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Young's experiment

  1. Sep 27, 2004 #1
    I was recently handed a link by a friend after a discussion about wave-particle duality that seems to me to be incorrect in certain areas. This is the link: http://www.jracademy.com/~jtucek/science/exp.html

    I'll have a quick go at dissecting parts of the page.

    Well this seems basically true, however I understood that given a large enough sample of single photons the interference pattern would be indistinguishable from that produced by a continuous light source. It would be dimmer with a smaller sample of photons. However, the next statement seems to contradict this...

    This seems to go against every other example of Young's experiment I've come across. What the author seems to be describing is the result of closing one of the slits. With both slits open an interference pattern will eventually appear over time...

    I'm not sure why!

    This just strikes me as wrong. The essential mystery of Young's experiment is that even when treating light as individual particles (photons) the light still produces behaviour that would imply it is acting as if it is a wave. This statement also seems to suggest that the interference patterns produced were not the result of any observations :shy: And then there's the fact that observing light's behaviour in other circumstances show it acting like a wave (e.g. diffraction and polarisation)

    Could anyone clear up my confusion please?

    (Hi btw :) I've been lurking for a while but hadn't signed up...)
     
  2. jcsd
  3. Sep 27, 2004 #2
    The great mystery of QM : if you do not know by which hole the particle went through, it went through both and inteferences are produced. That is only if by any mean you cannot know which hole, because if there is some kind of detector forcing the particle to go through only one hole, even when nobody watches the result of the detector, the interferences are broken. I think you have understood everything, you are just confused by this mystery. We are all. When nobody touches a particle, it behaves like a wave. When you try to catch a particle, you indeed get a corpuscle.
     
  4. Sep 27, 2004 #3

    ZapperZ

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    The source you are citing has major confusion about the subtle part of the experiment. Please refer to this one below and see if it is any clearer.

    http://www.optica.tn.tudelft.nl/education/photons.asp

    Zz.
     
  5. Sep 27, 2004 #4
    ZapperZThe source you are citing has major confusion about the subtle part of the experiment. Please refer to this one below and see if it is any clearer.

    http://www.optica.tn.tudelft.nl/education/photons.asp

    Zz.

    Detail from that page:

    To generate the coherent light needed for this experiment a He-Ne laser was used, with an average wavelength of 632.8nm.

    The problem is that even the most ideal laser light cannot show any non-classical effect here. Namely, if you were to place one detector behind each slit, the trigger by detector A does not exclude trigger by detector B since the laser light has Poisson distribution -- each detector triggers on its own whether or not the other one triggered (no collapse occurs). There is an old theorem of Sudarshan on this very question (the result also appears in a more elaborate paper from that same year by Roy Glauber, which is a foundations of Quantum Optics):

    E.C.G. Sudarshan "The equivalence of semiclassical and quantum mechanical descriptions of statistical light beams" Phys. Rev. Lett., Vol 10(7), pp. 277-279, 1963.

    Roy Glauber "The Quantum Theory of Optical Coherence" Phys. Rev., Vol 130(6), pp. 2529-2539, 1963.

    Sudarshan shows that correlations among the trigger counts of any number of detectors are perfectly consistent with classical wave picture, i.e. you can think of a detector as simply thresholding the energy of the superposed incoming wave packet fragment (A or B) with the local field fluctuations, and triggering (or not triggering) based on these purely local causes, regardless of what the other detector did.

    Thus there is nothing in these experiments that would surprise a 19th century physicist (other than technology itself). The students are usually confused by the lose claim that there is a "particle" which always goes one way or the other. If one thinks of two equal wave fragments and detector thresholding (after superposition with local field fluctuations), there is nothing in the experiment that is mysterious.

    Even the much stricter non-classicality test, such as Bell's inequality experiments are still fully explicable with this kind of simple classical models (usually acknowledged via euphemisms: "detection loophole" or "fair sampling loophole"). You can check the earlier thread here where I posted more details and references, along with the discussions.
     
  6. Sep 27, 2004 #5

    ZapperZ

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    I'm not sure what your point here. Are you trying to say that there are no photons? Or are you trying to convey that the interference phenomena are purely due to classical waves? What if I can show that ALL wave phenomena of light can also be described via the photon picuture? Then what? Is there an experiment that can clearly distinguish between the two? (This is not a trick question since I have already mentioned it a few times.)

    The detection loophole is well-known. If we have no such loophole, the EPR-type experiment would be a done deal. It is why we have to deal with the statistics of large number of data to be able to know how many standard deviation the results deviate from classical predictions. If we are not encumbered by such loophole, we could in principle just do one measurement and be done with.

    Zz.
     
  7. Sep 27, 2004 #6
    ZapperZ I'm not sure what your point here. Are you trying to say that there are no photons? Or are you trying to convey that the interference phenomena are purely due to classical waves?

    I am saying that nothing in the experiment shows that one has to imagine a particle, thus the common "paradoxical" description is misleading. All their frame-by-frame pictures show is precisely the kind of discretization a 19th century physicist would expect to see if a detector thresholds the energy of incoming perfectly classical wave packet superposed with the local field fluctuations.

    It does not show (and can't show since it isn't true) what is commonly claimed or hinted at in popular or "pedagogical" literature, which is that if you were to place two detectors, A and B, one behind each slit, that a trigger of A automatically excludes trigger of B (which would be a particle-like behavior, called "collapse" of wave function or a projection postulate in QM "measurement theory"). You get all 4 combinations of triggers (0,0), (0,1), (1,0) and (1,1) of (A,B). That is the prediction of Quantum Optics (see Sudarshan & Glauber papers) and also what the experiment shows. No wave collapse of B-wave fragment occurs when detector A triggers. The data and the Quntum Optics prediction here are perfectly classical.

    What if I can show that ALL wave phenomena of light can also be described via the photon picuture? Then what? Is there an experiment that can clearly distinguish between the two? (This is not a trick question since I have already mentioned it a few times.)

    The double-slit experiment doesn't show anything particle-like (the apparent discreteness is an artifact of detector trigger decision thresholding/discretization, which is the point of the Sudarshan's theorem).

    Of course, you can simulate any wave field phenomena as a macroscopic/collective effect of many particles at a finer scale. Similarly, you can simulate particle behaviors with a microscopic wave fields in wave packets.

    Whether fundamental entities are particles or waves has nothing to do with the double-slit experiment claims (in "pedagogical" and popular literature) -- no dual nature is shown by the experiment. All that is shown is consistent with a discretized detection of a wave phenomenon.


    The detection loophole is well-known. If we have no such loophole, the EPR-type experiment would be a done deal. It is why we have to deal with the statistics of large number of data to be able to know how many standard deviation the results deviate from classical predictions. If we are not encumbered by such loophole, we could in principle just do one measurement and be done with.

    That's incorrect characterization. The standard deviations have no relation with the detection or the fair sampling "loophole" -- they could have million times as many data points and thousand times as many standard deviation "accuracy" without touching the main problem (that the 90% of data isn't measured and that they assume ad hoc certain properties of the missing data). Check the earlier thread where this was discussed in detail and with references.
     
  8. Sep 27, 2004 #7

    ZapperZ

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    I didn't realize that this thread was about answering the validity of the photon picture. I was responding to the confusing brought about by the original link in the first posting of this thread.

    So you are asserting that if I stick to the photon picture, I cannot explain all the so-called wavelike observation as in the double slit expt.? See T. Marcella, Eur. J. Phys., v.23, p.615 (2002).

    So now we have, at best, the same set of experiments with two different explanations. Just because wavelike picture came first doesn't mean it is right, and just because photon picture came later, doesn't mean that is correct. Again, my question was, is there ANY other experiments that can clearly distinguish between the two and pick out where one deviates from the other? This, you did not answer.

    Zz.
     
  9. Sep 27, 2004 #8
    ZapperZ I didn't realize that this thread was about answering the validity of the photon picture.

    It got there after some discussion of the Bell inequality experiments.

    So you are asserting that if I stick to the photon picture, I cannot explain all the so-called wavelike observation as in the double slit expt.?

    I am saying that if you put separate detectors A and B at each slit you will not obtain the usually claimed detection exclusivity that a single particle going through slit A or slit B would produce. The detector A trigger has no effect on the probability of trigger of B. The usual claim is that when the detector A triggers, the wave function in the region B somehow collapses, making detector B silent for that try. That is not what happens. The triggers of B are statistically independent from the triggers on A on each "try" (e.g. if you open & close the light shutter quickly enough for each "try" so that on average a single event is dected per try).


    See T. Marcella, Eur. J. Phys., v.23, p.615 (2002).

    He is using standard scattering amplitudes, i.e. analyzing the behavior of an extended object, wave, which spans both slits. Keep also in mind that you can affect the interference picture in a predictable manner by placing various optical phase delay devices on each path. That implies that a full phenomenon does involve two physical wave fragments propagating via separate paths, interacting with other objects along the way.

    If you had a single particle going always via a single path, it would be insensitive to the relative phase delays of the two paths. The usual Quantum Optics solution is that the source produces Poisson distribution of the photons, with an average of 1 photon per try, although in each try there could be zero, one, two, three... etc photons. That kind of "particle" picture can account for these phase delay phenomena on two paths, but that is what makes it equivalent to classical picture as well.


    So now we have, at best, the same set of experiments with two different explanations. Just because wavelike picture came first doesn't mean it is right, and just because photon picture came later, doesn't mean that is correct. Again, my question was, is there ANY other experiments that can clearly distinguish between the two and pick out where one deviates from the other? This, you did not answer.

    You don't have a picture of a precisely 1 particle on each try producing the full set of double-slit phenomena (including replicating interference effects of the separate phase delays on each path). You can have a picture of "particles" provided you also assume that the particle number is not controllable, and that it is uncontrollable to exactly such degree that the detector triggers are precisely same as if a simple wave has split in two equal parts, each of which triggers its own detector independently of the other.

    Thus the particle model with the uncontrollable particle number is more redundant explanation since you need a separate rule or a model to explain why is the particle number uncontrollable in exactly such way to mimick the wave behavior in detector trigger statistics.


    The double-slit experiment is a weak criteria (from the early days of QM) to decide the question. The Bell's experiment was supposed to provide a sharper crietira, but so far it hasn't supported the "collapse" (of two particle state).
     
  10. Sep 27, 2004 #9

    ZapperZ

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    Sorry? I could have sworn the original question was on the double slit experiment, and that was what the webpage I replied with was also demonstrating. Where did Bell inequality came in?

    You lost me in this one. What detectors? The interference phenomena as described with photons/electrons/neutrons/etc. are NOT about these "particles", but rather the superpostion of all the possible paths! It isn't the issue of one particle going through either slit, it's the issue of the possible path interfering, creating the often misleading impression that a single particle is interfereing with itself. A single-particle interference is NOT the same as a 2-particle interference.

    Again, I have NO IDEA how this thread degenerated into a question of the validity of photons.

    If you have a solid argument against it, then let me request that you read this paper:

    J.J. Thorn et al., Am. J. Phys., v.72, p.1210 (2004).

    The abstract is in one of my postings in my Journals section. If you believe the analysis and conclusion is faulty, please send either a rebuttal or a followup paper to AJP. This isn't a PRL or Science or Nature, so it shouldn't be as difficult to get published there. THEN we'll talk.

    Zz.
     
  11. Sep 27, 2004 #10
    Quick question about non-locality


    Hello nightlight,

    I have read several of your postings as suggested and think that you thought the points well through. I also, however, like ZapperZ's attitude. To paraphrase him: "Well, what is the big point whether or not classical and quantum mechanics show the same result in these particular experiments?".

    For me the really interesting thing is the answer to the following: In your explanations and works that you refer to, is there a faster than light entanglement, or not?

    I hope that you say "yes" because then you help me to save time to compare sophisticated classical arguments (some of which I recognized myself) with standard quantum-mechanical arguments.

    Roberth
     
  12. Sep 27, 2004 #11
    If you have a solid argument against it, then let me request that you read this paper:

    J.J. Thorn et al., Am. J. Phys., v.72, p.1210 (2004).


    There is a semiclassical model of PDC sources (Stochastic Optics) which J.J. Thorn had used (just as there are for regular laser and thermal sources, as was known since Sudarshan-Glauber results from 1963).

    Therefore the detection statistics and correlations for any number of detectors (and any number of optical elements) for the field from such source can always be replicated exactly by a semi-classical model. What euphemisms these latest folks have used for their particular form of ad-hockery for the missing data to make what's left look as absolutely non-classical is of as much importance as trying to take apart the latest claimed perpetuum mobile device or random data compressor.

    That whole "Quantum Mystery Cult" is a dead horse of no importance to anybody or anything outside that particular tiny mutual back-patting society. That parasitic branch of pseudo-physics has never produced anything but 70+ years of (very) loud fast-talking to bedazzle the young and ignorant.

    Nothing, no technology no phenomenon no day-to-day physics, was ever found to depend or require in any way their imaginary "collapse/projection postulate" (or its corollary, the Bell's theorem). The dynamical equations (of QM and QED/QFT) and Born postulate is what does the work. (See the thread mentioned earlier for the explanation of these statements.)
     
  13. Sep 28, 2004 #12
    Cheers, that's a much clearer description of the experiment. I'll pass it on :smile:
     
  14. Sep 28, 2004 #13

    ZapperZ

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    I could say the same thing about the similar whinning people always do about QM's photon picture without realizing that if it is simply a cult not based on any form of validity, then it shouldn't WORK as well (eg. refer to the band structure of the very same semiconductors that you are using in your electronics and see how those were verified via photoemission spectroscopy).

    If you think you are correct, then put your money where you mouth is and try to have it published in a peer-reviewed journal. Till you are able to do that, then all your whinning are nothing more than bitterness without substance.

    Cheers!

    Zz.
     
  15. Sep 28, 2004 #14

    vanesch

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    I wonder what difference you see between Born's postulate and the collapse postulate ? To me, they are one and the same thing: namely that, given a quantum state psi, and a measurement of a physical quantity which corresponds to a self-adjoint operator A, gives you the probability |<a_i |psi>|^2 to be in state corresponding to eigenstate |a_i> of A, with value a_i for the physical quantity to be measured. If you accept this, and you accept that measuring twice the same quantity in succession yields the second time the same result as the first time, this time with certainty, then where exactly is the difference between the Born rule (giving the probabilities) and the projection postulate ?

    cheers,
    Patrick.
     
  16. Sep 28, 2004 #15
    vaneschI wonder what difference you see between Born's postulate and the collapse postulate ? To me, they are one and the same thing:

    Unfortunately, the two are melded in the "pedagogicial" expositions so a student is left with the illusion that the projection postulate is empirically essential element of the theory. The only working part of the so-called measurement theory is the operational Born rule (as a convenient practical shortcut, in the way Shroedinger originally understood his wave function) which merely specifies the probability of a detection event without imposing any new non-dynamical evolution (the collapse/projection) on the system state. The dynamical evolution of the state is never interrupted in some non-dynamical, mysterious way by such things as human mind (as von Neumann, the originator of the QM Mystery cult, claimed) or in any other ad hoc fuzzy way.

    What happens to the system state after the aparatus has triggered a macroscopic detection event is purely a matter of the specific aparatus design and it is in principle deducible from the design, initial & boundary conditions and the dynamic equations. Since the dynamical equations are local (ignoring the superficial non-locality of the limited non-relativistic approximations for potentials, such as V(r)=q/r) all changes to the state are local and continuous.

    There is no coherent way to integrate the non-dynamic collapse into the system dynamics. There is only lots of dance and handwaving on the subject. When exactly does the dynamical equations get put on hold, how long are they held in suspension and when do they resume activity? It doesn't matter, the teacher said. Well, something, somewhere has to know, since it would have to perform it.

    How do you know that collapse occurs at all? Well, teacher said, since we cannot attribute a definite value to the position (what exactly is the position? position of what? spread out field?) before the measurement and have the value (a value of what? the location of detector apperture? the blackened photo-grain? the electrode?) after the measurement, the definite value must have been created in a collapse which occured during the measurement. Why can't there be values before the measurement? Well, von Neumann proved that it can't be done while remaining consistent with all QM predictions. Ooops, sorry, that proof was shown invalid, it's the Kochen-Specker's theorem which shows it can't be done (after Bohm produced the counter-example to von Neumann). Ooops, again, As Bell has shown, that one had the same kind of problem as von Neumman's "proof", it's really the Bell's theorem which shows it can't be done. And what does the Bell's theorem use to show that there is a QM prediciton which violates Bell's inequality? The projection postulate, of course.

    So, to show that we absolutely need the projection postulate we use projection postulate to deduce a QM prediction which violates Bell's inequality (and which no local hidden variable theory can violate). Isn't that a bit circular, a kind of cheating? That can't prove that we need projection postulate.

    Well, teacher said, this QM prediction was verified experimentally, too. It was? Well, yeah, it was verified, well, other than for some tiny loopholes. You mean the actual measured data hasn't violated the Bell's inequality? It's that far off, over 90% coincidence points missing and just hypothesized into the curve? All these decades, and still this big gap? Well, the gap just appears superficially large, a purely numerical artifact, its true essence is really small, though. It's just matter of time till these minor technological glitches are ironed out.

    Oh, that reminded me Mr. Teacher, I think you will be interested in investing in this neat new device I happen to have in my backpack. It works great, it has 110% of output energy vs input energy. Yeah, it can do it, sure, here is the notebook which shows how. By the way, this particular prototype has a very minor, temporary manufacturing glitch which keeps it at the 10% output vs input, just at the moment. Don't worry about it, the next batch will work as predicted.
     
  17. Sep 28, 2004 #16
    I could say the same thing about the similar whinning people always do about QM's photon picture without realizing that if it is simply a cult not based on any form of validity, then it shouldn't WORK as well (eg. refer to the band structure of the very same semiconductors that you are using in your electronics and see how those were verified via photoemission spectroscopy).

    That's the point I was addressing -- you can take the projection/collapse postulate out of the theory, it makes no difference for anything that has any contact with empirical reality. The only item that would fall would be Bell's theorem (since it uses the projection postulate to produce the alleged QM "prediction" which violates Bell's inequality). Since no actual experimental data has ever violated the inequality, there is nothing empirical that must be explained.

    Since the Bell's theorem on impossibility of LHV is the only remaining rationale for the projection postulate (after von Neumann's & Kochen-Specker's HV "impossibility theorems" were found empirically irrelevant), and since its proof uses in an essential way the projection postulate itself, the two are a closed circle with no connect or usefulness to anything but to each other.


    If you think you are correct, then put your money where you mouth is and try to have it published in a peer-reviewed journal. Till you are able to do that, then all your whinning are nothing more than bitterness without substance.

    And who do you imagine might be a referee in this field who decides whether the paper gets published or not? The tenured professors and highly reputabe physicists who founded entire branches of research (e.g. Trevor Marshall, Emilio Santos, Asim Barut, E.T. Jaynes,...) with hundreds of papers previously published in reputable journals could not get passed the QM cult zealots to publish a paper wich directly and unambiguosly challenges the QM Mystery religion (Marshall calls them the "priesthood"). The best they would get is a highly watered down version with key points edited or dulled out and any back-and-forth arguments spanning several papers cut-off with the last word always for the opponents.

    Being irrelevant and useless, this parasitic branch will die off eventually of its own. After all, how many times can one dupe the money man with the magical quantum computer tales, before he gets it and requests that they either show it work or go find another sucker.
     
    Last edited: Sep 28, 2004
  18. Sep 28, 2004 #17

    vanesch

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    Not to my understanding. He only needs the Born rule, no ? Bell's inequalities are just expressions of probabilities, which aren't satisfied by some probabilities predicted by QM. If you accept the Hilbert state description and the Born rule to deduce probabilities, that's all there is to it.

    Let's go through a specific example, as given in Modern Quantum Mechanics, by Sakurai, paragraph 3.9. But I will adapt it so that you explicitly don't need any projection.

    The initial state is |psi> = 1/sqrt(2) [ |z+>|z-> - |z->|z+> ] (1)
    which is a spin singlet state.

    (I take it that you accept that).

    The probability to have an |a+>|b+> state is simply given (Born rule) by:

    P(a,b) =|( <a+|<b+| ) |psi> |^2 = 1/2 | <a+|z+><b+|z-> - <a+|z-><b+|z+> |^2

    Let us assume that a and b are in the xz plane, and a and b denote the angle with the z-axis.
    In that case, <u+|z+> = cos (u/2) and <u+|z-> = - sin (u/2)

    So P(a,b) = 1/2 | - cos(a/2)sin(b/2) + sin(a/2)cos(b/2) |^2

    or P(a,b) = 1/2 { sin( (a-b)/2 ) }^2 (2)

    So the probability to measure particle 1 in the spin-up state along a and particle 2 in the spin-up state along b is given by P(a,b) as given in (2) and we deduced this simply using the Born rule.

    Now one of Bell's inequalities for probabilities if we have local variables determining P(a,b) is given by:

    P(a,b) is smaller or equal than P(a,c) + P(c,b).

    Fill in the formula (2), and we should have:

    Sin^2((a-b)/2) < = Sin^2((a-c)/2) + Sin^2((c - b)/2)

    Now, take a = 0 degrees, b = 90 degrees, c = 45 degrees,

    sin^2(45) <= ? sin^2(22.5) + sin^2(22.5)

    0.5 < ? 0.292893...

    See, I didn't need any projection as such...

    cheers,
    Patrick.
     
    Last edited: Sep 28, 2004
  19. Sep 28, 2004 #18
    vanesch Not to my understanding.

    The state of the subsystem B which is (in the usual pedagogical description) a mixed state: 1/2 |+><+| + 1/2 |-><-|, becomes a pure state |+> for the sub-ensemble of B for which we get (-1) result on A. This type of composite system measurement treatment and the sub-system state reduction are the consequences of the projection postulate -- the reasoning is an exact replica of the von Neumann's original description of the measured system and the aparatus where he introduced the projection postulate along with the speculation that it was the observer's mind which created the collapse. Without the collapse in this model the entangled state remains entangled, since the unitary evolution cannot, in this scheme of measurement, pick-out of the superposition the specific outcome or a pure resulting sub-ensemble.

    Of course, there is a grain of truth in the projection. There is a correlation of cos^2(theta) burried in the coincidence counts as Glauber's Quantum Optics multi-point correlation functions or the actual Quantum Optics experiments show. In terminology of photons, the problem is when one takes the particle picture literally and claims there is exactly one such "particle" (a member of correlated pair) and that we're measuring properties of that one particle. In fact, the photon number isn't a conserved quantity in QED.

    The fully detailed QED treatment of the actuall Bell inequality experiments, which takes into account the detection process and the photon number uncertainty, would presumably, at least in principle, reproduce the correct correlations observed, including the actual registered coincidence counts, which don't violate Bell's inequality. The full events for the two detectors of subsystem B include: 1) no trigger on + or -, 2) (+) only trigger, 3) (-) only trigger, 4) (+) and (-) trigger. The pair coincidence counts then consist of all 16 combinations of possible outcomes.

    The "pedagogical" scheme (and its von Neumann template) insists that only (2) and (3) are the "legitimate" single particle results and only their 4 combinations, out of 16 that actually occur, the "legitimate" pair events (I guess, since only these fall within its simple-minded approach), while labeling euphemistically (1) and (4), and the 12 remaining pair combinations, which are outside of the scheme, as artifacts of the technological "non-ideality" to be fixed by the future technological progress. The skeptics are saying that it is the "pedagogical" scheme (the von Neumann's collapse postulate with its offshoots, the measurement theory and Bell's QM "prediction" based on it) itself that is "non-ideal" since it doesn't correspond to anything that actually exists, and it is the eyesore which needs fixing.
     
    Last edited: Sep 28, 2004
  20. Sep 28, 2004 #19

    vanesch

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    I don't understand what you are trying to point out. Do you accept, or not, that superpositions of the type |psi> = 1/sqrt(2) (|+>|-> - |->|+>) can occur in nature, where the first and the second kets refer to systems that can be separated by a certain distance ?

    If you don't, you cannot say that you accept QM and its dynamics and Born's rule, no ? If you do, I do not need anything else to show that Bell's inequality is violated, and especially, I do not need the projection postulate.
    In the state |psi>, the state |+>|+> has coefficient 0, so probability 0 (Born) to occur, just as well as the state |->|->. So these are NOT possible outcomes of measurement if the state |psi> is the quantum state to start with. No projection involved.

    I know that with visible photon detection, there are some issues with quantum efficiency. But hey, the scheme is more general, and you can take other particles if you want to. Your claim that quantum mechanics, with the Born rule, but without the projection postulate, does not violate Bell's inequalities is not correct, as I demonstrated in my previous message.

    cheers,
    patrick.
     
  21. Sep 28, 2004 #20
    vanesch I don't understand what you are trying to point out. Do you accept, or not, that superpositions of the type |psi> = 1/sqrt(2) (|+>|-> - |->|+>) can occur in nature, where the first and the second kets refer to systems that can be separated by a certain distance ?

    I am saying that such |psi> for the entangled photons is a schematized back-of-the-envelope sketch, adequate for a heuristic toy model and not a valid model for any physical system. Its "predictions" don't match (not even closely) any actually measured data. To make it "match" the data, over 90% of the "missing" coincidence data points have to be hand-put into the "matching curve" under the "fair sampling" and other speculative conjectures (see the earlier discussion here with details and references on this point).

    If you don't, you cannot say that you accept QM and its dynamics and Born's rule, no ? If you do, I do not need anything else to show that Bell's inequality is violated, and especially, I do not need the projection postulate.

    You've got the Born rule conceptually melded with the whole measurement theory which came later. The original rule (which Born introduced as a footnote in a paper on scattering) I am talking about is meant in the sense Schroedinger used to interpret his wave function with: it is an operational shortcut, not a foundamental axiom of the theory. There is no non-dynamical change of state or fundamental probabilistic axiom in this interpretation -- the Psi evolves by dynamical equations at all times. All its changes (including any localization and the focusing effects) are due to the interaction with the aparatus. There are no fundamental probabilities or suspension and resumption of the dynamical evolution.

    The underlying theoretical foundation that Schroedinger assumed is the interpretation of the |Psi(x)|^2 as a charge/matter density, or in the case of photons as the field energy density. The probability of detection is the result of the specific dynamics between the aparatus and the matter field (the same way one might obtain probabilities in a classical field measurements). You can check the numerous papers and preprints of Asim Barut and his disciples which show how this original Schroedinger view can be consistently carried out for atomic systems including the correct predictions of QED radiative corrections (their self-field electrodynamics, which was a refinement of the eralier "neoclassical electrodynamics" of E.T. Jaynes).


    In the state |psi>, the state |+>|+> has coefficient 0, so probability 0 (Born) to occur, just as well as the state |->|->. So these are NOT possible outcomes of measurement if the state |psi> is the quantum state to start with.

    And if that simple model of |psi> corresponds to anything real at all. I am saying it doesn't, it is a simple-minded toy model for an imaginary experiment. You would need to do the full QED treatment to make any prediction that could match the actual coincidence results (which don't violate even remotely the Bell's inequality).

    No projection involved.

    Of course it does have projection (collapse). You've just got used to the usual pedagocial omissions and shortcuts you can't notice it any more. You simply need to include the aparatus in the dynamics and evolve the composite state to see that no (+-) or (-+) result occurs under the unitary evolution of the composite system until something collapses the superposition of the composite system (this is the von Neumann's measurement scheme, which is the bases of the QM measurement theory). That is the state collapse that makes (+) or (-) definite on A and which induces the sub-ensemble state as |-> or |+> on B, which Bell's theorem uses in an essential way to assert that there is a QM "prediction" which violates his inequality.

    The full system dynamics (of A,B plus the two polarizers and the 4 detectors) cannot produce via unitary evolution of the full composite system a pure state with a definite polarization of A and B, such as |DetA+>|A+>|DetB->|B->. It can produce only a superposition of such states. That's why von Neumann had to postulate the extra-dynamical collapse -- the unitary dynamics by itself cannot produce such transition within his/QM measurement theory.

    Without this extra-dynamical global collapse, you only have A, B, the two polarizers and and the four detectors evolving the superposition via purely local field interactions, incapable even in principle of yielding any prediction that excludes LHV (since the unknown local fields are LHVs themselves). It is precisely this conjectured global extra-dynamical overall state collapse to a definite result which results in the apparent non-locality (no LHV) prediction. Without it, there is no such prediction.

    I know that with visible photon detection, there are some issues with quantum efficiency.

    This sounds nice and soft, like the Microsoft marketing describing the latest "issues" with IE (the most recent in never ending stream of the major security flaws).

    Plainly speaking, the QM "prediction" of the Bell's theorem which violates his inequality, doesn't actually happen in real data. No coincidence counts ever violated the inequality.

    Your claim that quantum mechanics, with the Born rule, but without the projection postulate, does not violate Bell's inequalities is not correct, as I demonstrated in my previous message.

    You seem unaware of how the projection postulate fits in the QM measurement theory or maybe you don't realize that the Bell's QM prediction is deduced using the QM measurement theory. All you have "demonstrated" so far is that you can superficially replay the back-of-the-envelope pedagogical cliches.
     
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