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Problem with Entanglement

  1. Jan 10, 2009 #1
    The experimental constructs designed to test entanglement (Alain Aspect et al) via Bell's theorem, have always made me question the interpretation of the evidence.
    I understand the reasoning behind the tests as follows:
    The experimental findings are considered evidence of the (conjugate) properties of the particles involved. This is a requirement of realism(local or non-local). As Bell's theorem is a test (resulting probabilities) for hidden variables, the experimental findings are sufficient proof that entanglement is not the result of hidden variables. The consiquence of no hidden variables is the requirement that entanglement, whatever that may be, is considered a non-local condition of certain particles.

    Under the premise that measurements of quantum action cannot be executed without influencing the quantum state in question - is it not possible that the properties attributed to particles that produce the findings of non-local entanglement, are in fact not properties of the particles, but conditions of the experimental construct that change according to the act of measurement leaving no (apparent) alternative but to conclude non-locality when such findings are attributed to the properties of the particles being measured?
    (Give me a second to inhale)

    Example:
    having attributed colour to a property of an experimental subject rather than to a property of the light striking my detection device, I inadvertantly attribute a change in detected colour as a change in the property (colour) of the subject. While the structure of the subject is normally considered the determining factor of its reflective properties, a change in the geometry of subject to light source will also produce detectable changes in its colour. The symmetry of the experimental construct must then reflect the symmetry of the conjugate property in question for a detected change to be attributed to a property of the subject rather than a condition of the experimental construct.
    While I'm not suggesting the experimental construct changes "during" measurement, it seems reasonable to question the spatial symmetry of the construct necessary to measure both entangled photons at FTL separations.
    Thanks for any help and/or references.

    P.S. What is the accepted mechanics occurring when both entangled particles are measured simultaneously?
     
  2. jcsd
  3. Jan 10, 2009 #2
    I don't think I understand the question. Could you give another specific example, maybe with spin-entangled electrons?
     
  4. Jan 10, 2009 #3

    DrChinese

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    I don't really think the evidence needs to be questioned until you are certain you follow what Bell's Theorem is trying to say. Bell's Theorem says, essentially:

    No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics (QM).

    No one is really questioning that QM makes good predictions. So the question is, what would it take to convince you that local realism is not tenable as a hypothesis? Bell is there to show us the issues. It does not assert there is a non-local causal mechanism, nor does it assert that realism (simultaneous well-defined values for observables, in defiance of the spirit of the Heisenberg Uncertainty Principle) is untenable. All it says is that one of the two of these (locality, realism) is wrong.

    Specifically, you need to see 2 important elements:

    1. When Alice and Bob are measured at the same setting, we see perfect correlations. This fits with your symmetry idea, and is not a problem per se for local realism. But clearly, it limits the range of suitable local realistic theories dramatically because the action at the measuring apparatus is IDENTICAL for both Alice and Bob, and yet it is random. We will see that this is a problem, because it implies that the results are actually predetermined. The randomness must have been "inserted" (so to speak) at the point the entangled pair was created if they give perfectly correlated results at a later time without otherwise communicating.

    2. When Alice and Bob are measured at certain specific setting s- let's say Alice at 0 degrees and Bob at either +120 degrees or -120 degrees (which is like 240 degrees too) - then the results clearly reflect a bias which implies Bob "knows" the setting of the Alice's measurement. It doesn't matter the order of the observations, but let's assume we observe Alice first. The likelihood of a coincidence is 25%, which is cos^2(Alice - Bob) which is the same as cos^2(120 degrees). No complexity there so far.

    Now a little thought will convince you: nearly all of the time, there is no coincidence (the other 75%). But if that were to be true, then it wouldn't matter if Bob was being observed at +120 degrees or -120 degrees. Either way, if Alice were an H (using Heads or Tails analogy), then Bob would be a T. But that would mean that a Bob was going to be a T at settings +120 or -120 most of the time (75% * 75% = 56.25%) - in other words a coincidence rate of 56.25%. And yet we already determined that 2 settings 120 degrees apart will have a coincidence of only 25%. So somehow, Bob knows that Alice is measured at 0 degrees. If you are a local realist, that is not possible.

    Conclusion: there is a strong bias between the results that cannot be accounted for unless Bob has advance knowledge of Alice's setting. But there cannot be internal consistency for the "hidden variables" unless the setting of one is factored in. So when you are trying to come up with your model, ask if it accounts for BOTH 1 and 2 above.
     
    Last edited: Jan 10, 2009
  5. Jan 13, 2009 #4
    Thanks DrChinese

    I am asking the question to find out if the model works "because" I am missing something or if it works because everyone else is.
    I am not questioning Bell's theorem, I understand it is not asserting non-local entanglement or local realism but offers a very logical principle of inequality by which one fails.
    But it addresses and fails local realism exclusively on the basis of hidden variables of the particles.
    It does not consider the "measured" correlations with respect to the local realism of the experimental constructs.
    In all the descriptions of the tests I've read, Alice and Bob are only found at the angles the experiment is designed to examine. We do not for example find Bob at 0 degrees unless the apparatus is detecting 0 degree strikes.
    This appears to me a "conclusion by exclusion". It does not make sense that detecting of one two mutually exclusive states, proves the second unless the two states are well defined as the only possible states.†
    It seems to me that the experimental constructs are such that the only correlation "proven" is one that might be considered the conjugate property of "construct - particle" states, not one exclusively of particle properties.

    If you consider the premise, local realism binds properties with a probability of detection that is violated by QM. One takes from this a prediction of QM regarding the states of the properties of particles. But as QM does not predict specific states, it is actually a prediction of QM regarding the outcome of measurements not the intrinsic, metaphysical structure of the particles. The outcome of a measure is as described above a conjugate property of the construct - the measuring system. Again we do not find Bob at 0 degrees when looking for him at 120 degrees. So the correlation expressed by the conjunction of expectation defining construct and total count of particles within that construct, appears to be evidence of a correlation of particle property and construct rather than a correlation of finding Bob where Alice points to him. For Alice will only ever point to Bob in the direction our construct tells her.

    † - As I understand the tests, this could only be accomlished by a single pair of photons in total isolation of all other (similar frequency) EM in the lab. But all tests are the accumulated data of millions of photon strikes.
     
  6. Jan 13, 2009 #5

    DrChinese

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    You have touched on a couple of points I would like to address.

    Yes, we cannot make a statement about Bob at 0 degrees when we are looking for him at 120 degrees (your example). So QM would say there is no meaning to Bob's property of 0 degrees at that time, i.e. it is non-realistic. I think a word that captures your description better is "contextual": when the context is a measurement of Bob at 120 degrees, any other non-commuting context is impossible.

    Second, you mention the test needing to be in isolation, and somehow the "millions of photon strikes" are perceived as a weakness. Unless you have something specific here, I think you are barking up a tree. Bell tests are performed every day in strong lab conditions in which extraneous light is filtered out (by wavelength, say <>810nm). Narrow "time bins" are used in coincidence counting to insure the proper photon pairs are matched. Of course, the results match theory and the theory's predictions long preceded the tests themselves. So that is an amazing coincidence if there is an experimental flaw.

    On the other hand, the tests match no local realistic theories, which these days have become quite convoluted in their attempts to explain how QM is "wrong" even though the results match predictions. And finally, in what is considered to be the coup de grace by many: the GHZ theorem was discovered nearly 20 years ago. Its predictions do not depend on a statistical mixture of results as do the Bell tests (not that that is an actual defect in the science for Bell tests anyway). The GHZ tests give a thumbs up or thumbs down to realism on each and every trial. Needless to say, realism is rejected and the results are completely consistent with Bell tests and with QM.

    I think you must accept the Bell tests as solid evidence, and instead turn towards understanding theory in that light. Keep in mind that in 1935, at the time of the EPR paper, Einstein wasn't so sure what the results might be. And Bell's Theorem didn't come on the scene for another 30 years. But today we have very active research on this topic: I would estimate that 100 papers per month are written on new theoretical AND experimental analysis of entanglement.
     
  7. Jan 13, 2009 #6
    Thanks DrChinese
    I'll get back to your first two points if necessary, but first I will look into the GHZ theory as I am not familiar with it.
     
  8. Jan 14, 2009 #7
    DrChinese, 2 Qs. 1 - What is GHZ? 2 - Why do you use 120 degrees? You're not the only one. I see that example a lot. I would think 45 degrees (or 135) would be better cos(45)^2=50%. If I understand, that means the results are half predictable. The other half is like flipping a coin.
     
  9. Jan 14, 2009 #8

    DrChinese

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    1. GHZ is a theorem that, like Bell, says there is a difference between the predictions of local realism vs. QM. It is a complicated proof, a truly ingenious discovery. The interesting thing is that every single data point - individually - violates local realism. There is no need for a statistical analysis. Some folks like that better, because it eliminates possible sample bias (although at this point such bias seems far-fetched). I would not tackle GHZ until I got a better grip on Bell, but the important point is that both tell us the same thing using different techniques.

    2. I think the 120 degree example is easiest to visualize. So that example has A=0, B=120, and C=240, each of which is a third of a circle.

    There are 2 other good sets of angles which I sometimes use:

    a. A=0, B=45, C=67.5 (variations on this are used for the Bell-type CHSH inequality).

    b. A=0, B=22.5, C=45. I think this is closer to what you had in mind. Remember that you need at least 3 settings, and only certain combinations do the trick. Now here is the contradiction for this A/B/C:

    Clearly, AC is 50% as you mention and these are only random correlated. But AB and BC are strongly correlated! AB=BC=cos^2(22.5 degrees)=85.4%. Imagine 3 sets of 100 coins (sets A, B and C, imagine them aligned in vertical columns) where the A coin and the C coin are alike half the time (i.e. 50% to match our example),. Now you try to fill in coin set B which is strongly correlated (i.e. 85 out of 100) to both the A coin set and to the C coin set... well, good luck! You CAN'T supply any such set. The best you can do is 75% correlation, not the 85.4% you need! The point is that there is not internal consistency for local realistic solutions that match experiment. That, in a nutshell, is Bell's Theorem. Bell discovered that there were a variety of such settings that failed, and his mathematical approach was different, but the effect is the same.
     
  10. Jan 14, 2009 #9
    Oh, I got it now! Thank you for that.
     
  11. Jan 14, 2009 #10
    Wait a sec! That doesn’t make sense! Let’s say you have a device that puts out 3 entangled particles at a time. (I hear that’s possible.) The 3 observers are set 22.5 degrees from each other so that A and C are 45 degrees apart. They each measure 20 photons. That should be enough to prove the point.

    A – 10101010101010101010
    B – 10101010101010111111
    C – 11111110101010111111

    So A and B match 85%. B and C match 85%. QM wise, we expect a 50% match between A and C. Mathematically, we expect 70%. We see 14 mismatches out of 20. That’s 70%. How can you possibly get 50%? Are one of these observers not allowed to take a measurement for some reason?
     
  12. Jan 14, 2009 #11

    DrChinese

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    My point exactly! Your perfectly good example above has:

    AB=17 of 20, 85% as expected
    BC=17 of 20, 85% as expected
    (so far so good)
    AC=14 of 20... oops, expected 10 of 20!

    If realism holds, MUST be able to produce a set of A/B/C that matches the QM predictions for AB, BC and AC. If realism does not hold, then the only requirement is that AB hold, or BC holds, or AC holds, according to whichever one you actually observe. So one could conclude that realism fails. Of course, the out there is that there could be FTL influences so that is why the Bell conclusion is that local realism fails. Clearly, the actual results are biased to match the observation that is actually performed, and the hypothetical observations do not exist - even in principle.
     
  13. Jan 15, 2009 #12
    OK, DrChinese, I have a challenge for you. The goal here is to separate the results from the experiment. I am accustom to QM being conceptually difficult but not logically impossible.

    Let’s say you have a black box that spits out a long piece of paper with 3 lines of test results labeled A, B and C. The results are only ones and zeros. You don’t know if what’s inside the box is quantum mechanical or classical. If it’s QM, the results come from measuring 3 entangled photons. The measurements are taken at 22.5 degree offsets to each other so that the first (A) and last (C) lines of results are for measurements taken at a total of 45 degree offsets. This is like the example we have discussed. If it’s classical, a single baseball is spun in random directions. Measurements are also taken at 22.5 degree offsets. They measure if the stitches are moving up or down. I feel like drawing a picture but I think you get it.

    Now I know a baseball is a bad model for a photon so it should be clear from the results which experiment is going on inside. (Here comes the tricky part!) Give me an example of test results that show that the box contains the QM experiment and not the baseball.

    As an example, I’ll do the baseball. There’s a 12.5% chance that the spin axis falls in the wedge between A and B. So they’re 87.5% correlated. Same with B and C. For A and C, the correlation is 75%. Correlation(AC) = Correlation(AB) + Correlation(BC)

    A – 1100110110101011
    B – 1100010110100011
    C – 1101010110110011

    B is 12.5% different than A. (2/16) C is 25% different than A (4/16) and 12.5% different than A. (2/16)
     
  14. Jan 15, 2009 #13

    nrqed

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    It is possible that I am missing the point of your question in which case I apologize in advance.

    But the whole point is that it is *not* possible to write down *any* string of ones and zeroes that will reproduce the QM result. That's the whole point! If there was such strings that woudl reproduce the QM results, it would imply that some local realistic theory can reproduce the QM results.
     
  15. Jan 15, 2009 #14

    JesseM

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    If you have three entangled photons, then presumably you have three experimenters, and each one is supposed to choose one of the three axes A, B and C. So, in your black box analogy it would be a little weird to have a line labeled A, another line labeled B, and another labeled C for each trial--are you implying that there are never any trials where two experimenters happen to pick the same axis to measure for their photon? With all the examples of QM violating Bell inequalities that I've seen, the violation comes about by the statistics of different combinations of choices, like comparing trials where two experimenters both picked the same setting vs. trials where the same two experimenters picked different settings. Perhaps it'd be more clear if you labeled the experimenters A, B, C instead of the three angles, and then you said that experimenter A had three choices of settings A1, A2, A3, and likewise for experimenters B and C. Then one trial might be A2/B2/C2, another trial might be A2/B1/C1, another might be A1/B2/C1, etc. (see the GHZ experiment for an example of a three-particle inequality that is violated in QM, although in this case each experimenter is only given a choice of two detector settings).
     
    Last edited: Jan 15, 2009
  16. Jan 15, 2009 #15

    JesseM

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    Maybe I'm misunderstanding something, but I don't think the symbols A, B, and C are supposed to represent hidden variables as you seem to be suggesting, rather they represent different detector settings. It is indeed impossible to write down a string of 1s and 0s representing values of local hidden variables on each trial such that if experimenters choose randomly which variable to measure they'll get a violation of a Bell inequality.
     
  17. Jan 15, 2009 #16

    DrChinese

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    You are correct, nrqed.

    thenewmans: Your baseball analogy is fine, and it shows exactly the point I was looking for. The comments are:

    a. The baseball does not respect the QM formula. Significantly, measurements do not follow the cos^2(theta) program. Although I am guessing that you thought it does follow the random correlation of 45 degrees (and maybe it does). But it is that pesky requirement of matching the QM prediction that always messes things up for realistic theories. It must be strongly correlated to a 22.5 degree difference (85%) but completely uncorrelated to the 45 degree difference (50%). Two steps of 85% is more like 72% than 50% (i.e. 22.5 + 22.5 = 45).

    b. Keep in mind that the simultaneous A, B and C are hypothetical for the realistic view but NOT for the QM view. Thus the QM view does not need to fill in the table with successful sets for A, B and C matching the cos^2 formula. It only needs to do 2 of the 3, which is just what you can measure anyway.

    (Interestingly, it is possible to have 3 photon entanglement BUT you do not end up with the same cos^2(theta) formula for it. You would expect that anyway, since we already know - per Bell - that the cos^2 rule does not hold for 3 angles. Therefore it is best to leave that alone, as it does not directly relate to Bell's Theorem.)

    c. So to answer your challenge question: only a test of QM reveals the cos^2 formula, and violates a Bell Inequality. Any other test violates the cos^2 formula, assuming that the observer picks the observation angles without a priori knowledge of what the results will be.

    JesseM: As to what A, B and C are: I am using those as you describe. I see them as different measurement settings; they are not intended to be separate particles or hidden variables.

    In fact, a realist argues that every particle - even a single particle - has simultaneous definite values for any A, B and C. As well as for D, E, F...etc. So the realistic position has nothing to do with entanglement directly.
     
    Last edited: Jan 15, 2009
  18. Jan 15, 2009 #17

    JesseM

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    But I take it you're using the numbers associated with A, B, and C (the three 1's and 0's in each column) to represent the hidden variables associated with a single photon (or a pair of identical entangled photons), i.e. the results it would give if it was measured on either of the three axes, even though each experimenter can only choose one on a given trial? That makes sense, but I don't think thenewmans understands the symbols this way, since the post with the baseball analogy referred to three entangled photons, and treated the three numbers as if they were all observable as output of the "black box".
     
    Last edited: Jan 15, 2009
  19. Jan 15, 2009 #18
    DrChinese,

    So what your saying is 3 entangled photons won’t follow the same correlation prediction formula. I can accept that. I figured the problem must be either the experiment or the formula. I thought the formula might be for some other spin than 1 or something like that. I’m going to keep thinking about this to see how I can do this with 3 or 4 entangled particles.

    Nrqed and JesseM, thank you both.
     
  20. Jan 16, 2009 #19
    Hi Chris. From what you've written, I'm not really sure what your problem with quantum entanglement is. :smile: Photon coincidence counts are correlated to changes in a global experimental variable (the angular difference between the filter settings in an archetypal two-sided optical Bell test, eg., Aspect et al 1984). LHV models based on the classical model of polarization don't precisely account for the range of QM predicted or actual experimental results -- though they do reproduce the observed cos^2 angular dependency, which suggests that both sides of the setup are dealing, in any given coincidence interval, with related incident sinusoidal waves of some sort. Exactly how they're related, and exactly where and how the relationship is produced is unknown. QM doesn't explicitly describe a nonlocal relationship in either the weak or strong classical sense of the term.
     
  21. Jan 16, 2009 #20

    DrChinese

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    Thanks for your clarifying comments. I hope thenewmans understands that the 3 photon scenario does not relate to Bell's Theorem and the entanglement issues we are discussing. The 3 settings (A, B and C) relate to the measurement settings of one observer or the other (of Alice and Bob). And the values are the hypothetical outcomes IF you could measure all 3 at one time, knowing perfectly well that with 2 photons you can only measure 2 of those settings at a time. And obviously, the experimental results indicate that there is a bias so that the particular pair of settings selected to be measured follow Malus (cos^2 rule).

    The tough thing about using the words "hidden variable" is that no one really know if it is a variable, set of variables, or maybe rules as well that relate to the measurement apparatus. I use the term as others do, but the black box might be the combination of the particle and the polarizer once they come together. Either way, it doesn't really change the results: you are still trying to piece together subsets that follow Malus and as we know, that cannot be done.
     
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