clockwise spinning may be called ‘spin down.’)

As for "special": I was reminded by the TV prog "Through the Wormhole" that the quantum vacuum is always producing pairs of particles. Presumably these are entangled. So there would be an awful lot of those.


 * Both your references say nonlocality, not action at a distance. The problem is that the term nonlocality is not well-defined outside physics: if they mean quantum nonlocality, they are perfectly correct in saying there's plenty of experimental evidence for that. But action at a distance, no, there's not a single iota supporting that. Actually, all our theoretical framework is based on the assumption that action at a distance does not exist; any experiment in its favour would have profound consequences for all of physics. Tercer (talk) 12:11, 6 June 2011 (UTC)

And yet both articles are about action at a distance. They do not separate this from non-locality. As an aside, Physics surely lived with the action at a distance of gravity and fields for a long time. Myrvin (talk) 14:12, 8 June 2011 (UTC) 4. I have said before that I don't like those coins. The section does imply that QE is different from coins (therefore, not as unmysterious), but doesn't say how. Myrvin (talk) 06:40, 6 June 2011 (UTC)


 * The last paragraph says how: "One might imagine that using a die instead of a coin could solve the problem, but the fundamental issue about measuring spin in different directions is that these measurements can't have definite values at the same time―they are incompatible. In classical physics this does not make sense, since any number of properties can be measured simultaneously with arbitrary accuracy. Bell's theorem implies, and it has been proven, that compatible measurements can't show Bell-like correlations,[11] and thus entanglement is a fundamentally non-classical phenomenon."


 * The issue is that the correlations produced by entanglement are stronger than the half-coin correlation; and to see this strength you have to use complementarity, which is fundamentally quantum-mechanical. Tercer (talk) 12:11, 6 June 2011 (UTC)

The general reader (and me) sees that the half coin example always results in Alice having a head and Bob having a tail. There can be nothing stronger than always. There needs to be an example that uses angles, so it can be shown that this differs in QM and in Classical mechanics. I don't see that the die helps at all. It just makes it murkier. By the way - I don't think anything in physics has been proved. Bell's has been tested and these tests have upheld it - or, rather, failed to break it. But then I'm just an old Popperian. Myrvin (talk) 07:08, 7 June 2011 (UTC)


 * I agree with you about physical proof; it does not exist. But that sentence in the article is referring to mathematical proof, and [11] is a mathematical paper. About the strength, correlations are a tricky business. The issue is that in the quantum system there are many directions (an infinite number, actually) that Alice and Bob can measure so that their results will be anti-correlated, whereas the classical coins only have one direction. Here lies the strength. Tercer (talk) 18:39, 7 June 2011 (UTC)

I wonder if that helps. In a sense, the coins can be looked at at different angles. Twist it a bit and the head will be a head - but at an angle; and v.v. (I realise (I think) that, for the electron, it doesn't always spin up if you look at that at any angle - so it may be like the head turning into a tail if you twist it a bit). Does this mean that there are no examples in classical mechanics that can be shown to differ from the QM examples? If so, what sense is there in saying that they differ, since there is nothing with which to compare QM, classically? Myrvin (talk) 14:09, 8 June 2011 (UTC)

Greene's Explanations
I don't have a lot of time right now to go through The Fabric of the Cosmos and pick up the points that Brian Greene makes. Basically he says that something happens and that what happens is very hard to reconcile with any attempt that tries to limit the reasons for some changes to physical processes that proceed at the speed of light. For right now, let me show you the chart that results when you follow through his argument/analogy about correlations. His way is the reverse of what Tercer says, as I have remarked before. I think this difference is a function of the way the experiments are set up, not due to any error on Greene's part.

He sets up (starting on page 107) the following analogy or thought experiment. There are two "boxes" linked to receptors for two sets of entangled particles. Each box gives a measurement of three different characteristics of the incoming particles by opening doors (labeled G(rey), W(hite), and B(lack) in the chart below). Opening each door gives a different measurement, and the measurements are reported in terms of red and blue lights (labeled r and b). If the two boxes give the same response (color) when a door on each is opened, then that is counted as "+1", and if one shows red and the other shows blue, then that result is counted as "-1."

Look at the second and third lines in the chart below (Preset and Match). If the boxes are pre-programmed (i.e., if the experiment is controlled by hidden variables) then when the G doors of the two boxes are opened, both see blue, if G is opened on one box and W is opened on the other box then blue is seen, when G is opened on one box and B is opened on the other box, then blue is seen on one and red is seen on the other (so no match). So if you go through and look at all possible connections, you win 55% of the time.

What he concludes is that if you are measuring pairs of phenomena in the same system of entangled particles, pure chance will let you "win the shell game" 55% of the time if there are hidden variables, but that Copenhagen quantum mechanics, if true, means that you can only win 50% of the time. Here is a picture of his two "boxes" and the chart I made:



If Bell is right, i.e., if there are no "gotcha" factors that will mess up his analysis, then experiments would either show a true 50% figure when QM predicts 50%, or not. If not, then QM is missing some factor of reality and is incomplete.P0M (talk) 14:55, 7 June 2011 (UTC)
 * Gee P0M, what will you do when you DO have the time? I too sometimes wonder if the QM world has lower correlations than the classical, even though the opposite is declared. See what I said above about the coins. Myrvin (talk) 14:18, 8 June 2011 (UTC)
 * This was low-hanging fruit, something I did a long time ago.P0M (talk) 17:34, 8 June 2011 (UTC)

Pages 11-12
Here are some points that Greene makes that I think are valid and either ought to be considered as background for the article or else ought to be made in our own way in the article:

"Quantum mechanics describes a reality in which things sometimes hover in a haze of being partly one way and partly another. Things become definite only when a suitable observation forces tehm to relinquish quantum possibilities and settle on a specific outcome. The outcome that's realized, though, cannot be predicted -- we can predict only te odds that things will turn out one way or another."

"With the ensuing twists of scientific progress, Einstein's paper can now be viewed as among the first to point out that quantum mechanics -- if taken at face value -- implies that something you do over here can be instantaneously linked to something happening over there, regardless of distance."

Pages 80-84
p. 83: Notes that a photon can enter a situation such as a beam splitter, where there is a 50% chance of its passing through or being reflected, and whatever it does will also be done by its entangled twin at any distance away.
 * That is very spooky. Myrvin (talk) 14:19, 8 June 2011 (UTC)
 * Something has to be "there" for interference to occur, right? I think it was Dirac who said that a photon can only interfere with itself. So if you look at the kind of "two mirrors and two beam-splitter" rectangular array that constitutes an interferometer used in some of the quantum eraser experiments, when a photon enters the apparatus the first thing it hits is a beam splitter. Common sense says that if it is reflected by the beam splitter (which sits at a 45° angle to the line of entry) then the photon goes "up" (in the schematic, that is), hits a first-surface mirror, goes horizontally, and then hits another beam-splitter where it could either go out the top or go out the far size from where it entered (but at the other corner). But if all that was involved was "the photon" and it went by way of a single line path, then there would be no interference with anything. (The experiment still works if one photon at a time enters the apparatus.)
 * It looks like there is a "decision" made at the first beam-splitter. Whatever the character of the event that constitutes the "decision" (or wave-collapse of some kind perhaps), it is carried through and it coordinates with the "other half of the photon" that goes by the alternative path. Nobody has a good word for the portion of the wavefunction that "goes by the alternative path." The whole thing is "spooky," but I think it is so only because we are unaware of it in everyday life. It seems to be extremely regular in behavior, with the only "irregular" element being the very regular way that the roulette wheel is balanced to give a certain number of "stops" at each number around the wheel (so to speak).P0M (talk) 17:34, 8 June 2011 (UTC)

Page 117
Discusses why information cannot be conveyed from one experimenter to another over distances and instantaneously by use of entangled particles. Basically, the person who first measures one of an entangled pair cannot determine what the measurement will show.

"...The majority of physicists sum it up by saying there is a harmonious coexistence between special relativity and Aspects results on entngled particles. In short, special relativity survives by the skin of its teeth. Many physicists find this convincing, but others have a nagging sense that there is more to the story."

0.
Before we get started on this stuff it is worth noting that the whole issue of "cause" is problematical for modern physics and especially quantum mechanics. If something "causes" something else to change by exerting a Newtonian force on the other thing's mass, then we may need some other word to use in discussions of changes that occur that are not occasioned by the application of force. The "action at a distance" dispute is probably a species of the "don't know why this particular photon chose to show up in this band of the interference fringe rather than some other band" type of problem. What "causes" a photon to "show up" or to "tunnel through," or to do whatever is possibly a matter of force being exerted, but if that is so it remains to be demonstrated by experiment that it is  so.

Einstein's original question in the EPR paper was, I think, basically the following: If two particles are entangled in the lab and one of the two is sent far away while its psi-function is characterized by a superposition of states such that its spin is undecided, why doesn't the remote particle just stay in that "conflicted" state? It may be a billion miles away or only a step away, but it is not in contact with the other electron, it is not subject to any force or signal traveling from the first electron, so the principle of sufficient reason ought still to hold. It has no "reason" to change. For Einstein the only answer to "why does it change" is to say that it does not change. Its spin has always been a function of the hidden variable that was set either when the particles were entangled or when they became physically separated.

If "cause" is equated with "exert a Newtonian force on," then interaction between entangled photons has to be limited to light speed transmission. Actually, such a simplistic explanation of "cause" can't stand. At a minimum one would have to say that a cause is "the changing factor or factors, in a constellation of factors that constitute the current situation/system, that is associated with a change in the system."

1.
I suggest that the first thing in the lead should be a concrete example of entanglement. Once the reader has an understanding of what would be seen in the lab or in nature, then a more abstract discussion can be given.

1a. One example that can help readers understand how things that were originally unconnected in regard to their quantum state can become connected is what happens when two hydrogen atoms join to form a hydrogen molecule. The two electrons spread out and share a new orbital with lower energy. They must have or acquire opposite spin to do so. So something about the electrons changes at that point. Separating the atoms would require energy, and so would ionizing the molecule by throwing off one electron. The departed electron's quantum state would reflect the changes that occurred with the formation of the molecule. The mixed spin state would be one such factor. A change in the state of the departed electron would cause (Is that a safe word? Does it imply "action"?) a change in the surviving molecular electron. (See Sci. Am. Reader, p. 147.) 1b. See also, Louis de Broglie, Revolution in Physics, p. 266f. 1c. See also,

2.
One of the first things that should be discussed is how one would ordinarily interact with a quantum system to make it leave a state of superposition and take on a definite spin or other quantum characteristic. Doing so would facilitate showing the difference between this kind of a change and the kind of chance that occurs within the context of quantum entanglement.P0M (talk) 08:26, 8 June 2011 (UTC) 2a. Schrödinger said: "When two systems interact, their psi-functions, as we have seen, do not come into interaction but rather they immediately cease to exist and a single one, for the combined system, takes their place. It consists, to mention this briefly, at first simply of the product of the two individual functions; which, since the one function depends on quite different variables from the other, is a function of all these variables, or 'acts in a space of much higher dimension number' than the individual functions. As soon as the systems begin to influence each other, the combined function ceases to be a product and moreover does not again divide up, after they have again become separated, into factors that can be assigned individually to the systems. Thus one disposes provisionally (until the entanglement is resolved by an actual observation) of only a common description of the two in that space of higher dimension. This is the reason that knowledge of the individual systems can decline to the scantiest, even to zero, while knowledge of the combined system remains continually maximal. Best possible knowledge of a whole does not include best possible knowledge of its parts -and that is what keeps coming back to haunt us." See:


 * It seems that this guy is a string theory man, using it to reconcile Einstein and QM. There is nothing in the article about string theory. There would have to be for this to go in. Myrvin (talk) 14:26, 8 June 2011 (UTC)


 * Greene is indeed interested in string theory, but there is nothing in what he says about entanglement that is explained by him in terms of string theory. He is writing a general coverage of modern physics for the interested non-technical reader. He is honest and forthcoming about his own theoretical leanings. What he says in his book is supported by other things that I have read, so I am in favor of using him as a model for a useful way of introducing things for Wikipedia readers -- not all of whom will want to take a third-year physics course in order to get a general idea of what the buzz about entanglement is all about.


 * Points 1 and 2 above are out of my general understanding first. I only went back to Greene because he has a lot of good ways of saying things in a sentence where I would take a paragraph -- and he is a physics professor with appointments at major U.S. institutions.P0M (talk) 00:38, 9 June 2011 (UTC)

3.
Introductory example and its possible interpretations (Einstein crowd vs. Copenhagen crowd)

3a. The first part of the lead should start with a concrete example, such as a situation in which an excited atom returning to its equilibrium state emits two photons in the same operation. They go off in opposite directions. When Kramer and Heisenberg were initially working on the dispersion of a beam of photons by a medium (e.g., oil), there was not even the idea that one photon would be absorbed and two photons would be emitted but at different frequencies and in different directions. At the dawn of quantum physics it was understood that a specific kind of atomic event was involved in such re-radiation. After Heisenberg worked out a matrix math way of accounting for the amplitudes and intensities of light that is emitted by a hydrogen lamp, and quantum mechanics was born, Einstein saw that the formal mathematical model that came from Heisenberg's initial breakthrough implied that when two photons were produced in the same operation they share a single quantum state, and it can be a state that is "going both ways at the same time," so to speak. Einstein argued that the mathematical model needed to be fixed so that it would not seem that each photon was "going both ways" (i.e., was in a superposition of quantum states) because that implication of the math model had a consequence he could not accept. So he insisted on the need for hidden variables to eliminate the possibility that appeared from the math, that if there were two entangled particles, A and B, then each would have the superposition of quantum characteristics (polarization, momentum, spin, etc., etc.) that the existing theory attributed to them, and that if one of the two were to be measured, forcing it to "decide" which way it was spinning (or whatever was being measured), then without any further intervention the second particle would either no longer be in a state of superposition or else would "know" how it had to come out of superposition when it was measured.

3b. Einstein called the precipitation of a "decision" of what characteristics to assume when measured by a measurement performed at a remote location "spooky action at a distance." In ordinary English, when we speak of action we mean that force is applied to some object thereby making it change in some way. Pushing a cart may make the cart move. Putting current through the coil of an electromagnet can cause a nearby iron object to be attracted toward it. Beating on a drum at one place can make an observer's eardrums vibrate at some distance away. In all of these cases changes are propagated through space, an operation that takes some finite amount of time. But the quantum model does not involve a trajectory through space between the first object measured and its entangled twin, nor does it involve a time for transmission term. The quantum state of A is the quantum state of B until something happens to A or to B that makes that one "show up as" having a certain spin or whatever. When one has a definite state the other is required to have a definite state if "the same" quantum object has special limits, e.g., the Pauli Exclusion Principle precludes two electrons in the same quantum system from having the same spin. Twin photons can't have the same spin, etc.

3c. The issue of "locality" refers to the human expectation that things have to be in the same place at the same time, or at least be in contact through a mediating field force, for what is done to one thing to have an effect on the other thing. Suppose the experimenters were working with two entangled electrons that were as close to each other as possible. Even then it would not be clear how measuring one could do something akin to measuring the other one. If such a circumstance were noted, it would probably be hypothesized that the same measuring operation unintentionally extended to both electrons. Separating them by a great distance would make the puzzle more apparent.

4.
4a. If something produces a change in some other thing but without exerting force on it, what do we call that kind of interaction?
 * Einstein has one way of discussing this problem in his "Autobiograpical Notes," [Albert Einstein: Philosopher Scientist, p. 85]:

"Now, however, the real situation of S2 must be independent of what happens to S1. For the same real situation of S2 it is possible therefore to find, according to one's choice, different types of Ψ-function. (One can escape from this conclusion only by either assuming that the measurement of S1 ((telepathically)) changes the real situation of S2 or by denying independent real situations as such to things which are spatially separated from each other. Both alternatives appear to me entirely unacceptable.)"
 * So Einstein speaks not in terms of "action" at a distance, but of "changes [in] the real situation," or a denial of locality.P0M (talk) 13:22, 9 June 2011 (UTC)

4b. One way around the appearance of a measurement of A "doing something" even if not "acting upon" B is to argue that there are hidden variables that are set at the time of the formation of entangled pairs and predetermine which one of them will take which spin, and so forth. Under this interpretation, it is not a matter of probability and chance which values A takes if it is the first of the twin particles to be measured. The value taken by B is neither due to "action at a distance" or any other form of interaction between the two particles but simply because B was set to take that value as soon as the entangled particles were created. So quantum mechanics would then do as it does now and attribute a common quantum-state description to both entangled twins, but it would also have an additional variable or variables that would determine how the superposition would eventually be resolved. (I suppose that one might wonder what the hidden variables do in cases of particles that are not entangled. Do they too decide things like spin? If so, they must "decide" on some reliable basis whether to pick one spin or the other, and something has to make sure that half of them choose each spin, etc. So, in that case, each entangled particle ought to have its individual arbiter of spin, and there is no obvious reason why the 50% rule would have to apply in the individual cases. Why not let one pair decide to both be clockwise as long as another pair decides to both be counterclockwise? But "who" does the bookkeeping?

5.
If Bell is right, there can be no hidden variables because the percentages that would emerge on that basis are not the ones that show up in the laboratory. And, if he is right, what accounts for the results actually produced? One answer to the "instantaneous resolution of superposition" paradox is to say that the quantum state is not a physical thing. It is a single set of characteristics shared by two particles or larger things that may be separated by a great distance in space. Since there is only one "thing" there is neither the need nor the possibility of resetting it twice for every measurement taken of A or B. It is not "action at a distance" or even "change at a distance" because there is no distance involved.

The above 5 points are a sort of draft. If I have not misrepresented anything, the the discussion can probably be boiled down quite a bit. I suppose we could also say something about the practical uses of entanglement. P0M (talk) 03:34, 9 June 2011 (UTC)

incorrect attribution
"Bell's theorem implies, and it has been proven mathematically, that compatible measurements can't show Bell-like correlations,[11]" --- No, this fact was well-know to experts much before my work. Boris Tsirelson (talk) 16:05, 8 June 2011 (UTC)
 * Aha! So it wasn't Boris. Looks like we need a new reference. Myrvin (talk) 19:18, 8 June 2011 (UTC)
 * It was me who added the reference. I did not mean to say it was your discovery, Professor Tsirelson, I cited the paper only because it says so clearly and has a simple proof of the fact. I don't think that it will be possible to establish clear priority on this discovery. But if you do know who first pointed this out I'd be grateful. Tercer (talk) 22:38, 12 June 2011 (UTC)