I think that's what it's called. For example if you created two electrons and sent one billions of miles into space, then if you did something to one it'd effect the other instantly.

Is this really true or just a theory? And how do you create two electrons? Why would they be connected to each other but not connected to any other electrons?

This looks like a job for... Wikipedia!

http://en.wikipedia.org/wiki/Quantum...ent#Background
http://en.wikipedia.org/wiki/Quantum...f_entanglement

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"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
"The Mayan symbol for "book" looks a lot like a triple hamburger, but I've never seen them claiming it as proof the Mayans had Big Macs." - KaiYeves
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

You may have a look at the experiments of Dr. Anton Zeilinger (http://en.wikipedia.org/wiki/Anton_Zeilinger

At the moment he is doing the first test runs for entangled photons in space distances

Here is the link to a site in German:http://derstandard.at/?url=/?id=3274428

As I said it is in German. But googling his name and "quantum entanglement" may lead to some English hits also.

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Andre

"They did not know it was impossible, so they did it!"
Mark Twain

I suggest you purchase yourself a copy of Amir D. Aczel's book 'Entanglement'. That should assist you in understanding this issue.

Its meant to be read by the non scientist, and explains the issue well. I have it in audiobook form from Audible myself.

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http://code.google.com/p/nmod/

Entanglement is a prediction of quantum mechanics, and all experiments on it so far have confirmed quantum mechanical predictions. However, none of them have required something you do somewhere to "affect the other instantly". The two offending words are "affect" and "instantly". An affect implies causation, and causality is limited to the speed of light (no entanglement experiment violates that). Also, "instantly" is a frame-dependent concept (a la relativity), and no entanglement experiment violates that either. What happens is, an experiment you conduct on one electron gives you information about the other-- information that no one else has and no one else needs to successfully use quantum mechanics to make their own predictions. The only way you see this as an "affect" is if you apply philosophical concepts that are outside of science, like if you say that the electron "has a wave function" and changes in the way you would describe its wave function somehow actually affect the electron. The fact is, the only time we ever know "the wave function" of anything is when we prepare a system to have a certain wave function, thereby erasing whatever history it may have had. When we don't do that, as we don't in entanglement experiments, then we only know the wave function that we are using to make our prediction for what will happen-- and someone else with different information will use a different wave function and will find that quantum mechanics works for them too.
When stated in a proper way, entanglement is experimentally verified. Unfortunately, there is a whole lot of baloney written about this effect, ranging from unnecessary philosophy to just plain wrong physical claims.
You don't create them necessarily, it's fine to use pre-existing ones. They can be entangled based on their history. But you are completely right-- it is quite possible, depending on the experiment, that they will also be entangled with other electrons in ways that don't matter to the experiment and we simply choose not to include in their wave function. That's the key point.

If one passes a particle through a grating, and collects/constrains a pair of particles that exit the grating, then moves the first of the constained pair of particles 1 ly away from the second, then forces some characteristic of the "local" member of the pair of particles, say the spin, to a specific state/sense, then (someone) measures the spin of the second (distant) particle of the pair some short period of time later (a period significantly less than 1 year). Will the two spins be found to be of the same sense? What will be found if this experiment is repeated a large number of times, by having passed through the grating, and collected, a large number of particles and particle pairs, in the first place?

Robert

You don't want to "force" the spin to be something, that won't do anything interesting. You want to "measure" the spin. If the two particles are entangled in some particular way (perhaps they must have opposite spin), then your measurement on the one electron will change your quantum-mechanically produced predictions for the results of someone else measuring the spin of that other particle. And when you test your predictions (statistically over a large number of trials as necessary), you will find they are statistically correct. But here's the kicker many overlook: the other person, who does not know of your result, will make their own prediction of their own measurement, will not incorporate your result, and will also conclude that quantum mechanics is working fine for them too! That's why "quantum mechanics is in your head", and there's no paradox about "instantaneous effects" when they occur only in your own thought process. There's an awful lot of hooey written about quantum entanglement! (And I don't mean Bell's theorem, that's all pretty rigorous stuff-- I wouldn't call it hooey, I'd call it over-interpreted.)

Does the mathematics of the prediction (in terms of the joint wave function) give the information, or do you mean the information stems from the measurement at one detector? I can see the joint probabilities for both electrons as being predictive, but when we talk about specific measured states, none of that is predictive is it? I appreciate that the measured state is kind of book keeping, but I still find it difficult to relate this book keeping as being common to two separated locations. I mean I cannot predict from the joint wave function that an entangled particle at source will evolve to have a specific measured up state at detector A and a specific measured down state at detector B can I? All I can say is that there is a 50% chance of it being up or down in either location and that the rules say if it is up in one detector it will be down in the other. Are you saying that the book keeping is just recording the nature of the predictive outcome, it is just the final part of the quantum prediction that gives a chance to tabulate the probability outcomes - the measurement should not be thought of as some kind of deterministic event that kicks in to ensure the other particle follows the rules, but rather the rules are inherent in the wave function which is a product of our experimental set up.

I don't wish go back over ground that was amply covered in the thread ("Spooky Matter at a Distance" - in General Science I think) but it seems like an opportunity to clarify a few points.

If it's just that measuring one particle tells you information about the other, and NOT that doing something to it has the same effect on the other (as it's often said to be), then where's the "action" in Einstein's "spooky action"?

That's an interesting question. I suppose one must distinguish "independent information" from "information transformed via a calculation". The former is the result of something that couples to reality (i.e., a measurement), and the latter is like a function that always gives the same output from the same input (i.e., the information out is just a reprocessed version of the information in, like a coded message). I see the process as gathering actual information from your experiment, then using a calculation to make a prediction about another measurement. That prediction is a form of information too, but it just converts the information you got from your experiment into a prediction. If it sounds like you are ending up with more information than you started with by doing that calculation, then you have overestimated how much information was "really there" in the first place.

We don't get information about that except by doing the measurements. The predictions are only about joint results (which is why the experiments always involve coincidence detectors).

You can get three things from the joint wavefunction of two particles. The first two are a statistical prediction of an observation on one particle, or on the other. Nothing at all strange will happen if you do that.

Or, you can get a prediction about joint probabilities for observations on both particles, and then you will get some results that people concern themselves with, but it will always be what the joint wave function predicted. So the "problem" is already there as soon as you accept a joint wavefunction as your representation-- yet we couldn't get very far in quantum mechanics if we didn't do that.

It's as though people were expecting joint wave functions to successfully predict the Pauli Exclusion Principle in white dwarf stars, and the "exchange energy" correction in two-electron atoms and molecules, all bizarre yet perfectly well documented, but expected them to break down somehow whenever they disagree with our classical intuition in EPR-type experiments. Go figure. One could say that the value of Bell's theorem is simply to elucidate the ramifications of quantum mechanics, but why this somehow is interpreted as throwing quantum mechanics into a tizzy is beyond me because I never attributed that theory with a particular set of philosophical principles based on classical expectations.
Yes, that sounds like what I'm saying indeed.
I don't mind at all, this point comes up a lot and it stands to get it out there. If I'm right, the more places it appears the better, and if someone can refute me, then I want to give them the best possible opportunity (because I'd like to know).

The key to all of this seems to relate to the distinction between two computing methods that can be used when dealing with these entanglement experiments. I mentioned in the other thread that these are described in a book that I am reading by Bernard d'Espagnat ("On Physics and Philosophy").

The one method he describes as being used by those who view the Aspect - type experiments in a "realist" manner - i,e, they imagine that wave functions are "real stuff" - that one wave function of the pair of photons is "reduced" on measurement resulting in the other photon getting its own well specified wave function. The upshot of this of course is that there is real physical influence that travels faster than light. This method he defines as the descriptive method and I think relates to the comment by Delvo regarding the notion of "action".

The other method he describes as the predictive method - those who view the Aspect - type experiments in this manner he describes as seeing physics as describing human experience. I should add that the whole theme of his book very definitely falls into this latter camp.

It is this predictive method that he outlines that is of interest to me in terms of your views, I can't decide if d'Espagnat is saying the same as you, or (given your comments and those of Grey in other threads) that in fact you are going beyond the current physics community consensus which I would imagine would also be going beyond what d'Espagnat is saying. I only say this because d'Espagnat describes these two methods in a very matter of fact way, as if they are accepted alternative ways of looking at the raw experimental data. I thought that if I include his word for word outline of this predictive method, you may be able to give me some clue as to whether or not I am justified in thinking that you are both basically saying the same thing - this will help me in being able to place d'Espagnat's views and yours in some kind of context. I appreciate there may not be enough detail here for you to make a meaningful comment, but the book is an overview of realism in physics in relation to quantum mechanics and so does not go into great depth with regard to the various topics covered.

He says:

"The other method at our disposal consists in not introducing at any stage any wave function other than just the one of the pair. To the mathematical expression of this wave function some calculation rules are directly applied that, according to the formalism, yield the joint probability of observing a given pair of results on the left and right instruments, and this for any pair of orientations of the latter that one may choose. This calculation thus yields correlation predictions and (fortunately!) the latter are identical to those obtained by means of the descriptive method (a confirmation of the fact that quantum mechanics is a consistent theory).

Note, that in this method, no faster than-light influence explicitly appears. But this circumstance is tightly linked with the fact that the method in question is purely predictive and lends itself to no interpretive picture*. As we just saw, it just consists in applying a set of observational predictive rules (the quantum mechanical ones) concerning which it has been found that up to now they correctly predicted what was observed. In other words, it is grounded on just induction, quite apart from any reference (not even implicit) to a realist interpretation liable to support the latter and make it somewhat plausible. At first sight, it may therefore be wondered whether it yields a genuine explanation of the observed correlation. In fact this may be considered a first illustration of the difference, noted in section 2-8, between explanation as understood by the objective realists and explanations as conceived of by upholders of the view that physics merely describes human experience."

"*The fact should be kept in mind that, in quantum mechanics, a statistical ensemble of pairs described by "the pair wave function" cannot be identified with a mixture of pairs whose orientations in space are well defined, differ from one pair to the others, and are statistically distributed. Relative to most correlation measurements these two ensembles lead to quantitatively different outcome predictions." (foot note by d'Espagnat)

I'll step in to point out (as I always do ) that this isn't really accurate. Ken G is correct that there is no way for us to use quantum entanglement to send messages that violate causality, or anything of that sort. However, Bell's theorem demonstrates that, for the results to be consistent with the predictions of quantum mechanics and observation, the whatever underlying mechanism determines the result at A must take into account information about the choice of measurement at B, which can be arbitrarily far away, and can be outside the light cone (past or future) of measurement A. It does not require ascribing any reality at all to the electron's wave function, or treating it as anything more than a bookkeeping technique to come to that conclusion.

Now, it's true that Bell's theorem does rely on a couple basic assumptions; all theorems do. If you're committed to preserving the assumption of locality, you can focus on those other assumptions as well. In some cases, that's hard to do (for example, one assumption is simply that the most basic rules of logic are valid), but others are a little trickier to defend (such as contrafactual definiteness, the assumption that the choice of measurement at B could have been different, and that if it had been, we would have seen definite results which still would have been consistent with the other measurements we made and the predictions of quantum theory). There's been a fair amount of discussion about all of that within the scientific community over the years, but most physicists whose views on the matter I'm aware of, either from direct communication or from reading their work, accept the conclusion of nonlocality.

Ken G seems to accept most of the steps of that argument, but balks toward the end, insisting that the universe is neither local nor nonlocal, preferring to use words like "holistic". Except that the way he uses "holistic" is essentially equivalent to a subset of possible nonlocal universes, as the term is used by everyone else. But for some reason, he doesn't want to use the term.

I've given up on convincing Ken G to think other than he does after many long conversations about it; I fear that we just go around in circles, and I don't have the time to devote to it these days. However, I always feel honor bound to follow after him in these discussions, and point out that his views are not mainstream in this matter. In one sense, that's not particularly a problem, he's welcome to hold his own views. But since he's extremely knowledgable about many aspects of physics and astronomy, very skilled at explaining them, and therefore seen as an authority here, it might be easy to assume that his views on this matter do reflect those of the majority of physicists.

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Conserve energy. Commute with the Hamiltonian.

I don't think that many people think that Bell's theorem throws "quantum mechanics into a tizzy". They just think that it shows that quantum mechanics is inconsistent with a local model of reality, and further, that since we now have experimental results in this matter (that unsurprisingly match the predictions of quantum theory), any future theory will also be inconsistent with a local model of reality. That would have really bothered Einstein, who had hoped to use the assumption of locality together with thinking about EPR-type experiments, to show that quantum theory could not be a complete description of reality. Instead, Bell was able to show that the assumption of locality itself was a problem. It was a big shock at the time, but unless you're still committed to a local model of reality, it shouldn't still be a big issue.

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Conserve energy. Commute with the Hamiltonian.

That does seem to be the trouble with this
subject, lots of philosophy but a derth of
clear experiments illustrating very very
clearly the paradoxes. I was chuffed however
to extract an agreement from Dr Chinese some
time ago that Bells inequality was another
manefestation of the curve of polaroid cut off
law known for 200 years. It has a name, sorry
I cannot recall it.

So just to be clear, I take it you are not talking about a faster than light influence here?

But that's not a "method", the method is science: organization and prediction of experimental results using mathematical axioms. No part of this is the "attribution of what is real" step, that part is merely a picture, to accomplish cognitive resonance in the mind of the scientist. That's fine when recognized for what it is, but all too often, it is mistaken for part of the method. Is not the most important aspect of scientific methodology its objective and demonstrable nature?

It is a description, yes, but not a method. The scientific method involves testing-- how does one test a physical influence that travels faster than light? No such test ever succeeds in finding anything real that travels faster than light, this is trying to tell us something.
The key point is that these are not separate approaches-- everyone uses the latter approach, it is a subset of the former. It is the objective subset, in fact-- it is the science part. People are welcome to take that science and build any structures in their minds that generate whatever level of cognitive resonance they like, while others go to church or for a walk in the woods to acheive a similar state of cognitive satisfaction. What is the distinguishing characteristic of science? It is the subset that gives you no choice, that is objective.
My approach is certainly not part of the consensus, but its goal is to notice the lack of consensus and point out that this is a good indicator that science has taken an unnecessary step.
Yes, that does sound like what I'm saying, except I add that the "predictive" piece he describes is in fact what science is, and adding anything to that makes it something less than what it is, not something more. It is a backtrack, a return to when the opinions of science were highly suspect (just ask Galileo). Ironically, you often see it in the very same types who come down most harshly on people who reject science as their paths to all truth, and it is that core hypocrisy that bothers me the most about it.


The key word is "fortunately", but it is not "fortunate" at all-- it is the simple expression of the fact that what is described is the science, there's no way the "other approach" could yield anything different and still be science. The one is a car, and the other is a car with a periscope that thinks it's a car/submarine. "Fortunately" they both drive on roads.
Right, except that it does lead to an interpretive picture-- any interpretive picture you want that is consistent! That's the beauty of interpretive pictures, they are tacked onto science in any way we like, often many in the same situation. That is quite common in science, you see it everywhere. Why did we expect quantum mechanics to be different, because it is a "theory of everything"? Please.
What an "explanation" is is a tricky subject, not really part of science. One can debate it, but one is not debating a scientific result, one is debating what one thinks the goal of science should be. But science is not defined by its goals, it is defined by its methods, and they give what they give.

I guess I'll have to step in and point out why that isn't accurate (though I'm glad you've come around to recognizing that the whole business can be successfully viewed as a form of bookkeeping without any "reality requirements" applied to the wavefunction, that's an important rapprochement). The only remaining key point is, a scientist at A using what he/she considers to be "the wave function" of the particle at A can do quantum mechanics perfectly well, and get perfectly consistent results, publish papers, and even win Nobel prizes on the data, without having the least idea of what happened at B. In fact, this is exactly what happens in real life! So I claim that simple observation invalidates the interpretation of Bell's theorem that says "for the results to be consistent with the predictions of quantum mechanics and observation, whatever underlying mechanism determines the result at A must take into account information about the choice of measurement at B". It's just clearly wrong, unless one places all kinds of significance in the phrase "whatever underlying mechanism determines the result at A". That's looking in the mirror and making all kinds of philosophical assumptions, science never gets to know that-- science just predicts what happens at A, and if it gets the predictions right, in a statistical sense, it is perfectly happy. That's all they do at CERN, after all.

Yes, and it all boils down to, it assumes science is something other than what it is. And we are lucky science isn't that, or we simply couldn't do it, and none of those Nobel prizes could have been earned (because they happened at A with no knowledge of B).

And I appreciate that, in the interests of "equal time". But I'm still right, because all I'm doing is look at what science is, and keep track of what scientists are actually doing when they build a theory like quantum mechanics. Bohr did that too-- and was largely misunderstood, in my estimation. I guess Bohr was ATM now?

I do agree that it does indeed point out that ramification of quantum mechanics, but my point is, we already know that, yet people still seem to get all bothered by it. We know it when we say that a whole star, a white dwarf, behaves as if its electrons were not individual particles but instead had to respect the fact that they were described by a huge joint wave function that treats them all as indistinguishable, even over a whole star! We know that when we find there is an "exchange energy" in atoms, which means that the energy of the atom comes not just from its electrons, or charge interactions, but also from interactions involving the indistinguishability of electrons and the need to use a joint wave function. We know it when a neutral hydrogen interacts with a proton and then separates in space, and we can't say which proton the electron is bound to so have to leave it in a pure state of both that could tunnel back and forth as needed, all without violating relativity. No, there's no local realism in quantum mechanics, but that's by now anobvious a ramification of quantum mechanics, we don't even need Bell to tell us that (but we can still appreciate the heads up). Yes Einstein had a problem with it, but he was welcome to try and use the scientific method to come up with a different theory that didn't have that "problem". We still have quantum mechanics, just as we still have classical mechanics, because science is not philosophy. So you cannot say both that I am ATM here, and that I am not saying anything that puts anyone in a "tizzy".

Well, I'm glad we can agree that it is not a big issue, that is a large part of what I've been saying (it's only impact is philosophical, but scientifically it is moot for anyone who expects quantum mechanics to work. That's been the core of my argument all along). Unfortunately, a lot of people do view it as a big issue, and worry about how a "real" wave function can violate local realism and still be consistent with relativity and subluminal influence propagation. But none of that is a problem if one just sticks with what a wavefunction is actually used to do in science (organize results and make predictions), and where it "lives" (in our heads). Neither of those statements are my own opinions-- they are facts about wave functions. Opinion and philosophy only appear if someone wants them to be more than that, at which point my opinion is they are making them less, while turning back the clock of science a thousand years.

Depends on what you mean by "influence". Is there any action that we can take when making the measurement at B that will predictably alter the result we get when we make a measurement at A? No, there is not. Does the outcome of the measurement at A nevertheless depend to some extent on the choice of measurement we perform at B? According to Bell's theorem, yes, it does.

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Conserve energy. Commute with the Hamiltonian.

This is like saying it's no big deal that space and time are not absolute, because we already know that. But a century or so ago, we didn't know that, and we assumed just the opposite. Sure, we know it now, but that's only because Einstein showed us it had to be that way. Up until Bell's work, it might have been reasonable to assume that any nonlocality in quantum theory was just an artifact of the system. One might have assumed that there was some other way of describing the world that was purely local. After Bell's work, we discover that isn't the case. The nonlocality is not just a quirk of quantum theory or some artifact of bookkeeping. It's an essential feature that has to be present in any theory that is consistent with the observations. It might show up in different ways depending on the theory, but it's always going to be there. And maybe everyone knows it now, but it was Bell who showed us that it was true.

I didn't say that you aren't saying anything that puts anyone into a "tizzy". I said that you were correct when you stated that Bell's theorem does not put quantum mechanics into a tizzy. Instead, it shows that what might have been thought of as a mere artifact of the math, that perhaps could be avoided in some more robust theory, is instead a crucial feature in any model of the universe. That doesn't cause any problems with quantum theory, but it was a surprise to some pretty bright people at the time.

Again, Bell's theorem makes no reference to wavefunctions, whether they have any realitry in and of themselves, or anything else of that nature. Bell's theorem is strictly limited to looking at the outcome of experiments. Those can be thought experiments, where one uses quantum mechanics and wavefunctions to determine what the outcomes should be, but they can also simply be real experiments, looking at what the actual outcomes are. Even in the case of thought experiments, Bell's theorem does not look at how the expected outcomes are determined, only what they are. You're misunderstanding it if you think it has to do with whether we ascribe reality to wavefunctions.

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Conserve energy. Commute with the Hamiltonian.

I don't believe I've ever claimed that there's a need to ascribe any reality to the wavefunction. Indeed, I've pointed out several times before that Bell's theorem does not depend in any way on the wavefunction itself, or in fact any detail of how quantum theory makes predictions.

Perhaps. But from what I can see, most of the physics community doesn't seem to think so. For myself, I was pleased to see here that you acknowledged that your view was nonstandard.

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Conserve energy. Commute with the Hamiltonian.

Again, the key correction here is that the correlation of outcomes between A and B depends on what you do at B. That makes much more sense, and is all that Bell's theorem really tells you. This is also why all experiments to verify Bell (or really, to verify quantum mechanical predictions involving correlations) are expressed in the language of coincidence detections. There is still no way that anyone at A can make any inferences about the choices made at B, the issue only shows up when you look at correlated measurements, which requires (subluminal) communication between A and B to even notice.

What you are actually doing here is making the philosophical leap that something that affects the correlation between A and B is also an "effect on A", but that cannot be logically argued without assuming local realism. We've already agreed that we know local realism doesn't apply to quantum mechanics without adding unnecessary bells and whistles that modern scientists rarely worry about (no big deal, were the words used), so it is inconsistent to reintroduce local realism when interpreting an effect on a correlation between A and B as an effect on a measurement at A alone.

See what I mean!?!

No, it is not like saying that at all. You see, the debates on Bell's theorem that continue to rage (we are having one now) are not about the historical significance of it, nor do they require we subtract any of our current knowledge, nor are they even about what the theorem says (anyone can look that up easily enough). They are in the here and now, about what this is telling us about science in general and quantum mechanics in particular, and what should be the role of philosophies about reality versus simply following the methodology of science. Bell's results are, above all, just another example of the reliability of quantum mechanics, when interpreted as an algorithm for making correct predictions, organizing existing data, and guiding future experiments. That is the science of quantum mechanics, nothing else.

Unfortunately, much debate continues outside science, that wants to be counted as science, that claims Bell's theorem shows that "there is a physical influence on A that is instantaneous, in contradiction to the expectations of relativity". That's the buzz here, that's what I am trying to put the lie to. If someone was only saying "possessing additional information alters the predictions you make", my reaction would be "no kidding". Indeed, this is exactly why I say quantum mechanics is a bookkeeping theory about how to keep track of information, not a theory surrounding the "reality of the wavefunction". That's all philosophical baggage, as is most of what is said about Bell's theorem and "instantaneous physically real influences" (the latter being the center of our debate, as you'll recall).

So you think these are all historical issues, about the sociology of the impact of Bell? That's why the topic appears constantly in science forums? No, people agonize over the ramifications of these nonexistent instantaneous influences. I'm just trying to get them out of their misery by accepting that the wave function lives in the head of a physicist making a prediction, just as Bohr tried to put Einstein out of his misery on the same topic.It's an artifact of the bookkeeping of correlation predictions, yes. All of science is an artifact of the bookkeeping, otherwise we'd have to argue that we know why a particular bookkeeping is useful and instructional and another isn't. Can we claim to know why the axioms we choose actually work, why the ones that lead to conservation of energy and the principle of least action are kept while others that require an ether are dropped? We define what is real by the artifacts that are useful, so we cannot pretend that reality has some other scientific meaning. We simply lose track of how we got here, and the shortcut looks like a philosophy of what is real that serves as a placeholder for all the artifacts that have proven successful. The mistaking of familiarity for understanding.

Put differently, we can do science, write papers, and win a Nobel prize, and never think we are doing anything but finding a clever way to keep the books, a way that has predictive and organizational power and lends insight into the next experiment that is needed to make progress. Where in the research is the place where we pledge allegiance to the reality of the wave function, for example? (You say the issue isn't about the reality of the wavefunction, but when you claim that changes in the wavefunction are "real influences", the contrary of which is what you claim is my "ATM stance", it sure sounds like that's the issue after all.)

And Chandrasekhar, and anyone doing research on molecules, etc. All Bell did was put it in the context where it most confronted people's classical prejudices. So that's a fine thing to do, more power to him, but I'm talking about the way those experiments still cause a buzz (like delayed choice quantum erasure). It is as though we keep expecting our philosophy to trump our science, and are surprised when it doesn't. All those experimental outcomes are exactly why we need to remember what the process of science actually involves, and stop imposing philosophical biases onto it, which merely creates non-issues and sets about agonizing over them.

Exactly what do you think I'm saying that lacks scientific evidence to back it up? I'm curious.

Again everything you say is prefaced with "at the time". I was never under the impression we were having a historical discussion here. If that's all you're saying, I can heartily agree. But that's not what brought you over here, is it?
I agree that Bell's theorem tells you that if you look at certain correlations, you cannot correctly predict those correlations if you hamstring your theory to obey certain philosophical principles. If that was the only issue involved here, again we are in complete agreement, but why do you think this would still be such a topic everywhere you find people interested in the interpretation of quantum mechanics? The actual reason that this is of interest is that we know the wave function approach is successful at predicting the results Bell's theorem uses. So yes, it's all about the meaning of the wave function, today, for us.

So much has been said that others probably can't or don't want to follow, so I will summarize the basic issues as I see them. Here are the basic claims on the table:

1) What both Grey and I agree on: Bell's theorem, derived from quantum mechanics and experimentally verified, says that you can detect correlations that depend on choices made for measurements on particles that are not causally connected at the time the choices were made. This puts the lie to the philosophical principle of "local realism", which would require not only that you could put a box around a particle and say that nothing causally disconnected from that box can alter or affect a measurement taken in that box, but it also asserts that this will continue to be true if you look at correlations between measurements taken in that box and measurements taken outside that causal domain. In effect, this means that reality breaks up into little disconnected "bits" of "what is true for that bit", regardless of anything that is true for other bits. The violation of that principle was predicted by quantum mechanics, disliked by Einstein, and demonstrated in various ways in the laboratory a long time ago (but people still keep trying).

2) What Grey claims that I disagree with: the fact (which we agree on) that when a measurement is made, the wave function of an entangled particle changes effectively instantaneously, implies that there must have been an instantaneous and physically real influence on the entangled particle stemming from the acausally connected measurement on the first particle. Or as he put it above, "whatever underlying mechanism determines the result at A must take into account information about the choice of measurement at B." I say that imagining such an "underlying mechanism" and equipping it with the property that correlations between A and B require affects on A is the source of the problem, and has nothing at all to do with Bell's theorem as he himself has described it. I say that if you are going to predict correlations, it is not at all surprising that you may need to include the choices of measurements on both objects, and to expect otherwise is to tack on philosophical baggage to quantum mechanics.

3) What I say that Grey (apparently) disagrees with: science is a process of finding a useful bookkeeping for organizing and predicting data, thereby "unifying the familiarities" of past experiments and guiding the creation of new ones. If that simple statement is applied to quantum mechanics, then the "wave function" is one such bookkeeping tool. Instantaneous changes in the wave function are thus instantaneous changes in our choices of how to quantitatively constrain our predictions for the system, i.e., are informed changes in our bookkeeping. There is therefore no problem with relativity or causality, and no "physical influences on the other particle", when we alter our information and resulting predictions about the system. I find it very important to recognize that two different researchers could disagree on "what is the wavefunction" of a particle, and can both do successful Nobel-prizewinning research using the wavefunction that is appropriate to the information they have. I also find it important that the so-called "influence" that the choice of measurement on B has on A in no way alters any predictions on A other than those that directly involve correlations with measurements on B. If Grey agrees with all this, I wonder why he felt the need to step in here, because this is precisely all that I am saying, along with an admonishment for the confusion that results when one mixes philosophy with science and looks for a need to label things as "physical influences" simply because they alter our predictions, even when they are not even unique among people making successful predictions on subsets of the same system.

I think I have been missing the importance of the predictive element inherent in the joint wave function when thinking about this entanglement question. On the basis that the joint wave function of the pair of particles is able to mathematically yield the joint probability of observing a given pair of results for A and B, for any pair of orientations that one may choose, then before we even look at the detector, the formalism ( I assume) has given us the prediction that when we come to tabulate the results, we will see a correlation between A and B. We don't have any choice of what the probabilities will give us as a specific outcome at either detector - we have to take what we get, but the correlation is going to be there anyway - it is contained within the wave function calculations. It doesn't depend on us knowing the exact outcome at the detector, that particular outcome will just confirm for us on paper (along with the results from B) the correlations between A and B. Tabulating the exact outcomes is the only way for our thinking process to check up on nature, but - importantly - it isn't nature in action. Nature in action (at our level) exists within the wave function predictions.

Am I missing something here? - this just seems a little too simple and straightforward, but it just suddenly seems to make real sense to me.

Right-- in characteristically quantum mechanical fashion, if we set up an experiment to look for a correlation, we'll find it, and if we set up an experiment that is not interested in the correlation, we won't encounter it in any way. The way I would say that is that the correlation is "built in" to the system, but how that manifests itself depends on the experiment, and in no case is there a need to imagine a nonlocal "influence" between the parts of the experiment. This is fortunate, because we don't necessarily want to have to "erase" the history of every particle we do experiments on (like cosmic microwave photons, most notably).
Right, quantum mechanics works.That's more or less how I think of it, yes. I think of scientific experiments as taking "projections" of nature onto "image spaces" of our choosing, determined by the experiment we set up or the observation we do. If you choose a different image space, you get a different glimpse of the nature, and you might be tempted to apply certain thinking about "underlying mechanisms" that explain the projection. But we're not seeing the underlying mechanism, we're just seeing the part we chose to look at. So when Grey says that the choice we make at B affects the correlation we find with A, I just say, "yes, that's the image space we chose, so that's where the 'influence' is."
If something makes sense, and seems simple, I'd say the burden falls on the other side of the argument to establish that something has been "missed".