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There did not seem to be a simple description of what the EPR paper actually said, so I have added it. I used Kumar's book. Myrvin ( talk) 21:39, 9 March 2011 (UTC)

I find the style of this article to be irritating. It is chatty and unencyclopedic. There shouldn't be headings like "Here is the crux of the matter", or " Here is the paradox summed up." It reads like a kiddy's book. Also, most of it is completely uncited. Where does it all come from? It reads like an undergraduate paper by someone who hasn't quite learned how to write one. Myrvin ( talk) 21:45, 9 March 2011 (UTC)

Intriguingly, the whole of the article seems to appear in this book: Quantum Computers by Jon Schiller PhD. It says "This is a report of the latest research found by searching the internet." It has an ISBN, and is available on Amazon. It also says "No part of this book can be reproduced in any form." Myrvin ( talk) 10:05, 10 March 2011 (UTC)

This looks to be a pretty clear case of reverse copyright infringement. Using the example of "Here is the crux of the matter" - it was introduced in this series of edits in January 2009 which is ambiguous, since the book was also published in 2009. When I look at that diff however, I notice that the paragraph at the bottom, "Incidentally, although we have used spin as an example" wasn't changed so I looked for its origin in the article and that particular phrase was introduced to the article back in 2004. Looking at that paragraph in the book I also noticed that there are two phrases underlined ( momentum and photon polarization) which just happen to be the two wikilinked phrases in the paragraph, so they didn't even bother reformatting that part. VernoWhitney ( talk) 21:01, 10 March 2011 (UTC)

You've done this before haven't you? What happens now? Myrvin ( talk) 21:16, 10 March 2011 (UTC)

I spend the vast majority of my time looking at copyvio issues, so yeah, I've done this once or twice. ^_^ I added the {{ reversecopyvio}} tag to the top of this page which when combined with my short explanation here should prevent it from being suspected of being copyvio again (from that source at least). I also marked it at resolved at the listing you placed at Wikipedia:Copyright problems/2011 March 10 and now that I noticed it will note that at WT:CP as well. That's pretty much all there is to it unless you have any other concerns. VernoWhitney ( talk) 22:24, 10 March 2011 (UTC)

The article currently says:

However, it is possible to measure the exact position of particle A and the exact momentum of particle B. By calculation, therefore, with the exact position of particle A known, the exact position of particle B can be known.

That conclusion was not stated in the EPR paper. It says that by knowing something about A one can know something about B, so B must have always had this characteristic. (The characteristic was "real.") In one experiment with A one could learn, e.g., the momentum of B, so the momentum of B is real. In another experiment with A one could learn, e.g., the position of B, so the position of B is real. So both the position and the momentum of B have to be real.

Where is the evidence for the interpretation presented in the article? The footnote quotes a book. Does the book explain why the experiment it describes is different from the experiment given in the EPR paper? P0M ( talk) 16:32, 4 June 2011 (UTC)

Kumar is a "science writer," so the citation is not very good evidence. The paragraph must be rewritten. P0M ( talk) 06:51, 6 December 2011 (UTC)

Hello PoM. I think it was me who used Kumar. The book says he has degrees in Physics and Philosophy. I put that quote in ages ago, and it seemed OK at the time - nobody objected. We are surely dependant upon writers (even science writers) for our secondary sources. The primary sources (EPR included) can be fairly opaque. The text seems clear that this is Kumar's view. It could be modified with some other secondary source. I'll look further. Myrvin ( talk) 08:03, 6 December 2011 (UTC)

Myrvin, hi,

The real problem, and it's not really Kumar's fault -- he just followed somebody else, is that Einstein did not go on to suggest that if you got one measurement on particle A you could get the complementary measurement on particle A'. Somebody else expressed that idea, and as I remember it appeared in print more than once and within a few years of the EPR paper. But the thought experiment assumes locality, i.e., it assumes that nothing changes with A' when you measure A, so if you measure position of A then you can get an uninfluenced measure of momentum of A'. But if A and A' share a wavefunction, then when A is measured the wavefunction that both share collapses. So at any time thereafter that A' is measured you would, according to QM, get a different result than you would have gotten had you measured A' before measuring A. Even Schrödinger was uncomfortable with that idea and contended, for a while at least, that after some time had passed the entanglement would just vaporize somehow of its own accord. I never tracked down who developed the "measure A and then measure A'" strategy. P0M ( talk) 08:40, 6 December 2011 (UTC)

That's confused me. Nobody said that the A' particle is actually measured, It's position (say) is calculated - deduced - by measuring the position of A after the interaction. Heisenberg seemed to be saying that it was impossible to know both position and momentum of the same particle. EPR (according to the commentators) said that (by measuring momentum in A and position in A') you could work out the momentum of A' and position of A without measuring them. Am I missing something? Myrvin ( talk) 09:36, 6 December 2011 (UTC)

PS Schrodinger in 1935 wrote of the derivation of both values "one by direct observation, the other by inference from an observation on the other system". Myrvin ( talk) 10:07, 6 December 2011 (UTC)

No, you are not missing anything. The question is whether Heisenberg et al. were right, or whether EPR were right. I think the thought experiment EPR originally proposed spoke of two masses that had been in contact on at least three different points (so they couldn't hinge and twist). Once they had been stuck together they had to be going in the same direction and their masses were not going to change. Then the experimenter was supposed to cause them to diverge. How that was to be done evidently was one of those things "left as an exercise for the student," or else I missed a footnote or something somewhere. To make things easy on myself I imagine two identical masses, maybe two .22 caliber lead slugs with slightly concave tail ends and they are positioned tail end to tail end. Between them there is a tiny charge that, when exploded, will produce a hot gas that fills the space formed by their concavities and pushes them apart with equal force. We now put a tiny ring barrier or something of that sort that is just big enough for one bullet to go through by squeezing it open slightly. Squeezing it trips a clock, so by that means we know where particle A is at x, y, z, t. We can't measure the momentum successfully because we have just slowed the particle down by making it squeeze the ring barrier. Never mind, we say, we can now know where the other slug is, so we put an impact meter in front of it and see how hard it hits that meter, thus giving us its momentum. Never mind if we do so a moment or two later than we measured the first slug's position. Since we knew when the little explosion went of, and where the slugs started out, we can measure the position of one of them at some later time and know its position. We reason that the other slug has to be at the "same" position in space-time in the opposite direction. So we know the position of A' by calculation. As I recall, all that the EPR paper said was that the momentum of the second particle had to be a reality, i.e., not a quantum mish-mash. It was inconceivable, according to them, that the second particle, quantum-cat-like, could not be doing something real. So it had to have a definitive momentum. Then other people, maybe Schrödinger first as you suggest, said that in that case one could simply measure the momentum of particle A' and by that means you could calculate the momentum of particle A.

What the article says gives the EPR/Schrödinger analysis as a fact about the universe. However, it is an argument based on feelings and beliefs about what the universe must be like. For a long time people had to say that EPR might be right and that Heisenberg et al. might be right. How would we ever know? Then Bell came along. The thing about the quantum theoretical understanding of the thought experiment that throws people, EPR being the first to take objection to it, is the assertion that when the experimenters disturb the momentum of particle A by measuring its position, they simultaneously disturb the momentum of particle A' and so it does not matter what momentum particle A' may be measured to have because it is going to be off by some multiple ≥+1 of h-bar/2. How can it be, EPR complain, that measuring A does something to the velocity of A'? They are not connected. Even though quantum mechanics does not assign a real position and a real momentum to either A or A' before measurement (the numbers just will not come out of the equations), there has to have been something about both A and A' that isn't covered in the quantum theoretical treatment that says what their real positions and momentums have to be. Why? Because it is inconceivable that something real would not have a real position and a real momentum, that's why. So there. But Bell came along and said, essentially, "That's what you think." P0M ( talk) 17:02, 6 December 2011 (UTC)

I fixed the section, but not perfectly. First, the section does not mention the fundamental premise held by Einstein et al., i.e., that positions and momentums are real no matter whether QM describes them that way or not. If QM doesn't account for their reality then QM is deficient. Second, I want to go back to the EPR paper and use it for citations rather than depending on Kumar. In a way, the EPR paper is better evidence because it is more wishy-washy. It is clear from the paper that Einstein, et al., are having trouble coming up with a defensible basis for their assertions. They want to say, "It just must be that way," but to do so would not be very "scientific." Pretty soon we are back to an argument about what is is. P0M ( talk) 17:22, 6 December 2011 (UTC)

I'm not sure I understand all you have to say, but I am happy with your change at the moment. I may need to study it again. Myrvin ( talk) 14:47, 7 December 2011 (UTC)

Hmm Intriguingly, if the measurements are not made at the same time, it produces an oddity. If A's position is measured first, then its momentum is screwed. You can (say EPR) deduce B's position at that time, but B continues to move. Then, when B's momentum is measured, we are supposed to be able to deduce A's momentum. But - at this time - A's momentum has been disturbed by the position measurement. All you can work out is what A's momentum would have been if it had not been measured. Perhaps they have to be measured at the same time. Myrvin ( talk) 14:57, 7 December 2011 (UTC)

It would be enough for EPR if they could say that at some time either particle A or particle B had both a determinate position and a determinate momentum. They appear to be resigned to the idea that after you measure the position of one of them then at any later time its momentum will have changed from whatever it was originally. So we lose certainty about the momentum of A after t=1, and we lose certainty about the position of B after t=1 (or maybe a moment later at t=2). But that's o.k. EPR just want to be able to say that both particle A and particle B did, at some time before the experimenters went at it, have determinate positions and determinate momentums. They appear to be resigned to the idea that it takes extraordinary steps to find out what they are (or were).

All that EPR were interested in was affirming that position was a reality (they said it was a reality because it was a something that could be accurately predicted and then found), and that momentum was a reality, and that both of these realities existed for one of the entangled particles. Then their argument was that since one particle had a real position and also a real momentum the quantum mechanics treatment of this state of affairs was inadequate since it could not account for the two real things, the two "features of reality.:

If you wait around for Bell and then get assured that quantum mechanics is right and EPR were wrong, then it doesn't matter whether the two particles are measured at the same time or not. The deal is that when particle A is measured for position, you immediately know what the position of particle B is too. That's because they shared the same quantum state and because that quantum state has now been replaced. When particle A is measured for position, its momentum is now known to have been changed by some multiple of h-bar/2. But the same thing applies to the momentum of particle B. So if EPR hurry over to particle B and measure its momentum as it heads out from where its position was just identified a nanosecond earlier, they will find that its momentum is correlated with that of particle A. It will also be fuzzy to the same degree. So the idea, given by Schrödinger or whoever it was, that you could get the position of B by measuring the position of A, and then get the momentum of A, i.e., the momentum it had before its position was measured, by measuring the momentum of B, turns out to be a pipe dream. The whole idea from EPR was that doing something here had no possible effect on something there, and vice-versa. So you could measure position here without affecting anything there, and you could measure momentum there without affecting anything here.

Suppose you tell somebody: Here's the deal. I have one coin balanced on edge here on earth. I have its mate balanced on edge on the planet Vulcan. If I pick up this cup causing the coin to lose its balance, it will turn up heads or tails, right? But if I do that and it turns up heads, then when the guy on Vulcan lifts his cup his coin must turn out being tails. Now here is the kicker. I don't know whether or not the guy on Vulcan will keep his word and wait until after I have lifted my cup. Maybe he has already done so. In that case what he found out on Vulcan will be make it for certain that when I lift my cup my coin will land the opposite to the way his did.

I think that most people would naturally want to know how something that happened on Vulcan could possibly reach out and fix the toss of the coin. And I think that the same kind of subjective certainty that there could be no spooky action at a distance was what made Einstein so reluctant to accept the probability aspect of quantum mechanics. P0M ( talk) 21:17, 7 December 2011 (UTC)

Check out the new stuff below. I think I have "digested" the EPR paper correctly. If so, maybe that will help. P0M ( talk) 21:28, 7 December 2011 (UTC)

It seems to me that the following paragraph in the section with the above title must be either removed or entirely rephrased:

"The EPR paradox has deepened our understanding of quantum mechanics by exposing the fundamentally non-classical characteristics of the measurement process. Prior to the publication of the EPR paper, a measurement was often visualized as a physical disturbance inflicted directly upon the measured system. For instance, when measuring the position of an electron, one imagines shining a light on it, thus disturbing the electron and producing the quantum mechanical uncertainties in its position. Such explanations, which are still encountered in popular expositions of quantum mechanics, are debunked by the EPR paradox, which shows that a "measurement" can be performed on a particle without disturbing it directly, by performing a measurement on a distant entangled particle."

Two simple facts are being neglected here:

(1) According to standard (Copenhagen) quantum mechanics, a measurement does consist in "a physical disturbance inflicted upon the measured system"; it's always the result of an interaction between system and apparatus, as Bohr himself stated uncountable times, and continued to do so until the end of his life.

(2) Even if by measuring the first particle's momentum we can indirectly ascertain the momentum of the second particle, this information is completely destroyed as soon as we perform a position measurement on the second particle - precisely because it is an uncontrolable "physical disturbance inflicted upon the measured system". In no way can the subsequent trajectory of the second particle (or the first, for that matter) be predicted. Old Palimpsest ( talk) 00:03, 17 June 2011 (UTC)

You're right. The paragraph errs by using the words "shows that." It should have said that EPR assumed that, hoped that, couldn't believe other than that...

In order to have their way make sense, and still accept the idea of the two particles having a shared quantum state, Einstein et al. had to rely on the idea of the two particles having always had determinate states, somehow, despite having a single shared quantum state. Hence the idea of hidden variables, i.e., hidden characteristics that would somehow come to the rescue and determine how the shared quantum state would collapse in a determinate way. Saying it the way I just did makes the whole idea seem a little silly, and I suspect that is the reason that the paper took such a roundabout way of implying that quantum mechanics was inadequate. It was "correct" as far as it went, but it was lacking in that it did not make mention of the hidden variables that just had to be there because otherwise physics would be describing an "unreal" situation.

This editing situation may be tricky if some recognized authority didn't do the explicit reasoning so that it can be cited. Lacking a clear explication, we would have to say something like this: "EPR said such-and-so. Bohr et al. said such-and-so. Nobody even imagined that there could be a physics experiment to discover which theoreticians were correct until Bell came around. There are still some diehards, but currently Bell seems to be accepted. P0M ( talk) 08:57, 6 December 2011 (UTC)

Looking back at the lead paragraphs, I think that it is wrong and probably the article got off on the wrong foot from there.

Then the position or momentum of one of the systems is measured, and due to the known relationship between the (measured) value of the first particle and the value of the second particle, the observer is aware of that value in the second particle. A measurement of the other value is then made on the second particle, and, once again, due to the relationship between the two particles, that value is then known in the first particle.

If my memory serves me well, that argument is not present in the EPR paper itself. P0M ( talk) 17:46, 6 December 2011 (UTC)

Based on PhysRev.47.777.pdf

MAY 15, 1935 PHYSICAL REVIEW VOLUME 47 Can Quantum-Mechanical Description of Physical Reality Be Considered Complete' ? A. EINSTEIN, B. PODOLSKY AND N. ROSEN, Institute for Advanced Study, Princeton, New Jersey (Received March 25, 1935)

Here is my summary:

Experimenters start with two systems whose states they know, bring them together, and at that point what used to be two systems becomes one system and it has a single state. Experimenters then separate the two systems. However, at that point the two systems share the original single state. To determine anything that is specific to one or the other of the now physically isolated systems, new measurements must be made. The question EPR pose is whether the experimenters can do experiments that will not lead to indeterminate or probabilistic values for at least one of the two systems. If they can do so, then there will exist a situation in which one system has, e.g., both a determinate position and also a determinate momentum. Since quantum mechanics cannot predict the values of both pairs such as P and Q, quantum mechanics cannot account for a system that has both a determinate momentum and also a determinate position. EPR maintain that since this determinately known pair of values actually must exist, then quantum mechanics must be incomplete. There must be something else left to be learned that would tell experimenters ahead of time what the determinate position and determinate momentum would be found by experiment to be.

When, after the pairing is broken up, experimenters measure the position of the first system they will disturb its momentum. However, they will by that operation be able to calculate the position of the second system, and a mere calculation will not disturb the momentum of the second system.* It will then be clear that the position of the second system is a feature of reality, and therefore something that ought to be subject to calculation by a complete theory. If, however, the experimenters measure the momentum of the first system and disturb its position, they will by that operation be able to calculate the momentum of the second system, and nothing they have done will exert any force on the second system.* It will then be clear that the momentum of the second system must also be a feature of reality, and therefore it ought to be possible to predict it using a complete theory.

Thus, by measuring either A or B we are in a position to predict with certainty, and without in any way disturbing the second system, either the value of the quantity P (that is p_k) or the value of the quantity Q (that is q_r. In accordance with our criterion of reality, in the first case we must consider the quantity P as being an element of reality, in the second case the quantity Q is an element of reality. But, as we have seen, both wave functions Ψ_k and φ_r belong to the same reality.

-- from the EPR paper

*These two places are where EPR make assumptions about what reality must be like. Quantum theoreticians would argue that despite their not being local to each other, measurement of the position of one system will affect the momentums of both systems, and measuring the momentum of one system will affect the positions of both systems. Bell discovered a way of experimentally determining which opinion on the matter is correct.

I think that what it boils down to is the conviction on the part of EPR that a real thing cannot fail to have a real position or fail to have a real momentum. P0M ( talk) 02:40, 7 December 2011 (UTC)

I started reading the discussion prior to the questions raised by Myrven above, and discovered that some time ago another editor also outlined the content and conclusions of the EPR paper. Search for "Preface to thought experiment" above. I think that we have said essentially the same thing.

I think that an article on the EPR paper should explain what it actually said, and go beyond that only to describe challenges to it, the Bell results being included in that. (A link should be sufficient.) The idea that one measures system I to learn the momentum of system II, and measures system II to learn the position of system I, and therefor escapes the indeterminacy that would result in measuring both position and momentum on the same system, is something that goes beyond EPR. Why would we need to include it? If we need to do it, it has to be separated from what EPR said because, at least as I see it (see above), it makes the logical flaw of using one's desired conclusion to prove one's case. P0M ( talk) 19:20, 8 December 2011 (UTC)

I haven't started to plan changes to the article, but there seem to me to be clear indications that it is misleading in some respects. If there are no corrections needed for what I have said above (and as long as I stick to what EPR said and leave any of my side thoughts out), will it not be o.k. to fix the things recently pointed out as wrong? If I don't see any objections I will start changing things. P0M ( talk) 19:30, 8 December 2011 (UTC)

I have just written the following from memory. I think it is too long for a lead. I want to look at it as an indication of what, in general, the article needs to say. (Details can follow.) I present it here in draft form. Please indicate any inaccuracies or places that are likely to mislead the general reader:

The EPR paradox was the answer of Albert Einstein and his associates Podolsky and Rosen to the probabilistic equations developed in quantum mechanics. To expose what they thought were fundamental shortcomings in quantum mechanics, they examined the logical consequences of a situation in which two particles are coupled together to form a single system, and then are physically decoupled. Imagine two atom-sized railway cars coasting together, linking, rolling together for some time, and then being unhooked and pushed apart by some force exerted between them. On this quantum mechanical scale of things, the consequences of the separation for the characteristics of the newly individuated particles are not what one would experience from everyday experience.

According to the equations of quantum mechanics, if two systems (the "railroad cars") each have a known description and the systems become united, then the new single system has a quantum theoretical description that can be calculated from the values of the original components. Since classical physics describes things like the addition of momenta in the case of life size railway cars, the analogous feature of quantum mechanics is not unexpected. However, according to quantum mechanics, when the atomic scale system described above is decoupled, the two resulting parts do not have individual quantum theoretical descriptions. They do not have separate states. Instead, they share a single state. At that point, to discover anything about their individual characteristics (e.g., position, momentum, etc.) it is necessary to perform new measurements.

When the position of one particle, EPR called it "System I," is measured, it becomes impossible to make a deterministic prediction of its momentum, and experimenters get only a range of probable momenta. However, since each particle shared the same wave function, once the position of one particle has been measured the position of the other particle is also known. EPR argued that if the second particle indeed had that position but not at the cost of making a physical intervention with it, a measurement, then the momentum of the second particle would not be changed. Furthermore, if the second particle did indeed have a position, then its momentum would not have been influenced by the determination of that position. On the other hand, if the momentum of the first particle had been measured instead, then the position of the second would be known without its momentum having been influenced by the act of measurement.

EPR went on to argue that since the arguments they had taken from quantum mechanics showed that the second particle had a real position, and because it showed that the second particle had a real momentum, there were two features of reality to be accounted for, and yet quantum mechanics provided one of them but not the other. If quantum mechanics, working from the single wave function of the combined unit and later shared by the two newly detached particles, could provide, after a measurement, only the position and a range of probabilities for the momentum, or else only the momentum and a range of probabilities for the position, and yet there had to be real values for both of them, then quantum mechanics was incomplete.

The key difference between EPR and those in the school of Niels Bohr was that Einstein and his colleagues argued that since the second particle was physically remote from the particle upon which measurements were performed, any measurement that was performed on the first particle and that would make indeterminate the measurement that could be expected of a second characteristic of the first particle would not influence the second particle. The Copenhagen group eventually held that when the first particle was measured and its wave function collapsed, when position became determinate and momentum became indeterminate, the same things could be said of the second particle, i.e., that not only did its position become determinate but its momentum simultaneously became indeterminate.

Any comments? This way is quite distinct from the present text in terms of real content. P0M ( talk) 21:19, 8 December 2011 (UTC)

Draft new lead:

The EPR paradox is an early and influential critique leveled against quantum mechanics. Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen (known collectively as EPR) designed a thought experiment intended to reveal what they believed to be inadequacies of quantum mechanics. To that end they pointed to a consequence of quantum mechanics that its supporters had not noticed. According to quantum mechanics, a single system has its own wave function, its own unitary quantum-theoretical description. If such a single system can be transformed into two individual systems, doing so does not create two wave functions. Instead, theory indicates that each system shares the single wave function. The question then becomes, "What happens to this wave function when one and/or the other of the pair of individual systems is measured?" Working through the equations, the EPR paper shows that measuring one feature of a system, e.g., the momentum of one of the pair of particles, will reveal the same feature of the other particle. Measuring one characteristic of the first system will, according to quantum mechanics, make any related characteristic, in this case position, indeterminate. The EPR experiment suggested the possibility that not only would the momentum of the second be made known without the need of further experimental measurement, but also that the position of the second particle would be predicted in an indeterminate form according to the rules of the Heisenberg Uncertainty Principle. EPR insisted, however, that since the two systems were physically separated action on one particle could not affect the other particle, and it was therefore impossible that any indeterminacy could be induced in the system that was not directly measured. They then concluded that quantum mechanics was incomplete since it depicted a pair of systems with one determinate characteristic and one indeterminate characteristic. In reality, they concluded, one could measure the first system to get a real value for position of the second, and one could also have measured the first system to get a real value for the momentum of the second, so the second system must have both a real position and a real momentum. They would both be determinate values, not just one of them as indicated by quantum mechanics.

If quantum mechanics is not incomplete, if quantum mechanics gives all of the information that is really available in nature, then, researchers conclude, changing some characteristic of one member of such a pair (now usually called an entangled pair) will not only make determinate the same characteristic of the other member of the pair, but it will also make indeterminate the second characteristic of the other member of the pair. The switch from a condition wherein both particles share the same wave function to a condition wherein one feature of one particle is made specific and its complex conjugate is made quantum mechanically indeterminate, and the same feature of the other particle is made correspondingly determinate while its complex conjugate is made quantum mechanically indeterminate, is something that occurs as the result of measuring the first feature in one of the paired particles, and that is reflected instantaneously in the other member of the pair.

<<The next part should probably be below the lead, a section on the history of the EPR paper and its consequences>>

The article that first brought forth these matters, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" was published in 1935. ^[1] Einstein struggled to the end of his life for a theory that could better comply with his idea of causality, protesting against the view that there exists no objective physical reality other than that which is revealed through measurement interpreted in terms of quantum mechanical formalism. However, since Einstein's death, experiments analogous to the one described in the EPR paper have been carried out, starting in 1976 by French scientists Lamehi-Rachti and Mittig ^[2] at the Saclay Nuclear Research Centre. These experiments appear to show that the local realism theory is false. ^[3]

Notes

This is my draft lead. If this lead is accepted it will probably push some changes in the rest of the text of the article. P0M ( talk) 03:27, 9 December 2011 (UTC)

Is lack of comment an indication of general agreement? It would be less disruptive to the article to fix any problems beforehand rather than after the old lead has been taken down. P0M ( talk) 16:14, 9 December 2011 (UTC)

The text currently says:

In 1948 Einstein presented a less formal account of his local realist ideas.

It has a footnote, but it is only a wikilink to "local realism," and does not identify the 1948 paper. Does anyone know which paper is involved? I'm working my way through the body of the paper to try to clear up any inconsistencies with the new lead. Thanks. P0M ( talk) 19:57, 10 December 2011 (UTC)

I think I've found it. March, 1936, "Physics and Reality," pp. 371-379

Originally:vol. 221, No. 1323-27 of Journal of the Franklin Institute, 221, 313–347, with Picard trans. starting p.380

Downloaded from: www.kostic.niu.edu/Physics_and_Reality-Albert_Einstein.pdf

There is a 1948 article with a similar title. Perhaps it is a reprint of the above?

The 1936 might be "less formal," but it is more difficult to understand and involves the idea of ensembles to which later doubters of the Copenhagen group's ideas have appealed too. P0M ( talk) 02:54, 11 December 2011 (UTC)

Here there's a report of Einstein's 1948 article. You may also want to read this article by P.R.Holland [1] which refers to the 1948 article and also discusses an earlier, unpublished (withdrawn) manuscript of Einstein of 1927. -- Chris Howard ( talk) 09:30, 11 December 2011 (UTC)

Thanks. It looks like there may be no way to get to the Dialectica article on-line. I'm a little leery of taking secondary sources entirely on faith. Nevertheless I guess the 1948 article should be mentioned too. P0M ( talk) 20:08, 11 December 2011 (UTC)

If everything looks o.k. so far, I will rewrite the short section on the "EPR paper." See the notes on what is actually in the paper above. P0M ( talk) 03:15, 11 December 2011 (UTC)

I think that attempts to "explain" EPR (e.g. the Alice & Bob story) have always been inferior to what the paper itself said, and are often not equivalent to the argument in the paper. Looking at it from a different perspective, evidently the core issue (indeed the core puzzle about quantum theory) lies in there supposedly being a qualitative difference in behavior between so-called "pure" and "mixed" states (identified back in Bohr's time as "collapse of the wavefunction"). The modern quantum theory of measurement is advertised as solving this problem, i.e. it shows how processes of observation are subject to the same quantum laws as the systems being observed; in particular the information state of an observer becomes "entangled" with the state of the thing that has been observed, and EPR really ought to be recast in those terms. Unfortunately I don't have specific wording for such an edit. Meanwhile, the attempts to paraphrase the argument should be replaced by quotations from the paper itself. — DAGwyn ( talk) 11:34, 1 January 2012 (UTC)

In looking over the article I see that I will have to revise parts later on that repeat misinformation that I removed from the lead. The idea that one could measure system A for X and thereby learn X for A', and measure A' for P and thereby learn P for A is dicey at best. As far as I know, nobody has shown that E, P, or R ever offered this idea. It's there in the literature, but I think it must come from Schrödinger or somebody else. We should nail down exactly what is in the EPR article. Anything critical or exculpatory should be clearly distinguished from what the authors themselves presented as their objection to quantum mechanics. P0M ( talk) 19:27, 1 January 2012 (UTC)

Material in "Greene version" is unsourced. I have checked through The Fabric of the Cosmos and Elegant Universe and have failed to find the experiment described. This section should be removed or replaced with something that can be traced down. P0M ( talk) 05:09, 13 January 2012 (UTC)

See The Fabric of the Cosmos, p. 113, for what Greene actually says about Aspect's experiment. P0M ( talk) 06:47, 13 January 2012 (UTC)

Looking back over the history, it is clear that there was never a clear statement that Greene said anything about pion decay. On top of that, the "Greene version" does not report what Greene says. I think that the experimental challenge to EPR needs to be covered. I'm looking at The Quantum Chanllenge by Greenstein and Zajonc, which seems clearer than Greene's work. Greene appears to have oversimplified things and came out with some math that doesn't match what others use. I think it may look at a simplified situation and makes numerical conclusions based only on that scheme. P0M ( talk) 07:13, 13 January 2012 (UTC)

I just got reminded that the "EPR paper" section still contains misinformation. The idea that you could learn about A by looking at B, and then turn around and learn about B by measuring A is not in the EPR paper. P0M ( talk) 07:38, 13 January 2012 (UTC)

I have rewritten the section that incorporates the speculation reported by Kumar. If his source could be tracked down it would be better to rewrite the section to explain how the ideas of EPR, which did not have the bi-directional measurements being made, were later expanded by someone else.

Your new words seem like pure OR POM. You shouldn't make your own comments on a source unless you have another source to cite. Myrvin ( talk) 18:51, 14 January 2012 (UTC)

I commented on what was represented as Kumar's position. If that was not an accurate representation, then the problem was not with Kumar but with the representation of his position. P0M ( talk) 22:19, 14 January 2012 (UTC)

However, I think I see the problem. I don't think Kumar says that EPR want to measure BOTH momentum and position for the systems. HE says (and I think the paper does too, that you could know the position for BOTH systems OR the momentum of both. I'll try to correct the text. Myrvin ( talk) 19:35, 14 January 2012 (UTC)

This position is indeed correct. I thought you wrote earlier that Schrödinger had something about working the trick two ways. The position does seem to be out there somewhere, but it is not really central to what EPR were doing. P0M ( talk) 22:19, 14 January 2012 (UTC)

I have deleted the section on Greene. Greene's discussion does not involve pion decay, but instead is based on experiments using elemental calcium excited by laser radiation, and the sequential emission of two entangled photons as an electron falls to its equilibrium state by way of a stop at an orbital in the middle. Study of the history of this article shows how the pion idea was probably written down first, then studies of this general type were attributed to "Greene and others," and still later the "others" fell along the wayside. The discussion is wrong in any event. Reconstituting the Greene discussion would probably be a mistake as it appears that he created an analogy, a sort of imaginary set of physical phenomena that are simpler than what the real world is like, and as a result the numbers that he comes up with to illustrate the Bell Inequalities are very much different from those used in formal studies. It's a good method, but he takes pages to set his analogy up, and there is no way it can all be jammed into one paragraph. I need to trace through the materials in Quantum Challenge to see whether a summary can be given than goes light on all the details that were given in that book for university physics students. P0M ( talk) 07:49, 14 January 2012 (UTC)

I've started to go over the lead again as Myrvin suggested.

I have deleted a comment about entanglement in lead. It's confusing enough to begin with so why bring in another mind boggling element? Entanglement was not part of the original discussion. P0M ( talk) 03:54, 23 February 2012 (UTC)

Quantum mechanics is a mathematical formulation for finding solutions to the diffusion equation like Schrodinger equation using complex exponential functions. Fourier analysis exploits the completeness and orthogonality possessed by complex exponential function sets with a single variable exponent. Because the Schrodinger equation is a linear partial differential equation distinct solutions added, superposed, are also solutions.

1 Normalization and Quantum entanglement

When interpreted as a probability, the solution squared magnitude is normalized to unity. For solutions in which the component terms are orthogonal, normalization entangles the component squared sum. A two state system with equally likely states would require the state squared magnitudes be equal when conventional event probability is used. If, however, Bayesian probability is used, the normalized sets are event outcomes when other outcomes are known. This normalization choice is a problem statement element that does not depend on state spatial separation and does not, therefore, require faster than light information transfer.

2 Wave function completion

When the exponential variable depends linearly on two independent variables, the complex exponentials no longer form a complete, orthogonal set with respect to the independent variables. To recover completeness, functions depending on a linearly independent exponent must be added. For the true wave equation these variables are φ1=b(r+at) and φ2=b(r-at) where “b” and “a” are constants. In quantum mechanics only one is employed. This makes trying to find solutions analogous to trying to fasten a shoe using only one hand with its fingers crossed: slipons and Velcro fasteners may be manageable, but buckles and laces are not.( HCPotter ( talk) 09:47, 26 February 2012 (UTC))

There appears to be a disagreement between this page and the Hidden variable theory page. Here, I find the statement "it turns out that the predictions of Quantum Mechanics, which have been confirmed by experiment, cannot be explained by any hidden variable theory", citing Bell's Theorem. The other page states that experimental evidence "rules out local hidden variable theories, but does not rule out non-local ones" and that "Assuming the validity of Bell's theorem, any classical hidden-variable theory which is consistent with quantum mechanics would have to be non-local". (And it seems to say that Bohm's theory fits that category.) Am I misinterpreting something, or is one of these pages incorrect (or misleading)? YancarloRamsey ( talk) 17:16, 16 April 2012 (UTC)

"Moreover, if the two particles have their spins measured about different axes, once the electron's spin has been measured about the x-axis (and the positron's spin about the x-axis deduced), the positron's spin about the y-axis will no longer be certain, "

This sentence refers to the "y-axis" but the "y-axis" has never been introduced. It says the spin along the "y-axis" will no longer be certain but never states at what point it was ever certain. — Preceding unsigned comment added by 199.89.103.13 ( talk) 19:15, 23 February 2012 (UTC)

I'll wait for the person who added that part of the text to respond; maybe there is some way to make it even clearer. However, in physics an object's position is given in three dimensions of space, customarily called x, y, and z, and one dimension of time, customarily called t. It is actually the "will no longer be certain" part of what you quoted that is the more problematical because for people who follow the Copenhagen interpretation "there is always a certain 'fuzziness' to the results of any measurement." [Greenstein and Zajonc,Quantum Challenge, p. 105] Since you start in fuzziness, you never quite get out of it, and all predictions (such as what the spin along the y-axis will be found to be) are given as probabilities. The article is trying to say that experimentally one can measure spin around three arbitrary axes. You decide where x is by the way you orient your measurement device number one. You set up a second measurement device perpendicular to the orientation of the first one, and call that one number two and say that it measures the y axis. Finally you set up measurement device three perpendicular to the other two and call the direction it is looking at the z axis. Once you have three measuring devices all set up that way you could move it around like messing around with a basketball in your hands, twirling it this way and that, and you would have a new set of arbitrary x, y, and z directions. Actually you don't want to do that since for as long as you are measuring one particle you don't want to mess things up. The particles that enter this setup are, of course, not trying in any way to conform to your arbitrary lab set up. One particle might have its axis of spin (assuming for the sake of argument that it actually has an axis of spin before you measure it) at an equal angle to all three axes.

The actual particle has only probabilities for where its axis of rotation is, and therefore it has only probabilities for how its axis of rotation will be mapped onto a 3-d coordinate system that is arbitrarily chosen. Measuring the particle with the x axis detector will force it to show up as having some kind of spin vector along that axis. Measuring the particle with the y axis detector will force it to show up as having some kind of spin vector along that axis.

What would happen if, unlike what is maintained by the Copenhagen conspiracy, the particle is already spinning in some definite way and you happen to have a total of three other entangled particles that you could measure for x, y, and z axis spins (expending one entangled particle for each of them). "Einstein held firmly to this traditional vision of science, which sought to account for everything in terms of a complete microscopic theory." (Quantum Challenge, 106} You ought to be able to get the exact spin components that "were always there." So you ought to be able to come up with a determinate knowledge of just how the particle was spinning.

Bell predicted, and experiment showed, that nature does not work that way. P0M ( talk) 03:36, 24 February 2012 (UTC)

"This sentence refers to the "y-axis" but the "y-axis" has never been introduced" If we replace the y in the offending sentence with the already introduced z it makes sense. I call typo and vote we change it in this way. "I'll wait for the person who added that part of the text to respond;" It is now March 2013 and still no reply from the original poster. The sentence as it stands is confusing, if not misleading - it needs to be changed. I'll come back in a month or two and see if there has been any more discussion. If none then I'll change it and let the powers that be reverse it and call me a vandal if they dare. :-) Count ludwig ( talk) 14:41, 7 March 2013 (UTC)

OK, a month has passed, so I edited it. Count ludwig ( talk) 20:03, 8 April 2013 (UTC)

What has happened to the lead in the past couple of months? It has been increased and has gone through several edits that were often ungrammatical and confusing. It is now much too big and still confusing, ungrammatical and unencyclopedic in places. Myrvin ( talk) 07:29, 22 February 2012 (UTC)

The current lead is 70 char shorter than the 12 January lead. Not to say that I have convinced myself that the current lead is better than the one of that earlier date, but I see only one point upon which the current lead has any grammar problem. And at what points do you regard the reading as "unencyclopedic"? P0M ( talk) 08:29, 22 February 2012 (UTC)

Yes it is shorter, but I think it is too long and repeats too much in the rest of the article. It uses words like: "According to quantum mechanics, a single system has its own wave function, its own unitary quantum-theoretical description.", "when we keep decreasing the intensity ", "Today, we call", "Even if we 'prepare' ", "Example of such a conjugate pair are ", "The EPR paper written in 1936 has shown that this explanation is inadequate. It considered two entangled particles, let's call them A and B, and pointed out measuring a quantity of a particle A will cause the conjugated quantity of particle B to become undetermined, even if there was no contact, no classical disturbance", "quantum effect we call non-locality". Maybe this has been going on longer than I thought. It is now reading like a kiddies' primer written by someone not an English speaker. There is too much use of us and we. Myrvin ( talk) 09:38, 22 February 2012 (UTC)

By the way PoM, your change to the lead was fine. This has happened since then. Myrvin ( talk) 09:58, 22 February 2012 (UTC)

I've been having some second thoughts about the article, and especially the lead. I think it would be better to stay as close as possible to what Einstein et al. said. At first I thought that the idea of talking about spin was better than talking about position and momentum. Then I realized that it can actually be made clearer if we talk about it the way EPR set things up.

If you start from the original article, and perhaps add the detail that Einstein added in some later discussion—that by there being two masses that are "together" for some time he means that they are continuously touching at a minimum of three points for some measurable amount of time—then it is easier to see what Einstein was flummoxed about.

There is a problem, for the quantum theoretical types anyway, right at the very beginning. It's something that nobody quite talks about. It is assumed that there is a wave function that describes the two-particles-bound-together-as-one, that the physicists start with this information, and then they use Schrödinger's equation to predict probabilities of where it will be and where it will be heading toward at what speed for some future time. Actually, they can't get a "certain" set of numbers for the particle-system by physical means if QM is right. They can get closer by improving their apparatus, but the h-bar factor still rules. So what they have to do is to assume a set of values and then ask what can be expected if they guessed exactly right. There is one state associated with this guess, and when the two halves of the particle are decoupled and they drift apart they each carry the same state. The next part is crucial, for QM in one way and for EPR in another way. For QM the total uncertainty is shared for conjugate pairs. Doing something in an experiment that makes the uncertainty less for one of them means that the other one has to take up the slack, as it were. However, all that statement really means is that the probabilities associated with the second of the conjugate pairs get changed in such a way that if, e.g., originally the physicists could make a fairly good bet that the photon would leave the laser and show up at a point diametrically opposite to the laser, after something was done to zone in on the position x,y,z,t of the particle then it was no longer such a good bet that the particle would end up dead center. All of this stuff goes on in the world of probabilities Heisenberg really messed up his audience when he brought in the analogy called Heisenberg's microscope because it is a reductio ad adsurdum. It says, in effect, "Even if the electron being viewed by my microscope were going with some determinate momentum to begin with, by hitting it with a gamma wave to measure its position I will have whacked it enough to change its momentum, but nobody will know by how much or in what direction it has been changed." So Heisenberg left the world of quantum mechanics and dropped back into the classical view. For this decision, he was criticized by Bohr.

For EPR, who assume that "things really have to be going somewhere," the mystery of entanglement involves the delivery of energy across space and time going faster than c, and they can't buy that. The way they see it, the 2-in-1 particle really was going somewhere at some speed and along a real trajectory. The two particles came unlinked. Measuring the position of particle A will mess up its original momentum in an unpredictable way. Einstein might have added, "Just as Heisenberg's microscope thought experiment shows." Einstein et al. don't have any particular problem with the idea that a measurement of one thing disturbs some other characteristic of the same thing. However, if you say that when the physicists measure the position of A then they will instantaneously change the momentum of B (some light minutes away), then you are claiming that B was originally going somewhere at a definite speed, and out of the blue some energy was delivered to it that accelerated it and so changed its momentum. That kind of thing is "action at a distance" even in the sense that "action" means "amount of energy delivered over amount of time" (a = e t).

Getting involved in the lead in statements based on what later thinkers had to say about it, their alternative thought experiments to demonstrate the same paradox, etc., is not helpful to the reader. It is especially unhelpful to the reader who does not know all this other stuff that is being offered in evidence. Moreover, as I think I have just demonstrated, the basic "denial of common sense" does not need to talk about anything that is out of the ken of ordinary people. They know about momentum. They know about position. They know about predictions in the classical world. They know about probabilities. So they are in a pretty good position to understand what it means if doing something to one "horse" changes the probabilities of another "horse" running a good race. It's at least different from the odd idea that spurring one horse would make a distant horse jump.

After looking at all the changes made recently, all without prior discussion, I am beginning to wonder what use it may be to discuss things beforehand. It seems that most people totally ignore what was, after all, either right or wrong, and just change things to suit themselves. Doing things that way can lead to disorder.

P0M ( talk) 03:13, 23 February 2012 (UTC)

I just went back through the edit history. One paragraph was removed by Waleswatcher, and another paragraph was removed by Frisch, but both did so without discussion. A lot of stuff was added by Cspan64, who thought that Heisenberg's uncertainty principle "now only has historical significance," and who added lots of stuff about beam-splitters... He listed it all as a "minor edit." Again, let me say that it has taken a great deal of effort to sort out what EPR were really trying to get at, to untangle their argument from the add-ons of others, etc. It is indeed difficult to write about some of these ideas. But it does not help the process to just dump work without trying to understand the intent behind it, to dump stuff without explanation, etc. P0M ( talk) 03:48, 23 February 2012 (UTC)

I also find the lead to be confusing and too wordy. I wrote a possible new lead and "Description of the paradox" section, trying to be concise and clear. Here it is. You're welcome to directly correct it, revise it, or use it to edit the article (something I'll do in a month if I see no discussion here):

---- Lead ----

The EPR paradox is a thought experiment meant to demonstrate that quantum mechanics is incompatible with local realism. It was first described by Albert Einstein , Boris Podolsky and Nathan Rosen (known collectively as EPR) in a 1935 paper. ^[1]

The experiment involves two distant particles, A and B, whose characteristics are correlated because of a previous interaction. Heisenberg's uncertainty principle, applied to the common wave function of the two particles, implies that making a measurement on particle A, would instantly make an observable indeterminate on particle B. If the two particles are distant enough, this may imply faster-than-light communication, something forbidden by special relativity.

EPR proposed two possible explanations. One is an actual nonlocal interaction between the particles. The other is the incompleteness of the wave-function description, and the possibility of a deeper description (by so-called ' hidden parameters').

Bell's theorem provided a quantitative basis for interpreting EPR-kind experiments. It is generally understood to show that the hypothesis of hidden parameters, favoured by EPR, is not a viable solution to the paradox. ^{[2] [3] [4]} Bell test experiments have been performed since, with results that generally agree with quantum nonlocality. ^{[5] [6]}

---- Description of the paradox ----

Physical observables can be associated in pairs called complementary variables. Examples of such pairs are position and momentum, or components of spin measured around different axes. According to Heisenberg's uncertainty principle, two complementary variables of a particle cannot be both determined with arbitrary precision.

Two particles (A and B) that have interacted (or are produced by the same event), are said to form a singlet state, and their physical observables are not independent. For example, these may be two photons with opposite polarization, or two electrons with opposite spin. We say the particles are entangled.

This means that if we measure a variable (say, up-down spin) on A, we get to know the value of the same variable for B as well. After this, we can no more determine the complementary variable (say, right-left spin) of B, for this would imply exact knowledge of both complementary variables, in contrast with Heisenberg's principle. Trying to measure this second variable would instead return random values. This way, the measurement of A appears to have an instantaneous influence over the measurement of B.

Now imagine the two measurement being separated by a space-like interval. This makes for a paradox, because in special relativity, only time-like separated events can have an influence on each other. In fact, for any two space-like separated events, their chronological order could be swapped by an appropriate Lorentz transformation, thus inverting their alleged causation relation.

Formally, the state of the system is described by a two-particle wave function, which encodes (probabilistically) the outcomes of possible experiments on the two particles. When a measurement is made on particle A, the wave function is said to collapse to a definite state (say, spin-up). As the wavefunction is unique, this collapse instantaneously applies to B as well, forcing it into a definite state (say, spin-down).

Yakamashi ( talk) 02:25, 28 June 2014 (UTC)

It quotes some 'Manjit Kumar' who directly contradicts basis of quantum mechanics.

<quote>"According to Heisenberg's uncertainty principle, it is impossible to measure both the momentum and the position of particle B exactly. However, according to Kumar, it is possible to measure the exact position of particle A. By calculation, therefore, with the exact position of particle A known, the exact position of particle B can be known. Also, the exact momentum of particle A can be measured, so the exact momentum of particle B can be worked out."</quote>

It is completely outragious to insert ref of unknown author. It should be removed and whole section should be rewritten. In fact, whole article needs to be rewritten. — Preceding unsigned comment added by Ikshvaaku ( talk • contribs) 15:22, 5 August 2015 (UTC)

Manjit Kumar was inserted by User:Myrvin on 9 March 2011. As far as I understand, these Kumar's words do not add anything to the EPR paper, and probably are not intended to add, but only to popularize. Thus, on one hand, Kumar "directly contradicts basis of quantum mechanics" no less no more than EPR do; and on the other hand, there is no need to quote him in the article. For a reader that needs such a popular presentation, Kumar's book may be cited in Sect. 8.2 "Books". Boris Tsirelson ( talk) 19:41, 5 August 2015 (UTC)

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We now know that the speed of gravity, usually is close to the speed of light in the void (classical void) but in the real world occur disturbances because complex arrangements of matter, interlink particles in ways that cause "cohesion distortions". Gravity is not a fundamental force, the "graviton" is simply the superluminal "briefion" that connects briefly any particle, not necessarily only parts of the same compound particle. The graviton/briefion is nothing other than any virtual boson (can also be individual particle) of the other three fundamental forces• the gravitational field is a compound statistical mechanism of the electroweak gauge field and the strong/chromodynamic gauge field while the two interact indirectly (not as a first step of a feynogram [Feynman diagram] but as a further step, thus intermediate steps are required, and that constitutes gravity so weak, for it's only a secondary statistical effect of the interaction of the electroweak gauge field with the strong/chromodynamic gauge field inside the Higgs connection field) through the Higgs connection field. In huge accumulations of matter, statistically few entanglements occur, the actual entanglements are not enough to justify gravity, but we have to calculate the infinite virtual particles created using as a measure of time the ultimate Planck sequence. That infinity becomes renormalized due to the curvature of spacetime that doesn't allow infinite perfect alignments when relativistically observed at Planck sized microholograms (ultimate quantization of spacetime). Thus a non infinite amount of entanglements occurs. These entanglements transfer instantaneously quantum information, but the electroweak gauge field and the strong/chromodynamic gauge field continue to transfer information at luminal (thus not instantaneous) speed. All particle arrangements should constantly lose energy toward nothingness, because almost all virtual particles dissapear without being materialized (objectified). Gravity is the mechanism that maintans the overall energy (although no gravitational system is closed, and all lose energy towards the Universe; even the Universe isn't a closed system inside the Megaverse, and becomes so diffused with the passage of time so it reaches the upper limit of quantum decohesion, thus then the virtual particles are compelled to become actual [materialized/objectified] to fill the gap, this event is a Big Bang without singularity, and it occurs when entanglements are no longer possible) through the Higgs connection field, and brings matter closer to the center of gravity, in order energy is maintained.

— Preceding Steven Weinberg comment added by Steven Weinberg ( talk) 23:29, 29 April 2016 (UTC)

The diagram of Bob and Alice shows their axes rotated by 45 degrees. The text does explain why this is necessary. — Preceding unsigned comment added by 62.56.70.12 ( talk) 08:42, 21 March 2012 (UTC)

I agree, I also think the diagram is confusing. Suggest rotating the Bob circle 45 degrees anti-clockwise and removing the caption '45 (degrees)'. Then it makes sense. Count ludwig ( talk) 13:34, 7 April 2013 (UTC)

I also agree with Count ludwig. Septate ( talk) 11:35, 6 July 2014 (UTC)

The section under "the crux of the matter" is wrong. By only measuring the x or z axis you cannot distinguish between a classical system with hidden variables and a quantum system. One has to measure at 45 degrees also. The diagram is right, the description is wrong. --Jules — Preceding unsigned comment added by 83.82.131.247 ( talk) 13:32, 23 October 2015 (UTC)

I agree that the text is confusing / misleading, but I disagree that you need to "measure 45 degrees also" to distinguish between classical and quantum. I think you are referring to an experiment measuring polarization angles of entangled photons in the 45 degree planes X=0 and X=Z. This example is about measuring spins of an entangled electron and positron about orthogonal axes X=0 and Z=0. (But I may be wrong)

"You might imagine that, when Bob measures the x-spin of his positron, he would get an answer with absolute certainty, since prior to this he hasn't disturbed his particle at all. Bob's positron has a 50% probability of producing +x and a 50% probability of −x—so the outcome is not certain. Bob's positron "knows" that Alice's electron has been measured, and its z-spin detected, and hence B's z-spin has been calculated, but the x-spin of Bob's positron remains uncertain."

1) I've fixed the above, and hopefully made the meaning of the text clearer. I removed a bit of passive voice and highlighted where the reader's assumptions might follow ("It's as if"), and where they might be contradicted ("But it turns out that").

2) But I don't understand the point about "certainty" vs "50% probability" of a measurement (and nor does the person who put an HTML comment at that point).

2a) What is the difference in certainty between Bob making his measurement before Alice makes hers, or after, or what if she doesn't make a measurement at all?

2b) Is it because he measures his positron's "x"-spin twice and gets a different result the second time? Except he doesn't, because "he hasn't disturbed his particle at all."

3) But I think he *has* measured it already, and this is the "crux of the matter". In a classical system it's the same the second time ("certain"), but in a quantum system it can be different ("50% probability").

4) Actually, I think the text in the whole section "Measurements on an entangled state" is practically unintelligible - a reader would have to know what entanglement is and how it works already before they can make any sense of the text, and even then it is still confusing.

5) So I propose a rewrite. — Preceding unsigned comment added by Count ludwig ( talk • contribs) 18:43, 12 January 2017 (UTC)

The claim written in that section: "The EPR paradox has deepened our understanding of quantum mechanics by exposing the fundamentally non-classical characteristics of the measurement process. Before the publication of the EPR paper, a measurement was often visualized as a physical disturbance inflicted directly upon the measured system. For instance, when measuring the position of an electron, one imagines shining a light on it, thus disturbing the electron and producing the quantum mechanical uncertainties in its position. Such explanations, which are still encountered in popular expositions of quantum mechanics, are debunked by the EPR paradox, which shows that a "measurement" can be performed on a particle without disturbing it directly, by performing a measurement on a distant entangled particle. "

is basically nonsense as many college level texbooks still teach that and I would say that the measurement problem has not really been solved. Moreover it contraddicts Heisenberg uncertainty principle. — Preceding unsigned comment added by 155.69.199.255 ( talk) 10:49, 10 January 2017 (UTC)

Do you doubt that a "measurement" can be performed on a particle without disturbing it directly? Boris Tsirelson ( talk) 11:30, 10 January 2017 (UTC)

About Heisenberg uncertainty principle. Without EPR one could hope that q and p (the coordinate and the momentum of a given particle at a given moment) cannot be known both, but still, can exist both (hidden variables). According to EPR, there is no such hope (assuming locality, of course); if q and p exist both, then they can be known both. True, this way we can know their past values, before the measurement, not their current values; but it would violate the uncertainty principle, still. Boris Tsirelson ( talk) 12:37, 10 January 2017 (UTC)

The HUP has really little to do with measurements. The uncertainty lies in the states whether we measure them or not. But, I'd give you right that in order to make a measurement on a system, then we have mess with it. Period. Then one can argue. Is there really something like a system of two distant entangled particles comprised in such a way that when one measures, one messes only with one of the particles? I don't know. The statement in the article is strong indeed. YohanN7 ( talk) 13:03, 10 January 2017 (UTC)

To explain where my ignorance comes from; one is in the beginning taught to think about particles in a system to not have individuality (this is part of disabusing people from thinking classically about QM). Now one is asked to again think of particles in a system to have some sort of individuality. YohanN7 ( talk) 13:46, 10 January 2017 (UTC)

Thinking more about it, the statement in the article could be weakened (or strengthened if you will) to claim that we can find out facts about a particle without doing measurements on it. This would be cleaner and leave measurements and their effect out of the discussion. They tend to blur. YohanN7 ( talk) 14:05, 10 January 2017 (UTC)

No individuality? Just holism? Then, why locality, at all? Boris Tsirelson ( talk) 16:23, 10 January 2017 (UTC)

Like I said – I don't know. I just accept QM and mathematical facts like Bell's theorem. Then I try hard not to think hard about various "paradoxes" and what they mean. Bell's theorem b t w, I tend to think about as an expression of conservation laws (typically angular momentum) of nature (the form forced by QM). Goofy? YohanN7 ( talk) 09:31, 11 January 2017 (UTC)

Oops, no! I think about it as something purely informational. Generally not related at all to any conservation law. See also [2]. Like Aaronson: User:Tsirel#Quantum mechanics is not a physical theory. Boris Tsirelson ( talk) 18:57, 11 January 2017 (UTC)

I fully agree with User:Tsirel#Quantum mechanics is not a physical theory. (But I wonder what editor Chjoaygame would have to say about that.) QM is a mathematical framework that can be applied to yield physical theories. YohanN7 ( talk) 13:16, 13 January 2017 (UTC)

To be more specific. Conservation laws emerge from symmetries, and are violated when space-time is far from flat. But Bell inequalities are still the same (as well as their quantum counterparts). Relevant devices may differ, but the maximum over all possible devices is still 0.75 (or 0.853...). Boris Tsirelson ( talk) 19:13, 11 January 2017 (UTC)

That (broken conservation laws) is definitely new to me. Need to digest this. YohanN7 ( talk) 13:21, 13 January 2017 (UTC)

Except for electric charge conservation, though. Boris Tsirelson ( talk) 16:02, 13 January 2017 (UTC)

For those with phd in theoretical physics - perhaps, for those who peruse wikipedia this is garbage, not explained at all for layperson Juror1 ( talk) 14:27, 16 June 2017 (UTC)

Landau's contributions do matter (and are cited more than once in my articles). However, "any model whether local or non-local will obey Bell's inequality"?? Landau did not (and could not) write anything like that. Probably, the anonymous editor means Landau's Proposition 2: "In a classical theory with joint distributions |R|<=2." However, in the absence of locality the observable R is irrelevant; conditional probabilities are relevant. Moreover, Bell's work on this matter started with the observation that a nonlocal classical theory can reproduce quantum predictions; namely, the De Broglie–Bohm theory does. Boris Tsirelson ( talk) 17:47, 22 August 2017 (UTC)

Interesting Ray Streater claims that both you and Landau proved such a thing. Would love to hear you hear your thoughts on Streater :) 197.234.164.85 ( talk) —Preceding undated comment added 19:38, 22 August 2017 (UTC)

With every respect to Ray Streater, "such a thing" is wrong (see above), and therefore all its proofs (if any) must be erroneous, and their authors must be guilty.   :-)   (I happened to be guilty, shame on me, but not in this case.) Boris Tsirelson ( talk) 20:00, 22 August 2017 (UTC)

Can you elaborate on your statement that R is irrelevant without locality? I have re-read Landau's paper as well as Streater's argument. Streater's view is that locality is not being used in Landau's proof only the assumption that R is a combination of observables represented by random variables on a joint probability space. If by R being irrelevant without locality, you mean that you are supposing a non-local mechanism that prevents the observables being represented as random variables on a joint probability space, well our assumption is ruling out that possibility. By the assumption any non-local mechanism present would have to be one that does not affect our ability to use the joint probability space. But in that case the non-local mechanism does not block the derivation of |R|<=2. So assuming locality in addition to the ability to use a joint probability space is redundant. A similar argument is made by Hess et al. in this paper https://www.researchgate.net/publication/308130326_Counterfactual_Definiteness_and_Bell%27s_Inequality where they note that locality is a redundant assumption if one assumes counterfactual definiteness (in the manner they define it). 197.234.164.85 ( talk) —Preceding undated comment added 13:32, 23 August 2017 (UTC)

Sure.

Bell scenario is not about the expectation of the "Bell observable", that is, an observable of the form ${\displaystyle \sum _{i,j}c_{i,j}A_{i}B_{j}.}$ Rather, it is about a linear combination ${\displaystyle \sum _{i,j}c_{i,j}E(AB|i,j)}$ of conditional expectations of the product ${\displaystyle AB}$ under different ${\displaystyle i,j.}$ One may treat the settings ${\displaystyle i,j}$ as non-random parameters, which leads to ${\displaystyle \sum _{i,j}c_{i,j}E(A_{i,j}B_{i,j}),}$ since in the absence of locality each parameter may influence each spin. Alternatively, one may treat ${\displaystyle i,j}$ as random variables (and indeed, nowadays they are randomized, intentionally and carefully). In both cases one may assume (in addition) the usual ("classical") probability theory. In both (equivalent) cases the classical upper bound for CHSH is 4, not 2.

Locality says that each spin measurement is influenced by one setting (not both); and then, indeed, one may use the expectation of the "Bell observable" as an equivalent formulation.

It is vital for Bell scenario to be formulated in phenomenological ("experiment-related") terms, that is, in terms of two spatially separated devices, each with its input and output (setting and outcome). Not in terms of an algebraic expression in the framework of a given formalism (classical or quantum). Without locality the "spatially separated" means nothing, and Bell inequality fails evidently.

Boris Tsirelson ( talk) 18:11, 23 August 2017 (UTC)

The same applies to counterfactual definiteness (in the manner I define it). Boris Tsirelson ( talk) 18:20, 23 August 2017 (UTC)

The information transported through scalar waves separate from the energy flows faster than light?  — Preceding 
unsigned comment added by 
Majorado (
talk • 
contribs) 13:36, 4 February 2018 (UTC) 

How come there's a portrait of Einstein here, but no portrait of the other two, Podolsky and Rosen? Just asking. Vlad Patryshev ( talk) 15:03, 21 February 2018 (UTC)

   A colleague who may well be a better physicist than I has just reverted my extensive edit -- IIRC, some 600 new characters, beyond anything I simply replaced or reworded. What I clearly recall is that my improvement of the clarity of the scope of the first 'graph is objectionable, bcz the colleague apparently thinks the function of the lead 'graph should be to address matters that users who already have an overall grasp of the topic would rather not be slowed down by!
   (I'm constrained by a lousy interface for wiki-editing, and haven't yet seen a diff for either the net changes of my several edits over the last several hours, nor for any of my individual saves; it may be a few days before I get to where I can assess the value of my changes to various passages. --- It'd be great if the colleague would critique them in terms of individual sentences instead of claiming e.g. that my whole complex of probably a dozen or two independent minor changes can rightly be reverted without being individually addressed.)
   So for now, I'm playing my persona as wise old pre-9-11 veteran who appreciates that discussion, and lack of urgency to race twd a perfect, simple solution is what has built this edifice.
-- Jerzy• t 10:45, 9 September 2018 (UTC)

While this article is far from properly-worded (as the cleanup tag says, it's written like an essay instead of a summary) your wording is... peculiar: quantum physics is a "physics specialty"; the "obvious conjecture" about the initials EPR; "novel model"; and so on. If you are a physicist, please feel free to improve the accuracy and phrasing of the article (using references to reliable sources), but please avoid the personal style and essay style. Bright☀ 12:54, 10 September 2018 (UTC)

Also, there should be a moratorium on adding words to the introduction. Metaquanta ( talk) 12:54, 28 October 2018 (UTC)

IP editor 129.11.174.xxx and I have some disagreement on proposed revisions to the lede which, in my opinion, do not represent an improvement. I reverted his/her revisions and have copied the disputed edits below. I don't have time now to detail my concerns, but maybe later on today, I will be able to delineate the points that I do not consider satisfactory. Prokaryotic Caspase Homolog ( talk) 17:56, 20 November 2018 (UTC)

Specific critiques highlighted in color:

• Terrible English: "dichotomy that explanation" does not make sense.
• The substitution of "fled" with "left" understates the circumstances of his departure.
• Original research, so far as I can tell. Need to back up with reliable sources.

Prokaryotic Caspase Homolog ( talk) 10:28, 21 November 2018 (UTC)

129.11.107.120 may be the same person as well- they added that phrase 'dichotomy that explanation' in October. -- Spasemunki ( talk) 05:56, 22 November 2018 (UTC)

Proposed lede revisions by IP editor 129.11.174.xxx

The Einstein–Podolsky–Rosen paradox (EPR paradox) is a thought experiment in Physics which yields a dichotomy that explanation of physical reality according to Quantum Mechanics is Incomplete. ^[7] In the article Can Quantum-Mechanical Description of Physical Reality be Considered Complete?, Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen (EPR) attempted to mathematically show that the wave function does not contain a complete information about physical reality; hence the Copenhagen interpretation was deemed unsatisfactory. Resolutions of the paradox have important implications for the interpretation of quantum as well as classical physics, as for the latter case, one could question if it was at all possible, contrary to intuition and common sense, to have a quantum picture without having a classical one at first.

The work was done at the Institute for Advanced Study in Princeton University in 1934, which Einstein had joined the prior year after he had left Nazi Germany.

Need help here

Up to now, I had given 129.11.xxx.xxx the benefit of the doubt and tried to treat him as a misguided good faith editor.

With the edit summary to his latest edit, with his intentional misspelling of Einstein's name, it is clear that we are dealing with a vandal. I had not put warnings on the talk pages of the previous versions of his IP address, because of my previous misapprehension of him as being simply misguided. What is the procedure here? Prokaryotic Caspase Homolog ( talk) 16:42, 27 November 2018 (UTC)

I retroactively applied vandalism 1 and vandalism 2 templates to a couple of this user's IP talk pages, with the explanation that I did not previously understand that these edits were vandalism rather than good faith, and have applied a third level warning to his current talk page. I don't see anything in Wikipedia policy pages regarding this particular situation, and am just doing the best that I can figure. Prokaryotic Caspase Homolog ( talk) 22:26, 27 November 2018 (UTC)

I have reported this IP user on WP:AIV as shown here. Prokaryotic Caspase Homolog ( talk) 03:57, 28 November 2018 (UTC)

It was recommended that I report this user to WP:AN/I instead. Prokaryotic Caspase Homolog ( talk) 11:38, 28 November 2018 (UTC)

This Article is unsatisfactory from a history of science perspective.

(1) Whatever its contents, its title should not monopolize E-P-R, but should be changed to "Further Study/Discussion/Investigation of E-P-R" [or "Elaboration on E-P-R"]. A different Article should limit itself to the original E-P-R and exclude the John Bell presentation from it altogether. Otherwise this Article sounds like an Informercial for John Bell. Would you substitute the words of Aristotle in the stead of those of Plato ? When Plato quoted Socrates, he was careful to preserve the distinction between who said what and who now says what.

(2) Scientific experiment validates, but cannot sew the fabric of theory. Where distinct theories are validated by experiment, their respective "sewing patterns" can be of interest in themselves, even if they can later be shown to be equivalent to one another. Sometimes more than one are needed, such as the wave(propagation)-particle(emission-absorption) duality.

NOT FOR PUBLICATION. COMMENT FOR THE EDITORS ONLY.

98.164.228.122 ( talk) 11:28, 2 February 2019 (UTC)

The modern resolution—that quantum theory describes the system and not individual particles—should be sourced. I remember sourcing it on another article but if anyone else has a source it would be good to prevent the appearance of an "isolated study", when this description is actually widely adopted by physicists. Bright☀ 10:02, 4 August 2018 (UTC)

From the little I have learnt about the subject I find this "modern" resolution to sound very much like Bohr's original explanation to Einstein in their letters. I also don't find it fully clear how "measurable properties have well-defined meaning only for the ensemble system" differs from "hidden local variables" of the ensemble system. I have more objections to this paragraph, but for now it is sufficient to say that I would really like to find the source of this information, so that I could verify that the editor has understood it correctly. — Preceding unsigned comment added by 87.96.232.233 ( talk) 00:23, 22 June 2019 (UTC)

"Violations of the conclusions of Bell's theorem are generally understood to have demonstrated that the hypotheses of Bell's theorem, also assumed by Einstein, Podolsky and Rosen, do not apply in our world.[5] Most physicists who have examined the issue concur that experiments, such as those of Alain Aspect and his group, have confirmed that physical probabilities, as predicted by quantum theory, do exhibit the phenomena of Bell-inequality violations that are considered to invalidate EPR's preferred "local hidden-variables" type of explanation for the correlations to which EPR first drew attention.[6][7]"

utterly incomprehensible. it starts with the violations that never actually get explained. also 'hypotheses of Bells theorem' needs thorough decoding: how many of those hypotheses are there? what they are? could not they simply be referred as 'Bells theorem'??'also assumed by E,P and R': does this mean that they agreed to bells theorem?? then how comes that bells theorem is described as a statement that the EPR paradox is a mistaken idea? needs clarification. a LOT of clarification. 'do not apply in our world': is this an overcomplicated way of restating bells theorem, like quantum models do not apply to objects several times the magnitude of elementary particles? if that was not meant to say then i am the living proof that the wordig is overcomplicated and instead of explaining the subject to a relatively educated laicist just obscures the thing it was supposed to clarify. 89.134.199.32 ( talk) 21:09, 3 September 2019 (UTC).

The change made to the introduction back in December and reverted back and forth since is unclear (and ungrammatical). The current version is much more satisfactory, although it does commit the common error of presuming that "the Copenhagen interpretation" was/is a well-defined thing, rather than a label applied well after the fact to the views of physicists who differed among themselves on important points. XOR'easter ( talk) 21:15, 29 January 2020 (UTC)

The current lead is terrible. Strange prose, contentious interpretation of the paper, and the talk about "Copenhagen interpretation" is decidedly anachronistic. Tercer ( talk) 23:07, 29 January 2020 (UTC)

Now that my headache has receded and I can think and express myself a little more clearly... yeah, "more satisfactory" is not good, by a long shot. I'm not a fan of they attempted to mathematically show that the wave function does not contain complete information about physical reality — it's just unclear what that is trying to say. The third paragraph (The essence of the paradox...) is not very clear either. On face value, it's not even right: it sounds like the conclusion was that one can measure both the position and the momentum of both of two correlated particles more accurately than Heisenberg's uncertainty principle allows. At least, I think that's what it is saying. But that's not at all what EPR actually argued. XOR'easter ( talk) 03:36, 30 January 2020 (UTC)

OK, I have tried to do something with the lead, but I'm sure it still needs work, and the rest of the article is in a pretty miserable state. It doesn't describe Bohr's reply (the measurements of position and momentum are complementary experiments requiring different laboratory apparatus, so inferences from one can't be combined with inferences from the other). It doesn't include Bohm's version of the EPR thought experiment (measuring two entangled atoms with Stern–Gerlach devices). Somehow, it manages both to give only a cursory explanation of how Bell's theorem was a conceptual advance beyond EPR, and to jam in names and dates and terminology about variations on Bell's theorem that add nothing to an article that isn't about Bell's theorem. I tried to get away from the "the Copenhagen interpretation" talk in the lead, but it recurs in the article body, and every instance is an example of not paying attention to historians of science. It complains about oversimplified popularizations of the uncertainty principle, and in the next paragraph, endorses an oversimplified popularization of quantum computing. Etc. XOR'easter ( talk) 04:30, 30 January 2020 (UTC)

Thanks for your edits, the article improved a lot. I've worked a bit on the lead, to eliminate repetition, use more straightforward language, and emphasize the point that EPR were not merely arguing against Bohr, but rather in favour of a hidden variables theory to supplant quantum mechanics.

I think the biggest problem with the article is the one I hinted at in the history section: it focusses only on the argument given in the EPR paper, which Einstein was not happy with. For him, what was crucial was not the violation of the uncertainty principle, but rather that he had demonstrated nonlocality in quantum mechanics, and proposed hidden variables as a way to heal it. This is the point Bell was addressing in his 1964 paper, showing that Einstein's cure couldn't work. Tercer ( talk) 17:47, 2 February 2020 (UTC)

The new lead is better; thanks for working on it. I agree that the article needs to say more about Einstein's own view (which, IIRC, he stated in more places than just that 1936 essay), in contrast with the EPR paper. XOR'easter ( talk) 18:14, 2 February 2020 (UTC)

Indeed, I've seen it in his correspondence with Schrödinger. We can use the version presented in section IV.C of arXiv:0706.2661, it's simple and precise (I'm feeling a bit bad about repeatedly citing this paper, as I completely disagree with the authors' epistemicity. I have to admit though that they did a great job on the history part). Tercer ( talk) 18:40, 2 February 2020 (UTC)

There's also his contribution to the 1949 volume edited by Schilpp (cited in section V.A of arXiv:0706.2661). I recall the phrasing in that version being more polished than in the letter to Schrödinger, which might help if we're looking for any exact quotations. XOR'easter ( talk) 18:51, 2 February 2020 (UTC)

Are you sure? I just read Einstein's essay, and he doesn't describe the argument at all there. He just makes some general remarks about why he thinks hidden-variable theories are a good idea. Tercer ( talk) 19:38, 2 February 2020 (UTC)

Ah, so it was in the Autobiographical Notes section, not in the Reply to Criticism essay. I didn't think of looking in there. Thanks for including it, but I think it is in general not a good idea to directly quote primary sources, and in particular I find the version in arXiv:0706.2661 more clear. In particular, we should mention that Einstein didn't care about the uncertainty principle part, but only about nonlocality. Tercer ( talk) 21:21, 2 February 2020 (UTC)

Overall I think I'd be happier with a paraphrase (and maybe a shorter quote than what I included, from one source or another), but for the sake of getting a section in place, I figured a briefish blockquote would be serviceable. Actually, I had typed it up with all the math tags to leave in a comment here, and then, after all that, I had the idea that it could go into the article itself. XOR'easter ( talk) 21:25, 2 February 2020 (UTC)

Ok, I'll work on it tomorrow. Tercer ( talk) 21:39, 2 February 2020 (UTC)

The new version looks good. XOR'easter ( talk) 15:01, 3 February 2020 (UTC)

I'm glad you liked it. I was unsure whether to formalize Einstein's argument using the hypotheses of state space separability and locality, as they were precisely stated only by later authors. In the end I decided to write the argument in an informal style, it's a bit refreshing to see such a simple and straightforward argument in this complex discussion. Technical question: do you know how to cite a reference inside a reference? I tried to do that to mention that Ref. 15 is reproduced in Ref. 12, but I couldn't get it to work. Tercer ( talk) 15:45, 3 February 2020 (UTC)

I believe one way to do something like that is to have a reference inside an endnote, using the {{ efn}} template. See, e.g., the notes in thorium. XOR'easter ( talk) 17:52, 3 February 2020 (UTC)

Thanks for the tip, done. Tercer ( talk) 18:49, 3 February 2020 (UTC)

There has been a lot of outright blanking of information sourced from peer-reviewed publications outlining the evolution of understanding from Bohr, Bohm, Bell, "CHSH", Stapp, Eberhard, Fine, Pitowsky and more recently Griffiths, Philipp, Hess, Streater. Without this info the reader is back in 1935 and is left unaware of the progress that has been made in both theory and research. But presumeably the blankers decided they don't like the findings of these not insignificant researchers. 197.234.164.85 ( talk) —Preceding undated comment added 17:57, 4 February 2020 (UTC)

The neutrality of the removed material was at best debatable, and in-depth discussion of Bell(-CSSH) inequalities belongs in an article about Bell(-CHSH) inequalities, not one on the EPR paradox. Mashing them together makes it much more difficult to distinguish what Bell did from what EPR did. This article, as it currently stands, does not leave the reader back in 1935, since it summarizes the Bohm version of EPR (1951), Bell's theorem (1964), and Sakurai's hidden-variable toy model (here credited to the 2010 edition, but IIRC it's in the 1994 one). XOR'easter ( talk) 18:06, 4 February 2020 (UTC)

The mentioned authors represent a wide spectrum of views and all are well established academics whose findings and conclusions are published in peer reviewed journals so a claim of dubious neutrality doesn't stand. Looks more like WP:JDLI from recent editors. 197.234.164.85 ( talk) —Preceding undated comment added 18:47, 6 February 2020 (UTC)

If you could be specific about what material you think should be added back we can discuss it. A generic complaint about blanking is not productive. Tercer ( talk) 19:47, 6 February 2020 (UTC)

It is of course possible to write non-neutrally (or worse yet, just unclearly) about findings published in peer-reviewed journals, for example by taking obscure debates about niche aspects and blowing them out of proportion. In any case, the material is still there in the edit history, and I'd be happy to discuss specifics. XOR'easter ( talk) 20:06, 6 February 2020 (UTC)

We should add a section about steering in this article. It is a formalisation of the EPR paradox, introduced in the seminal paper of Wiseman et al. arXiv:quant-ph/0612147 (arguably also by Schrödinger back in the day), and it his how EPR is often understood nowadays. Tercer ( talk) 15:50, 6 March 2020 (UTC)

Sounds like a good idea. I think the term steering itself originated with Schrödinger ( e.g., 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.) XOR'easter ( talk) 17:55, 6 March 2020 (UTC)

Yep, he did. I'm just saying that it's a bit of a stretch to attribute the current formulation of steering to Schrödinger. Anyway, I just checked, and someone created an article on quantum steering a couple of months ago. It's pretty bad. Also, steering is mentioned in a sentence in the quantum nonlocality article, and in a paragraph in the quantum entanglement article. Tercer ( talk) 18:43, 6 March 2020 (UTC)

Should the "History" section say that Einstein left Nazi Germany or fled Nazi Germany? The rationale for the former was read the sources; check what WP itself says; and don't be so dramatic - take a look at weasel [3]. But "flee" and "flight" are used in reliable sources (e.g., [4] [5] [6] [7] [8]), Wikipedia is not a reliable source for itself, and WP:WEASEL is a warning against text that is vague or evasive, which doesn't seem to apply here. XOR'easter ( talk) 19:59, 28 June 2021 (UTC)

• The source added to justify "left" instead of "fled" is about Einstein skedaddling at the last possible moment (less than two months before Hitler became Chancellor), after the Nazi rise was obvious. I'd say that "fled Nazi Germany" is an acceptable shorthand for "fled Germany when the Nazis were the largest party in the Reichstag, Hitler was heading a coalition government and the writing was on the wall"; perhaps a slightly more detailed phrasing like "fled the rise of Nazi Germany" would be a bit better. XOR'easter ( talk) 23:30, 28 June 2021 (UTC)

The consequences of Bell's inequalities are presented incorrectly. Bell's inequalities require the assumption of statistical independence -- that is, the libertarian free will of the experimenter to choose the settings of the experiment. This is a fundamentally unscientific assumption (as it violates methodological naturalism, an absolute requirement of any scientific approach). Even John Bell himself in a BBC interview in 1985, pointed out that a complete and total absence of free will (by which he specifically meant libertarian free will as compatibilist models don't provide the sort of freedom needed) would allow local realism to still hold in the form of superdeterminism. Despites claims of loophole-free Bell experiments, it is literally and proofably impossible to rule out superdeterminism (and in fact, it's effectively necessary to maintain the methodological naturalism on which science depends). Lrwerewolf ( talk) 15:22, 22 October 2022 (UTC)

I tweaked the short description. It's tough to fit this one in a few words, but "leveled" is not one of them. Johnjbarton ( talk) 22:43, 14 August 2023 (UTC)