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What Is an Element of Reality?

  1. Feb 1, 2005 #1
    In "Do we really understand quantum mechanics? Strange correlations,
    paradoxes and theorems." by F. Laloe, Laboratoire de Physique de l'ENS, LKB, 24 rue Lhomond, F-75005 Paris, France,
    Laloe explores the meaning of "element of reality":

    "3.2 Of peas, pods and genes
    When a physicist attempts to infer the properties of microscopic objects from macroscopic observations, ingenuity (in order to design meaningful experiments) must be combined with a good deal of logic (in order to deduce these microscopic properties from the macroscopic results). Obviously, some abstract reasoning is indispensable, merely because it is impossible to observe with the naked eye, or to take in one's hand, an electron or even a macromolecule for instance. The scientist of past centuries who, like Mendel, was trying to determine the genetic properties of plants, had exactly the same problem: he did not have access to any direct observation of the DNA molecules, so that he had to base his reasoning on adequate experiments and on the observation of their macroscopic outcome. In our parable, the scientist will observe the color of flowers (the "result" of the measurement, +1 for red, -1 for blue) as a function of the condition in which the peas are grown (these conditions are the "experimental settings" a and b, which determine the nature of the measurement). The basic purpose is to infer the intrinsic properties of the peas (the EPR "element of reality") from these observations.

    3.2.1 Simple experiments; no conclusion yet.
    It is clear that many external parameters such as temperature, humidity, amount of light, etc. may influence the growth of vegetables and, therefore, the color of a flower; it seems very difficult in a practical experiment to be sure that all the relevant parameters have been identified and controlled with a sufficient accuracy. Consequently, if one observes that the flowers which grow in a series of experiments are sometimes blue, sometimes red, it is impossible to identify the reason behind these fluctuation; it may reflect some trivial irreproducibility of the conditions of the experiment, or something more fundamental. In more abstract terms, a completely random character of the result of the experiments may originate either from the fluctuations of uncontrolled external perturbations, or from some intrinsic property that the measured system (the pea) initially possesses, or even from the fact that the growth of a flower (or, more generally, life?) is fundamentally an indeterministic process - needless to say, all three reasons can be combined in any complicated way. Transposing the issue to quantum physics leads to the following formulation of the question: are the results of the experiments random because of the fluctuation of some uncontrolled influence taking place in the macroscopic apparatus, of some microscopic property of the measured particles, or of some more fundamental process?

    The scientist may repeat the "experiment" a thousand times and even more: if the results are always totally random, there is no way to decide which interpretation should be selected; it is just a matter of personal taste. Of course, philosophical arguments might be built to favor or reject one of them, but from a pure scientific point of view, at this stage, there is no compelling argument for a choice or another. Such was the situation of quantum physics before the EPR argument.

    3.2.2 Correlations; causes unveiled.
    The stroke of genius of EPR was to realize that correlations could allow a big step further in the discussion. They exploit the fact that, when the choice of the settings are the same, the observed results turn out to be always identical; in our botanical analogy, we will assume that our botanist observes correlations between colors of flowers. Peas come together in pods, so that it is possible to grow peas taken from the same pod and observe their flowers in remote places. It is then natural to expect that, when no special care is
    taken to give equal values to the experimental parameters (temperature, etc.), nothing special is observed in this new experiment. But assume that, every time the parameters are chosen to the same values, the colors are systematically the same; what can we then conclude? Since the peas grow in remote places, there is no way that they can be influenced by the any single uncontrolled fluctuating phenomenon, or that they can somehow influence each other in the determination of the colors. If we believe that causes always act locally, we are led to the following conclusion: the only possible explanation of the common color is the existence of some common property of both peas, which determines the color; the property in question may be very difficult to detect directly, since it is presumably encoded inside some tiny part of a biological molecule, but it is sufficient to determine the results of the experiments.

    Since this is the essence of the argument, let us make every step of
    the EPR reasoning completely explicit, when transposed to botany. The
    key idea is that the nature and the number of "elements of reality"
    associated with each pea can not vary under the influence of some
    remote experiment, performed on the other pea. For clarity, let us first assume that the two experiments are performed at different times: one week, the experimenter grows a pea, then only next week another pea from the same pod; we assume that perfect correlations of the colors are always observed, without any special influence of the delay between the experiments. Just after completion of the first experiment (observation of the first color), but still before the second experiment, the result of that future experiment has a perfectly determined value; therefore, there must already exist one element of reality attached to the second pea that corresponds to
    this fact - clearly, it can not be attached to any other object than the pea, for instance one of the measurement apparatuses, since the observation of perfect correlations only arises when making measurements with peas taken from the same pod. Symmetrically, the first pod also had an element of reality attached to it which ensured that its measurement would always provide a result that coincides with that of the future measurement. The simplest idea that comes to mind is to assume that the elements of reality associated with both peas are coded in some genetic information, and that the values of the codes are exactly the same for all peas coming from the same pod; but other possibilities exist and the precise nature and mechanism involved in the elements of reality does not really matter here. The important point is that, since these elements of reality can not appear by any action at a distance, they necessarily also existed before any measurement was performed - presumably even before the two peas were separated.

    Finally, let us consider any pair of peas, when they are already spatially separated, but before the experimentalist decides what type of measurements they will undergo (values of the parameters, delay or
    not, etc.). We know that, if the decision turns out to favor time separated measurements with exactly the same parameter, perfect correlations will always be observed. Since elements of reality can not appear, or change their values, depending of experiments that are performed in a remote place, the two peas necessarily carry some elements of reality with them which completely determine the color of the flowers; any theory which ignores these elements of reality is incomplete. This completes the proof.

    It seems difficult not to agree that the method which led to these conclusions is indeed the scientific method; no tribunal or detective would believe that, in any circumstance, perfect correlations could be observed in remote places without being the consequence of some common characteristics shared by both objects. Such perfect correlations can then only reveal the initial common value of some variable attached to them, which is in turn a consequence of some fluctuating common cause in the past (a random choice of pods in a bag for instance). To express things in technical terms, let us for instance assume that we use the most elaborate technology available to build elaborate automata, containing powerful modern computers if necessary, for the purpose of reproducing the results of the remote experiments: whatever we do, we must ensure that, somehow, the memory of each computer contains the encoded information concerning all the
    results that it might have to provide in the future (for any type of
    measurement that might be made).

    To summerize this section, we have shown that each result of a measurement may be a function of two kinds of variables:

    (i) intrinsic properties of the peas, which they carry along with them.
    (ii) the local setting of the experiment (temperature, humidity, etc.);
    clearly, a given pair that turned out to provide two blue flowers could have provided red flowers in other experimental conditions. We may also add that:
    (iii) the results are well-defined functions, in other words that no
    fundamentally indeterministic process takes place in the experiments.
    (iv) when taken from its pod, a pea cannot "know in advance" to which sort of experiment it will be submitted, since the decision may not yet have been made by the experimenters; when separated, the two peas therefore have to take with them all the information necessary to determine the color of flowers for any kind of experimental conditions. What we have shown actually is that each pea carries with it as many elements of reality as necessary to provide "the correct answer" to all possible questions it might be submitted to."

    The complete paper "Do we really understand quantum mechanics?
    Strange correlations, paradoxes and theorems." can be found at:
    http://arxiv.org/PS_cache/quant-ph/pdf/0209/0209123.pdf

    All the best
    John B.
     
  2. jcsd
  3. Feb 1, 2005 #2

    DrChinese

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    Embarrassing. We all understand the "common sense" of the local realistic position. That and a quarter will get you 25 cents.

    1) What are you saying, other than quoting other people? Are we to deduce from the quote that it is an exact representation of your position? Or are you being coy, and hoping we will misread your position? If you have something to say, why won't you say it? (That is normally incumbent on those who start threads.)

    2) How do peas prove EPR? You are going to have to do better than that. We understand that some people hypothesize the existence of little teeny tiny attributes that we cannot see. Most of us call those "hidden variables" and don't need to call them pea DNA by childish analogy. We also understand that no-one knew about DNA a few hundred years ago. Also a poor analogy.

    EPR envisioned that the so-called hidden variables would eventually be uncovered. That hasn't happened in 80 years of looking. Instead, it has become obvious to scientists that there is no combination of hidden variables that can mimic the results of certain experiments (per Bell). Please tell us - SPECIFICALLY and not hand waving - how you conclude otherwise. If there is an "element of reality" we are missing, please, do show us. I, for one, am all ears.
     
  4. Feb 1, 2005 #3
    EPR never said ANYTHING about hidden variables - if you can find one instance of EPR talking about hidden variables, I will give you my car.

    All the best
    John B.
     
  5. Feb 1, 2005 #4

    DrChinese

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    What kind of car do you have?

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

    If the more complete description is dependent on finding something which is now hidden, I would call that "hidden variables". The definition of "hidden variables" is usually taken to be those variables which supply the missing description.

    It certainly isn't pea DNA, and I notice that you completely sidestep all of my questions as per your usual. Do you have any position? Or is your objective to stir controversy?
     
  6. Feb 1, 2005 #5

    JesseM

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    They used the phrase "element of reality", and made it clear that they believe there is an element of reality corresponding to the value of both of two physical properties with noncommuting operators, like position and momentum--this exactly what is meant by "hidden variables". From the EPR paper:
    So, they reject the view that position Q and momentum P are not both elements of reality which exist prior to the measurement of the entangled particle--this means they are arguing for hidden variables.
     
    Last edited: Feb 1, 2005
  7. Feb 1, 2005 #6
    No "hidden variables" were needed. All Bohr had to do in order to complete QM was admit the calculated (unobserved) variable - Einstein claimed that if he could predict it with probabiliy 1, then the calculated (unobserved) variable was an "element of reality", that is, it was as valid as the observed variable. Bohr would not agree to this since it would invalidate Heisenberg uncertainty. So, no hidden variables were ever needed. This is just one more example of QM people putting words in Einsteins mouth.

    All the best
    John B.
     
  8. Feb 1, 2005 #7

    JesseM

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    But that's what the phrase "hidden variables" means--don't get hung up on the word "hidden", it just means "a variable not directly measured, although some may believe its value can be inferred".

    Do you agree that if Bell's theorem is violated in an experiment involving spin measurements, then it is impossible to explain the results of the experiment using the idea that each spin-value had a preexisting value without giving up locality?
     
  9. Feb 1, 2005 #8
    No, if Einstein's Principle of Local Action is not valid, then neither is experimental science.
     
  10. Feb 1, 2005 #9

    JesseM

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    So does that mean you think it is impossible for Bell's theorem to be violated? Or do you disagree that a violation of Bell's theorem discredits any theory that postulates that all these variables have preexisting values and also respects the principle of local action?

    Also, what do you think of Bohmian mechanics? This is a deterministic interpretation of QM which says particles have a definite position at all times (even when we measure their momentum), and which includes faster-than-light effects, but nevertheless can be proven to make all the same predictions as ordinary QM.
     
    Last edited: Feb 1, 2005
  11. Feb 1, 2005 #10

    DrChinese

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    I would say that this is the most moronic thing I have ever seen written, but that wouldn't be a nice thing to say.

    Reality is what it is. It certainly does not matter to reality whether your purely semantic argument is correct. Meanwhile, the results of experiments are exactly as Bohr envisioned. So who has the last laugh? How do experiments of entangled particles correlate in violation of Bell?
     
  12. Feb 2, 2005 #11
    But that is the whole point - for Einstein, it was not hidden.
     
  13. Feb 2, 2005 #12

    ZapperZ

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    No, for Einstein, it was "hidden" from QM!

    There are hidden variables in classical statistical mechanics of coin-tossing. It's perfectly deterministic. But due to our ignorance of the intricate details of its complete dynamics, we lump them all into statistical probabilities. Thus, all those intricate dynamics are hidden from the statistical description of coin-tossing.

    Einstein is claiming the same thing. He said that there has to be some underlying mechanism of QM that is not included in its formulation. So these are hidden from the theory. In fact, this idea was later on used by Bohm as the hidden variables.[1]

    Irregardless of what you think, there has been no controversies till now that the EPR paper is in fact claiming that QM is incomplete, and that this is due to variables not contained within the formalism. They may not explicitly use the pharse "hidden variables", but the implied presence of them has never been disputed within this paper.

    Zz.

    [1] D. Bohm, Phys. Rev. v.85, p.166 (1952).
     
  14. Feb 2, 2005 #13

    DrChinese

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    "...when you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes (Sir Arthur Conan Doyle)

    It is pretty clear from the experimental record: A measurement at one system determines the "reality" of the observable at the other. For spin entanglement, there is complete reality only when the polarizers are at 0 or 90 degrees. That is our "element of reality."
     
  15. Feb 2, 2005 #14

    JesseM

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    Aside from what ZapperZ said, "hidden variables" is just a technical term, as long as all physicists understand what this term means in the context of QM, it doesn't matter if the words completely match their ordinary-english meaning. It's like how the "flavor" of a quark doesn't have anything to do with the ordinary meaning of the word "flavor".

    And you still haven't answered my question--do you think it is impossible that Bell's theorem can ever be violated, or do you just deny that a violation of Bell's theorem discredits "local hidden variables", meaning the idea that noncommuting variables like position and momentum all have exact values even when we don't measure them, and that no influences can go faster than light?
     
  16. Feb 2, 2005 #15
    The fact is that the quantum community has revised the Einstein side of the EPR argument to fit their desires for the past 75 years. I think the TRUTH is a better approach. When someone says that Einstein said something, that something should be what Einstein said.

    Bell's 4 dimensional Hilbert space has almost nothing to do with the real world. As far as the Bell Test experiments, until a more mature model of the photon is developed, the Bell Test experiments will prove nothing. Are you familiar with the single photon interference experiments (a photon undergoing interference with itself).

    All the best
    John B.
     
  17. Feb 2, 2005 #16

    JesseM

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    They haven't revised anything. Einstein believed that particles have definite values of position and momentum (and other noncommuting variables) at all times, even when we don't measure them, and that's what quantum physicists mean by the technical term "hidden variables". Again, it's unimportant whether the words match their ordinary english meaning, they could have called it "electric ostriches", and as long as all physicists knew what was meant by that term in the context of QM, it wouldn't matter that exact simultaneous values for noncommuting variables have nothing to do with large flightless birds.
    Bell's inequality has nothing to do with any "4 dimensional Hilbert space", it is just based on basic logic and probability. Here's a quickie explanation of the meaning of Bell's Theorem I wrote up on another forum. First, check out this analogy from the book Time's Arrow and Archimedes' Point:
    The situation in one version of the EPR experiment is almost exactly like the situation with these imaginary Ypiarian twins, except that instead of interrogators having a choice of 3 crimes to ask the twins about, experimenters can measure the "spin" of two separated electrons along one of three axes, which we can label a, b, and c (this is not the only type of EPR experiment--the one that is usually tested experimentally is one involving photons called the Aspect experiment--but I'm discussing this one because it's so similar to the 'Ypiarian twin' analogy above). Whichever axis the experimenter chooses, she will find that the electron is either "spin-up" (+) or "spin-down" (-) along that axis, and if the other experimenter chooses to measure his own electron along the same axis, then when they compare results they will always find the electrons had opposite spins on that axis (you can only choose one of the three axes to measure though, because there is an uncertainty relation between spin on each axis similar to the position-momentum uncertainty relation). One might try to explain this by saying the electrons each started out with a well-defined spin along all three axes, with each having the opposite spin as the other along all three; for example, if you imagine one electron's spins along axes a, b and c were + - +, then the second electron's spins must have been - + -. But if you make this assumption that each had a well-defined spin along each axis, then some simple math shows that something called "Bell's Inequality" would be expected to hold. As this wikipedia entry on Bell's Theorem explains:
    But in reality, the Bell inequalities are consistently violated in the EPR experiment--you get results like P(a+, b+) > P(a+,c+) + P(c+,b+). Again, this shows that you can't just assume each pair of electrons had well-defined opposite spins on each axis before you measured them, despite the fact that whenever the two experimenters choose to measure along the same axis, they always find the two electrons have opposite spins on that axis. There are some ways to save the idea that the particle has a well-defined state before measurement, but only at the cost of bringing in ideas like faster-than-light communication between the electrons or the choice of measurements retroactively influencing the states of the two particles when they were created.
     
    Last edited: Feb 3, 2005
  18. Feb 2, 2005 #17
    No, he was right. He had the proviso that the questions asked each twin were not the same. This gives the correct probability: 2 cases / 6 cases or 1/3.
     
  19. Feb 2, 2005 #18

    JesseM

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    Ah, I didn't catch that. Still, it seems like the connection with EPR-type experiments would be better if you assume each interrogator picks his question at random right before he asks it to the twin he's interrogating, so that when each twin answers there's no way he could know anything about what question his brother was asked (assuming information can't travel faster than light).

    edit: Or perhaps he meant that the experimenters do choose their questions randomly right before they ask them, but that we restrict our attention to the subset of cases where they randomly happened to ask different questions, and throw out the other 1/3 of cases where they happened to ask the same question. Out of this subset, a "hidden-variables" theory where you assume the twins had already decided on answers to all three questions would indeed predict that they'd give the same answer in at least 1/3 of the interrogations.
     
    Last edited: Feb 2, 2005
  20. Feb 2, 2005 #19

    ttn

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    You mean, no hidden variable theory can predict the correct answers for the Bell/EPR correlation experiments? That's just plain false. Bohmian mechanics does so.

    Or maybe you meant that no hidden variable theory which respects Bell's Locality condition can predict the correct answers for such experiments. That's true; it's Bell's theorem.

    But this is no argument against hidden variable theories, since orthodox QM itself violates Bell Locality. Remember, Bell Locality essentially amounts to the idea that joint probabilities for space-like separated events should factorize when you conditionalize on a complete specification (call it "L") of the world in the past light cones of the two events. Mathematically,

    P(A,B|a,b,L) = P(A|a,L)*P(B|b,L)

    where A and B refer to measurement outcomes, a and b refer to any other relevant parameters local to the two measurements respectively, and L is the complete specification across the past light cones.

    Bohr (and all subsequent opponents of hidden variables) invites us to identify L with the quantum mechanical wave function psi. But according to QM,

    P(A,B|a,b,psi) = P(A|a,psi)*P(B|b,psi)

    is not valid. That is, orthodox QM (considered complete) violates Bell Locality.

    And it is therefore a tragic (but admittedly widespread) mistake to argue against hidden variable theories on the grounds that they have to be non-local. Show me a theory that agrees with experiment and *is* local, then that objection might hold some water. But if one's only alternative to the (allegedly) preposterous-because-nonlocal hidden variable theories is orthodox QM itself, well, one would be shooting oneself in one's own foot...

    ttn
     
  21. Feb 2, 2005 #20

    JesseM

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    An Everett-type interpretation, where there is no nonlocal "collapse of the wavefunction", might be able to do this--this was discussed a bit on the thread Aspect/Innsbruck Interpretation which respects SR locality. I posted some links to papers that argue this:
    I also came up with this analogy to think about how an Everett-type interpretation might in principle be able to explain violations of Bell's theorem in a local way:
     
    Last edited: Feb 3, 2005
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