Talk:EPR paradox

A question of fact

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)

"Implications for Quantum Mechanics"

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)

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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)

Draft -- please check my reasoning

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)

Ready to change?

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)

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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. 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 at the Saclay Nuclear Research Centre. These experiments appear to show that the local realism theory is false.

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)

Missing evidence -- see call for inline citations

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)

Other needed changes

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)

The lead

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)

The lead, point by point

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)

This sentence makes no sense

"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)

Hidden variables subsection

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))