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Entanglement Explained with Epistomological Probability Theory

  1. Apr 2, 2008 #1
    I'm interested in published papers, if any, addressing the issue of whether Bell type experiments can be explained simply with classical, epistomological probability theory. In particular, can the expected "quantum" result (i.e. the probability that photons A and B will both pass through their polarizers positioned at theta1 and theta2 is equal to 1/2 * cos^2(theta1-theta2)) simply be derived from probability theory and Malus' law without the need to assume non-local communication?

    Note I'm not asking if any hidden variable theory can explain the results; merely if there's been published treatment of the hypothesis that entanglement experiments can be explained with classical probability theory.
     
    Last edited: Apr 2, 2008
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  3. Apr 2, 2008 #2

    Mentz114

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    Years ago I came across this guy, Thomas Smid who claims to have it. I disassociate myself from his ideas, but you did ask. You can find him with a Google search.

    Another one is in the arXiv, the number is quant-ph/0112019. Same caveat.
     
  4. Apr 2, 2008 #3

    Hans de Vries

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    Well, almost all published papers about experiments do just this. They try to explain
    the results with Malus law and polarizer angles....

    This generally fails, Malus law introduces more randomness as observed in the
    experiments. It is then said that Bell's-hidden-variable-model fails, where
    the hidden-variable is the polarization angle.

    The polarization angle is said to be a "hidden-variable" because the experiment
    is set up so that the polarization angle of individual photons is unknown. (it is said
    to be in a superposition)

    Malus law functions as a random generator and the randomness depends on the
    polarization angle. At one angle the result is 100% determined while the result is
    100% random at angles rotated over 45 degrees.



    If a second experiment is set up so that the polarization angle IS known then it's
    not a hidden variable anymore. However, Malus law has to fail just as well. The
    correlations should not become less....

    ( The second experiment could have fixed polarization, with the unit containing the
    polarizers/detectors slowly rotating during the experiment to average out the angles)



    Now, what does this all really prove? In my opinion this is the following:

    1) If the results of both experiments is the same then this supports the statement:
    A photon in superposition of two polarization states is the same a a photon
    NOT in a super position state where the polarization angle is determined by the
    added EM fields.

    2) In any case, it proves that Malus law generally fails in these experiments.
    That is, it is NOT the polarization angle ALONE which determines the outcome
    of the experiment.

    The polarization angle is taken to be determined by the E and B fields thus
    they can not be the hidden variables. I would say that the only hidden-variable
    candidates remaining from (mainstream) physics are the potentials A and V
    which have extra degrees of freedom. They are not uniquely determined by
    the E and B fields.



    Regards, Hans
     
    Last edited: Apr 2, 2008
  5. Apr 2, 2008 #4
    But of course you are!
    That is the entire point of EPR-Bell argument; that there is no classical probability explanation that can describe the results observed in entanglement experiments.

    The moment you produce a probability theory using local & realistic rules that does not ditch discrepancies into “lossy observations” but accounts for all events to produce the Malus statistics then you have a viable “hidden variable theory”. You, you do not even need to prove that it is a correct - if there is one there could be another. And the negative proof of EPR-Bell tests are totally dependent on there being no possible such description.
    Just producing such a theory on paper would mean EPR-Bell was incomplete and something more complete than QM could exist.

    And the Thomas Smid example is far from a complete description.
     
  6. Apr 2, 2008 #5
    What exactly are the A & V potentials ?
     
  7. Apr 2, 2008 #6
    So what you're saying is that if a classical probability derivation could explain the results, Bell's theorem couldn't be true, and that such a theory in and of itself would prove that there is a hidden variable theory "out there," even if we don't know what it is yet.

    I too was wondering what "A & V" meant.
     
  8. Apr 2, 2008 #7
    No that is not quite what I said.
    I believe Bells theorem is true, just the conclusions people make from it are wrong.
    Meaning the needed classical probability derivation must violate the Bell inequity and match the Malus Line.
    May not be proof that a HV is correct; just that the proof a HV is impossible is incorrect.
    And since anything goes in piecing such a thing together like this; coming “close” doesn’t count, it needs to produce the Malus Line without "losses".
     
  9. Apr 2, 2008 #8

    Hans de Vries

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    These are simply the electric potential V and magnetic vector potential A.

    The E and B fields determine the force on electric charge but the V and A fields
    do modify the QM phase of the electrons because of the interaction with its charge
    density. The A and V potentials modify interference patterns even if the E and B
    fields are zero.

    The B and E fields modify the phase of the moving electron due to the interaction
    with its magnetic moment. The derivatives of B and E determine the force on the
    electron due to its magnetic moment. (Stern-Gerlach experiment)


    Regards, Hans
     
  10. Apr 2, 2008 #9
    Randall, I'm just confused by your statement:

    In short, is Bell's theorem compatible with a local, realistic, statistical explanation of entanglement, if one could be found?
     
  11. Apr 2, 2008 #10

    JesseM

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    No, Bell's theorem proves absolutely that the results predicted by QM in experiments with entanglement cannot be compatible with any local realist theories. You might take a look at this thread for a discussion of the logic of the proof.
     
  12. Apr 3, 2008 #11
    Yes. This is true.
    Since local realist theories are ruled out, there are two alternatives remaining:

    1.Nonlocal realist theories. Namely where the wave function is a real entity. In this case the detection/measurement itself is a nonlocal(relativity violating) time evolution of a real physical entity.

    2. Local nonrealist theories namely the Copenhagen interpretation(CI), where the wave function is not a real entity(thus nonrealist), and where reality(associated whith the quant to be measured) even does not exist until you measure it. Or in other words where we can only talk on potential reality but not actual reality prior measurement.

    The choice is matter of taste. I for my part would rather sacrifice relativity (by preferring its Lorentzian interpretation where the apparent/observed validity of Lorentz Transformations for space and time is only an obervational consequence of Lorentz invariant physical laws, thus not a real symmetry of spacetime itself but only an apparent symmetry ) and I would prefer to assume that "we still don't know how the wave function dynamically evolves during measurement", rather then accepting the second one. This is not because I reject to swallow the new hard concept of "potential reality" and its distinction from "actual reality" but because:

    1. CI does not answer the question "under which actual real conditions this "potential part" of the reality becomes an actual reality" in other words because it uses the term measurement without presenting us its definition,namely without answering the question which "macroscopical/classical" setup (namely which form of the actual reality) leads to an event that we may call "measurement".

    2.No real measurement has an infinitely precise outcome for the value of an observable. Thus even immediately after measurement there is an uncertainity of the apparently observed variable. Thus there is no actual reality in strict sense even after the measurement but only an extreme narrowing of the already existing uncertainty. So in fact in CI the term "measurement" does not mean picking one of the potential realities but it is just a apparantly sudden/stochastic change of the uncertainty function (wave function). Thus describing the measuremnet in terms of potential/actual reality does not make any sense at all even in CI .

    Thus I would not have a problem with the idea "God plays dice" . However if a theory contains a claim that there is a fundamentally stochastic(random) process that is fundamentally irreducible to a deterministic process, it should provide us with a quantitative relationship, that describes under which conditions this stochastic events happen or likely to happen. Since CI does not provide this, it is incomplete imo.
     
    Last edited: Apr 3, 2008
  13. Apr 3, 2008 #12
    The reason I ask is because probability theory such as Bayes Theorem frequently involves situations where KNOWLEDGE about the outcome of an event affects the probability of another event - even though the two events are not causally connected. So I thought, perhaps, that that concept could explain entanglement in purely epistomological terms without the need to resort to hidden variables or anything else deeper than the statistics themselves.

    I also found this paper online which makes such a claim:

    http://www.physics.umd.edu/rgroups/ep/yskim/boston/kracklau.pdf

    But it doesn't appear to be published and I find his purported explanation of Aspect experiments using classical probability rather confusing, and I suspect not logically sound.
     
  14. Apr 3, 2008 #13

    DrChinese

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    Like a lot of purported classical explanations, it fails to take on the Bell argument directly. He does not address the main arguments of EPR, namely that there are "elements of reality" independent of the act of observation. He basically just tries to say that Malus' Law is classical, and that matches the predictions of QM. But he does not address the main counter-argument of Bell, that there must exist simultaneous values for A, B and C in a realist scenario.

    I suspect that would be the approach of ANY purported explanation in classical terms, basically to ignore Bell by waving your hands.
     
  15. Apr 3, 2008 #14
    [Whoops, sorry that post was incomplete]

    So I guess the bottom line is that one can indeed abandon "realism" in the sense that the photons truly don't have any properties other than what are observed. Is that really "ignoring Bell" or is it simply abandoning realism in exchange for locality? Sure, there is no causal influence between the two distant particles, but there are also no inherent properties to those particles at all independent of whether they "pass" or "don't pass" through the polarizer.
     
  16. Apr 5, 2008 #15
    I’m a little unsure what the confusion might be?
    1) What do you think it means.
    2) Do you recognize the difference between “Bell” and “EPR-Bell”

    That may also help clear up what you mean when you say :
    Do you expect that any theory in order to be viable must allow for abandoning "realism"? If that is “the bottom line” it would exclude theories currently out there that retain realism but expect a “Non-local reality”.
    I don’t think the evidence reviewed here justifies such a bottom line conclusion.
     
  17. Apr 5, 2008 #16
    Is this psychotherapy? :)

    I assume EPR-Bell means the EPR paradox that QM is incomplete or local realism is wrong, plus Bell's theorem which says that no local and realistic hidden variable theory can produce the results of QM. So when you say "ERP-Bell" is incomplete do you simply mean EPR-Bell is wrong?

    I said *can*, not *must*.
     
  18. Apr 5, 2008 #17
    It wasn’t clear that you understood you cannot necessarily abandon realism when someone is using a non-local approach that already accounts for the problem.
     
  19. Apr 5, 2008 #18
    No it’s trying to make sure we are talking about the same thing.
    I’m sure we are not, as I take it you do not know the difference in this context.

    Bell's theorem “Bell” does not say “no local and realistic hidden variable theory can produce the results of QM”
    “Bell” is a mathematical theorem by a Local Realist (J Bell) designed to help define HVs hoping to satisfy the Einstein claim of Local Realism. If by itself “Bell” proved the QM case there would have been no need for Aspect and others to run experiments or interpret real results against the theorem. (Although J Bell agreed more and better experiments were warranted, he acknowledged he considered it unlikely a HV would be found.)


    “EPR-Bell” is the application of 1)real observations 2)the theorem and 3)rational Logic; to reach conclusions about the truth of reality. And the widely accepted consciences is the “EPR-Bell” confirms that reality must be “Non-Local” and/or “Unrealistic” with no preference for any individual theory within those types. And it does so by providing a negative proof that: “no local and realistic hidden variable theory can produce the results of QM”.

    SO my statement that you were confused by:
    “Just producing such a theory on paper would mean EPR-Bell was incomplete and something more complete than QM could exist.”
    Simple means that if you personally without conducting an experiment sat down with Alice giving her a long list of individually numbered photons including details for each photon as many variables (known or hidden in real life) you wish to define. And provide a theorem using whatever “classical epistemological probability theory”, as mentioned in your OP, you want to divide the photon list into two photon groups H & V for a particular measured angle.
    But unlike a real experiment Alice can apply your theorem again to the same written set of photon descriptions to as many different measurement angles as you like with every angle having a H & V list created with each photon individually identified. No need to wait for Bob to report measurements made at a distance.
    If Alice and Bob are using the same translation against the same set on Data they will both produce the same results.
    It is a simple paper exercise to track which photons on each list have the same unique ID to build a correlation pattern.

    The challenge is to have the paper theory produce correlations between the various angles that match cos^2 Mauls expectations thus violating the “Bell” inequity line. Any successful effort would falsify the “EPR-Bell” interpretation of “Bell” that “no local and realistic hidden variable theory” can do so.
    I.E. it just takes one.
     
  20. Apr 7, 2008 #19

    JesseM

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    I don't get your argument here. Bell did prove that the theoretical predictions of QM were incompatible with local realism; the point of the experiments was just to test whether the predictions of QM were in fact correct with regards to entanglement. But if you think there's any possibility that QM's predictions could be exactly correct in all circumstances and local realism could be true, then you're wrong, this has been ruled out definitively.
    Suppose we replace the written list of information with a computer program which stores the properties of each numbered particle, and then the computer has some algorithm to decide what result Alice will get on each numbered particle (based on these stored properties) depending on which of three measurements she chooses to make (perhaps she has a choice of typing "A", "B" and "C" for each simulated particle). Suppose further that we send a copy of the program to Alice and another copy to Bob. Certainly we can design the programs so that it is guaranteed that whenever Alice and Bob choose to make the same measurement on identically-numbered particles, they will get the same result back. But if Alice and Bob make their choices independently of each other, and there is a spacelike separation between the events of each making their choice, then in a local realist universe it is absolutely impossible to design the programs in such a way that they always get the same results when they make the same measurement, and that the Bell inequalities, which concern the results Alice and Bob get when they choose to make different measurements on identically-numbered particles, will be consistently violated. Bell's theorem proves this impossibility. The proof is completely rigorous, and therefore we can be sure that no one will ever come up with an example of a program that would allow us to violate these inequalities in a local realist universe, in the same way that the proof of Fermat's last theorem allows us to be sure that no one will ever come up with three nonzero integers a, b, and c which satisfy a^n + b^n = c^n, where n is some integer > 2. Would you disagree that the proof is rigorous in this sense?
     
    Last edited: Apr 7, 2008
  21. Apr 7, 2008 #20
    Indeed, I tried doing exactly this. Oddly, the program violated the inequalities sometimes, but I think only by random chance, and not by as much as the QM results do. There are local realist models one can program to get very close to the QM results, such as pre-programming results for every conceivable polarization angle, but it's never perfect.

    What would be a good example of a local, non-realist interpretation of QM or entanglement? Is MWI local and non-realist?
     
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