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Question on experiment

  1. May 18, 2007 #1
    I've been trying to study up on the experiments where people have taken entangled particles and done measurements that suggest that they are able to communicate faster than the speed of light.

    The couple experiments I've read up on seem to have a device that pairs the particles and then fires them outward towards two detectors. Quantum Mechanics suggests that both particles exist in all states until they are measured, so the thought goes that both particles are in all possible states and the measure of one of them causes the other to snap to attention and measure the same or opposite value.

    All books and examples I've read provide a really neat example of having two boxes that are separated by miles and one person opens the box takes a measure, then the other person and they determine that they are the same. They use this to state absolutely that 100% of the time this happens just as suggested by QM.

    After reading a bit, I am seeing signs that the experiment is only capable of firing the particles and taking a single measurement as they pass through a magnetic detector to note whether the spin is up or down. This device can't give exact measurements so I'd think if one particle were at a 15% or even a 45% different spin, the detector would not know this.

    I also assume that the particles can only be measured once and in a single orientation. I get this idea from the way the experiment is described so please correct me if I'm wrong on any of these points. If this is true, the multitude of people describing this experiment as a box that you can open and check over and over are doing an extreme dis-justice to the experimental results.

    I've also read of a recent experiment where someone shot the particles between islands and measured them. This would appear very interested as I'm not sure how they'd know anything at all of the particles after they'd been hit by light, air, birds, and everything else in between. Yet this experiment was also tauted as further proof of QM.

    Then I've read the fact that these experiments are very finicky and require extreme care be taken to make sure nothing touches the particles until they've been measured, otherwise they become unpaired and the results can't be depended on.

    So, assuming all of what I've read is true, here is my question:

    How can anyone state the facts as they've stated them supporting QM with this experiment if you can only measure the particles once? I would suggest that when the particles are paired they have opposite spins which would support the test results. I'd also say that anything you do to touch the particles would break this and therefore you'd no longer see the results you are thinking you see.

    A better experiment might work as follows: Shoot two paired particles (Pa and Pb) apart. At point A we measure Pa only and note its spin. Then at point B along the path of the particle Pb we measure its spin only.

    Then at the end of both, we measure Pa and note Pb. In my opinion only this result would prove what is being claimed if:

    1) Pa had spin X at point A.
    2) Pb had spin Y at B.
    3) Both particles had yet another spin at the final point and matched each other. This would tell us that the particles were changing over time and yet were somehow matching each others spin at each point of measurement.

    The experiments in their current form (unless I"m still not understanding them) do not allow you to claim absolutely one thing or another as they are way too basic and touchy.

    Could anyone explain where I'm wrong with this line of thought?

    Thanks,

    glenn
     
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  3. May 18, 2007 #2

    DrChinese

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    glenn,

    Have you really read the details of how the experiment is performed? Check some of the papers I have provided as reference previously, including the following:

    Violation of Bell's inequality under strict Einstein locality conditions

    These experiments are considered conclusive to most scientists. The photons are often sent through fiber optics, which does NOT cause collapse of the wave function. While the experiments are often called "finicky", this is an issue to the experimentalist and is not representative of their conclusions.

    Your hypothesis (1,2,3) does not make sense because after entangled particles are measured, they no longer display the characteristics of entanglement.

    As to having opposite spins and not being entangled: Only entangled particles can have this attribute. But this itself is not a proof that there is something "freaky" going on! It takes Bell's Theorem to get us to that point. And that theorem involves tests at angles OTHER THAN opposite. So you are mixing your criticisms.
     
  4. May 18, 2007 #3
    Yes, I really read them. What physical medium the particles are sent through really isn't important. What seems important to me is the fact that 1: You can't touch them until the magic moment, and 2) Once you touch it the party is over. Its like making a claim that two baseballs always communicate with each and change their spin instantly when one is looked at. But you can only look once because after that point it no longer holds true. How can you make the claim that something "ALWAYS" happens when in reality you can really only see it happen 1 time. And even then, Only when great care has been taken to set things in motion?


    But is this not the entire point of my argument? My point was that only if you could do such a test could you make the overwhelming claim that is being made. The fact that you can't do the test was never mentioned but seems to backup my point even further. If you can't do anything but a single test that you've basically setup from the start to pass, then I don't see how its so important.


    I'm not sure I follow this. I know the tests are done at different orientations, however, the original two particles are hooked together through this entanglement process. So of course they are related and therefore any test on one is going to show similar results on the other. You've set them up to be that way from the start of the experiment.

    You yourself accept that once you've touched either particle you've broken the link. Therefore, its like having my 2 baseballs and you make the claim they always know about each other and instantly change, until I hit one with a baseball bat. At that point it doesn't hold true any longer.

    Perhaps I'm not fully grasping the magic quality of this experimental result. When I first read about this test I was intrigued as it did sound pretty interesting based on the "Particle in a box" example that was given. However, as soon as I read how simple the test was and how touchy it was, I lost the magic. Perhaps there is still something not being explained properly that I'm missing?

    Thanks,

    glenn
     
  5. May 18, 2007 #4

    DrChinese

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    1. Your hypothesis is factually false. It is not the responsibility of QM to provide a description which is inaccurate, nor does it need to describe everything. It need only be useful. You can set the bar wherever you like, just don't expect others to agree with it.

    2. There are set up to be entangled, yes. And the entanglement leads to predictions which are incompatible with local realism. The predictions are related to the observer, and not solely the source particles themselves (as would be expected in a classical world). Bell specifically addresses the incompatibility issues and the "naive" view that explains the "perfect" correlations. The naive view cannot address the correlations at other angles, however, and that is the issue.

    3. Why should they remain entangled forever? This criticism makes NO sense. Besides, it is not strictly true that they stop being entangled when you hit them with a "baseball bat". Only the non-commuting observables are affected. A polarization observation does not affect such observables as position or momentum.

    4. What you are missing is that there is nothing "simple & touchy" about the results, which agree with the predictions of QM within 50+ standard deviations - and are FAR outside the range for classical explanations.
     
  6. May 18, 2007 #5
    I never said anything about responsibilities to explain everything. I only stated that I do not, and still don't understand how something so specific has been stated based on this experimental evidence. The link you sent even states that currently they are only able to measure 5% of the particles that even move through the device. So we're basing something on 5% of measured particles. But this is really not as much a problem for me. Its more the fact that the experiment is so basic. Yet there have been volumes written on how this experiment proves the completeness of QM.

    Where would this be? Where are the measurements that can't be explained any other way, except through QM? You mess around with two baseballs and get them to spin opposite each other. You then fire them out into a field and take a single measurement on them and determine, hey, these things are spinning opposite each other, and when I measure that one over there (one time only), this one over here happens to be spinning in a relation to that one. But didn't we setup the experiment for this to exist? Didn't we begin the very first step of the experiment to correlate the two particles? So wouldn't it be more amazing if they were not still spinning like that?

    Even you admit that after you measure one particle that you can't do further measurements because its likely they are not entangled any longer. This would hold true to my "classical" point of view, that the only reason they are still spinning the way they are is because no one has touched them. As soon as you start jacking around with them we will no longer be able to be sure things had not changed.


    I never said they had to. I only stated that you use the term as if its mysterious that they are entangled at that first point of measure for observer Allison. This to me is not mysterious at all but can be explained in the world in which I live. I just think we're giving a little too much credit to an experiment that quite honestly doesn't seem prove anything at all.

    To state the particles are entangled seems to actually mean that you've gotten them to spin in relation to each other. Thats it. Its not that they had a conversation with each other and transmit information faster than light, its more that we related their spin from the start of the experiment and then sent them on their way. To forever stay that way unless anything at all touches them.

    Again, what are these things that can't be explained?

    Thanks, Just trying to understand...

    glenn
     
  7. May 18, 2007 #6

    JesseM

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    What do you mean "a 15% or even a 45% different spin"? Spin is a quantum property where whenever you make a measurement of spin on a particular axis, the measurement always collapses the wavefunction in such a way that the particle is 100% spin-up or 100% spin-down on that axis.
     
  8. May 18, 2007 #7
    Hmm, I think that from what I've been reading that the techniques for actually measuring spin up and down are with the use of a device that has opposing magnetics. From what I understand (which could be wrong) the spin up and down come from the fact that as the particle flies through the magnets it is either deflected up or down which is why they say it has spin up or down. So my point is, that when the particle flies through, we have absolutely no way to determine if the actual spin is 100% up, or has a 10% deflection. All we know for sure is that it passes through our device and is deflected up or down.

    So unless there is some way to measure things exactly I would say my statement has just as much relevance as to say things are always 100% up or down. To further prove my point, you can take the device and rotate it to say 45% and a certain percentage of the particles still moves through the device while a certain percentage are blocked. This would seem to say that 100% up or 100% down is not exactly correct. Its all related to the orientation of the device itself that is measuring the particles as they pass through.

    Are there other methods of measuring these things that I need to read up on?

    Also: To clarify the purpose of this post, its not to bash anyone or QM. I am only confused due to people stating as fact things that appear on the surface to be completely unknown. Blame my current state on all the books I've read... :-) I just really want to understand this stuff...

    Thanks for you time,

    glenn
     
  9. May 18, 2007 #8

    DrChinese

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    As has been explained, there IS nothing surprising about the results you describe above IF that was what was going on. This situation was originally described in the 1935 EPR paper (in a little different manner).

    But your example is one that is referred to as LOCAL REALISTIC. In such a theory, it doesn't matter how each of the 2 observers' measurement settings are oriented - the results are always predetermined for any angle. Bell discovered that this could not be true IF the cos^2(theta) held. And this is the significance of the Bell tests.

    Specifically, your hypothesis requires that all possible outcomes have a likelihood of occurance in the range of 0 and 100%. It turns out that some of these outcomes actually would occur on the order of -10% of the time. So your hypothesis fails. QM does not make the same assumptions you do, so it does not have this problem.
     
  10. May 18, 2007 #9

    DrChinese

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    Electrons are tested for spin with magnets sometimes, while photons are tested using polarized crystals of varying types.

    But your idea about spin is way off. If you take a particle with measured spin oriented at 0 degrees - and then test its spin at 0 degrees a hundred more times, it will still show as having that orientation each time. It will NOT have a 50% chance each time. So the idea that there is some kind of range is invalid. If your idea was correct, it would have been obvious a long time ago.

    And, of course, your idea continues to run afoul of Bell's Theorem which rules it out completely.
     
  11. May 18, 2007 #10
    Ok, So you are saying that the measurement of a particle doesn't change its orientation? Since earlier we were saying that we can only measure the particle once because it decouples it with the other.

    Also, I'm still confused about my angle point because you are assuming I'm talking about a single particle measurement over and over. I'm actually talking about the following: 1 particle route through 1 device. You sent 1000 particles through the device: 1) Do you see all 1000 come through? Reason for question is that from what I've read you do not. 2) if you do see them all come through can you guarantee me that all 1000 have exactly 0 degree spin up? Or could one have been 5% off dead center and another 10%? I don't see how you can tell me since a polarized lens or a magnet are not going to block all particles except those that meet top dead center.

    From your first post above: The measurements are always what is expected? First of all are you telling me someone has captured more than a small percentage of the particles to test? The article you sent specified 5% was as high as they got on their captures. Secondly, Can we change the line of the conversation to only discussing your point of expected results?

    Could you please give me an example of what would be different between QM and classical in the following example so I can better understand where the strangeness enters.

    Classical: I say that if you successfully entangle two particles that the following will happen: (keeping in mind its possible you think you entangle but they may not in fact be) I say that as the two particles pass through detectors that are oriented the same way that they will show the opposite results (ie: spin up on one and down on the other). If they are at different angles then they will show different results but based off of the same spin up down orientation.

    So what exactly is seen? What is the specific point that QM describes that can not be described in classical physics?

    Thanks again for you time, sorry I'm being so hard headed... :-)

    Also, I am correct when I state that two entangled particles each spin opposite each other aren't I? Or do they both spin up and I have gotten myself confused?

    glenn
     
  12. May 18, 2007 #11

    jtbell

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  13. May 18, 2007 #12

    JesseM

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    When you measure a particle's spin on a given axis, it collapses its wavefunction so it's totally spin-up or spin-down on that axis, but there's a random element to what you'll find if you then measure on a different axis (the probability of collapsing into spin-up or spin-down on that axis depends on the angle between it and the first axis). So if you measure on axis A, then measure again on axis A, you're guaranteed to get the same spin on the second measurement as the first (and will continue to get the same spin if you measure on A more times); but if you measure on axis A, then measure on a different axis B, then measure on A again, you may get a different spin on the second A-measurement than you got on the first.
    What you see in QM but would never see in classical physics is violations of Bell inequalities. On another thread I posted an analogy to help explain what this means:
     
  14. May 18, 2007 #13

    DrChinese

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    I'll do my best, but you are all over the place. :smile: Because you don't follow a single point all the way through, it makes it difficult to drive the point all the way home.

    1. No one knows ACTUALLY what happens. We know that it appears to happen AS IF a measurement of one instantaneously affects the other so it matches. But whether or not that actually happens is a guess. Maybe there is some other mechanism (but not LOCAL REALISTIC) at work.

    2. Not sure what you mean. In a normal stream of (randomly) entangled particles, 50% will pass through regardless of the orientation. Once a photon passes through a polarizer lens, it is oriented at that angle.

    3. All of the properly entangled pairs are measured. Keep in mind that most photons entering the PDC apparatus do NOT turn into an entangled pair. They come straight out and are diverted to aplace where they can be ignored. Many pairs come out entangled, but they are not at quite the proper wavelength. These too are diverted. The successful pairs are then tested. Most of these are seen, but a small percentage yield a detection on one side without a detection on the other. This is due to detector efficiency.

    Keep in mind that most Bell tests use polarizing beamspitters rather than filters. Therefore, the photons on each side are seen as either hortizontal or vertical (H or V is arbitrary).

    4. I keep trying to explain that your classical description FAILS in actual experiments because there are hidden assumptions. You are ignoring the hidden assumptions. Specifically, these are detailed in Bell's Theorem. If you want to see the assumptions and the related math for yourself, go to my page on the subject:

    Bell's Theorem with Easy Math

    By the way, this page follows the logic of Mermin per the article cited by JesseM, but may perhaps be easier to follow... or not.

    5. That is a good question. In Type I PDC, the photons have identical polarization. In Type II PDC, the photons have orthogonal polarization, which is to say they are 90 degrees apart. Orthogonal is also referred to less precisely as "crossed" from time to time.

    I hope this helps.
     
  15. May 18, 2007 #14
    JesseM,

    Thanks for the information. I understand in theory the point, however, I'm still very much confused as to what specific element of the noted test falls into this card game. First of all, we are responsible for entangling the particles which does not appear to me to be as simple as choosing randomly 2 playing cards. We are basically aligning those particles to each other before we start our test.

    Next, unlike the game, we can't sit and play over and over with the same particles to see what happens. After we play once we must throw away the 2 cards and draw another 2. Because of this we loose the ability to get anything useful out of the game.

    Next we have the issue with the ending measurements (when detected) being of the same relationship and we therefore imply that the two particles have communicated with each other faster than the speed of light would have allowed. But what I'm trying to get in my head is exactly what magic thing is happening here that I can't provide an explanation for in the classical sense.

    I am not arguing with you, if you actually could show me the cards or a box with two particles in it that acts the way all the books and articles I've read explain it to work, then I'd be very intrigued indeed. However, when getting down to the nuts and bolts there are no 2 boxes, there are no cards. There are only 2 particles that we setup to run a test on by entangling them through whatever means, then send on their way. There is only a single test that can be run on them before the relationship between them is broken.

    This all makes perfect sense to me. I'm still trying to find the part that doesn't make sense. Can you explain it without actually getting into boxes and card tricks but using only 2 particles that can only be tested once?

    Again, using your example I agree completely that something strange is going on, but I'm fighting with understanding what in this test would lead to this conclusion.

    Thanks,

    glenn
     
  16. May 18, 2007 #15
    Dr Chinese,

    Thanks for all the info, I'll take a look at your site and get back with you guys tomorrow if I have any more questions. I'm sorry I'm jumping around as you said, I'm trying to stay focused on this one issue but there are a few different aspects of it...

    Talk to you tomorrow and thanks again for your time.

    glenn
     
  17. May 18, 2007 #16

    JesseM

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    I didn't say anything about "randomly choosing" the cards. In fact, since whenever we both choose to scratch the same box on a given trial, we always get the opposite answer, it's obvious that the cards cannot be generated in a completely random way. If you assume that there is a definite fruit behind each of the three boxes on a given card, then in order to explain this correlation, you must assume that whoever is sending us these cards is always taking care to send me a card with the opposite fruit behind each box as the one that's sent to you--if my card's "hidden fruits" are a cherry behind the left box, a lemon behind the middle box, and a lemon behind the right box, then your card's "hidden fruits" must be a lemon behind the left box, a cherry behind the middle box, and a cherry behind the right box. If the person sending out pairs of cards wasn't taking care to correlate them in this way, how else could you explain the fact that on every trial where we both choose the same box to scratch, we always get opposite fruits, even if we repeat the experiment for thousands of trials?
    But the correlations that violate Bell's theorem have nothing to do with measuring the same particles over and over. Rather, they involve doing the experiment over and over with a new pair of entangled particles on every trial, and noting that on every trial where both experimenters happen choose the same axis to measure, they always get opposite results for the spin of their particle. This is just like the scratch lotto game, where you do the experiment over and over again with a new pair of cards on each trial (imagine the cards self-destruct after you reveal one box), and you note that on every trial where both of us chose to scratch the same box on our respective cards, we found opposite fruits behind that box.
    It's not clear that you're actually understanding the experiment I'm proposing with the cards. But yes, using quantum physics you could simulate these results--say instead of an actual physical card, on each trial our computer monitors each display an image of a card with three hidden boxes, and we click on a box to reveal the fruit there, after which the card disappears from the screen and we then see a new card with three hidden boxes on the next trial. If our computers were hooked up to measuring-devices measuring the spin of entangled particles, and our choice of which box to select determined which angle the device would be set, and which fruit the computer displayed would depend on whether the particle was measured to be spin-up or spin-down on that axis, then you could get exactly the results I described--whenever both of us clicked the same box on a given trial we'd always get opposite fruits, yet on the set of trials where we clicked different boxes, we'd get opposite fruits less than 1/3 of the time. If the computers weren't allowed to use quantum effects to determine what fruit to display, though, this pattern would be totally impossible to explain classically! Read over my explanation again if you don't see why.
    Again, although a given pair of entangled particles are only measured once, the violation of Bell inequalites which violates classical expectations is based on the statistics when you repeat the experiment many times with multiple pairs of entangled particles.
     
    Last edited: May 19, 2007
  18. May 19, 2007 #17
    Looking at related experiments like the delayed choice quantum erasor can help you believe that the quantum states aren't pre-set at emission. This experiment doesn't set out to prove this antecedent.
    The conclusion is false. You don't have to use the same coin to do probability tests on coin-flipping. Again, understanding previous experiments will help. You're jumping into the middle of the QM story.
    See comment #1. You first have to be convinced that the photons' states are indeterminate before detection. This is a tenent of QM.

    It follows from that if the states of the photons are indeterminate to start with, then when you collapse the wave function of the first particle, something happens which causes a property of the second particle to be determined as it is flying to the second detector. That something is the entanglement of the particular (i.e. spin) property of the two photons. It's as if information is exchanged, but faster than the speed of light.
     
  19. May 19, 2007 #18
    You're thinking about "relation" in the wrong way. There is no rod connecting them. Also, you haven't gotten them to "spin" at all, until they reach the destination. All they have are the words, "spin me the same way as you spin the other ball", written on them as instructions to the catcher.
    No, it's not.
    Yes it is.
    You said it, we *related* their spin. You don't seem to understand "related", though.

    Here is another way to look at the situation. Consider the two photons as part of a computer program. Photons have a class which defines their behavior. You create two photons/objects using the photon/class-template, and each has an independent set of variables and functions. Accessing one of the variables calls a random number generator to set the variable if the value is "undefined", so you can expect that variable, "spin", has no correlation between the two photon/objects.

    Now, to entangle the "spin" variables, immediately after you create the photon/objects, you override the accessing method to call the random number generator, get a random value, and set the "spin" variable of BOTH photon/objects to that value (or it's inverse)[if undefined]. You have now "related" the [spin] variable of the two photon/objects.

    The photon/objects continue merrily in your execution loop, until one gets a "detector" event, accesses the appropriate variables (i.e. "spin"), and then is destroyed. You can see that the photon/object remaining in the loop now has a value for it's "spin", and that will be the value delivered to the detector.

    In the program, there is no delay between setting the two values, in terms of the loop counter, which holds the "time" value for the photon/objects (disregard the CPU clock cycles). For real photons and everything else, there is supposed to be a delay based on the speed of light.

    This is a pretty direct analogy [better than cards, coins, baseballs] to what QM tells us about entanglement, IMHO.
     
    Last edited: May 19, 2007
  20. May 28, 2007 #19
    I think I understand what you are saying but I really don't see how your example makes the "relate" process any different from my point. By related, they have something to do with each other.

    Definition: Correlate: to place in or bring into mutual or reciprocal relation; establish an orderly connection

    Definition: Entangle: To twist together or entwine into a confusing mass

    Whether you want to say things don't exist or do exist at the point they are entangled or only later when they are actually measured is a ridiculous (or would seem) argument since you have absolutely no way to prove it true or false.

    So we just have to stick with the fact that they are entangled at the source, or at the point of our constructor for our two classes. However, even in your example, at the point of calling our detect function, you have agreed that the two particles are in fact entangled at this point which is the only point I'm concerned with.

    So here are a couple questions to make sure I understand this experiment fully, then I"ll ask my next question.

    1) When the particles are created and begin their path through whatever medium we've setup for our test, they are entangled so as to share some relationship to each other?

    2) When we measure one particle we find that the other immediately snaps to an opposite orientation of the first?

    3) The single item on our list that you are saying can not be explained through classical physics is not the effect of the two particles sharing their relationship, but the fact that 25% of the time they do when they shouldn't.

    To further explain my question: All material I've read on the experiment describes 3 switches on each device that are each chosen completely randomly. 100% of the time when the switches are the same, we get a matching light. Since we have 3 switches and two boxes, we should expect to get a 33% matching rate and a 66% non matching rate. However, what the test reveals is a slightly more matching rate. Its described as being 50% match and 50% non match. It says 25% but would seem 17% would be more exact unless I'm doing my math wrong.

    So we're mainly concerned with this extra matching of the lights when the switches were NOT set on the same marks?

    Before we continue I want to make sure I'm understanding the test.

    Thanks,

    glenn
     
  21. May 29, 2007 #20

    JesseM

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    Yes, experiments to test Bell inequalities involve pairs (or occasionally triplets or more) of entangled particles.
    Only if both experimenters set their detector at the same angle are they guaranteed to measure opposite spins.
    25% is just a number I picked because it looks nice, all that's important is that it's less than one third. And it's not that the number is less than one third on all trials, it's that it's less than one third on the subset of trials where the experimenters have chosen two different angles.
    Well, only if you set it up so that you get a "matching light" when the spins are opposite rather than the same...but yes, as long as you define "matching" this way you'll get 100% matching when the angles are the same.
    Not necessarily, classically the matching could be anywhere between one third and 100%. Imagine that on each trial, the three "hidden spins" on the angles of the detectors are always +++ for one particle, and --- for the other. This will ensure that when both experimenters choose the same angle, they always get opposite spins, but it will also ensure that even when they choose different angles they always get opposite spins. On the other hand, if the source always creates particles in non-homogeneous hidden states like +-+ and -+-, then when they choose different angles they'll get opposite spins one third of the time. If the source sends out some mixture of pairs that are in homogeneous hidden states and pairs that are in non-homogeneous hidden states, then when they choose different angles they'll get opposite spins somewhere between one third and 100% of the time.
    Who said it was described as 50% match and 50% non match? It all depends on what three angles you pick and on the probability of getting opposite results for each possible pair. For photons, for any two angles X and Y the probability of getting opposite results is the cosine squared of Y - X. So suppose A = 0, B = 60, and C = 120. Then there are 6 possible cases where they choose different angles: experinter 1 chooses A and experimenter 2 chooses B [1A, 2B], experimenter 1 chooses A and experimenter 2 chooses C [1A, 2C], and so on for [1B, 2A], [1B, 2C], [1C, 2A], [1C, 2B]. So, total probability of getting opposite spins when different detector settings are chosen would be 1/6*P(opposite spins given [1A, 2B]) + 1/6*P(opposite spins given [1A, 2C]) + 1/6*P(opposite spins given [1B, 2A]) 1/6*P(opposite spins given [1B, 2C]) + 1/6*P(opposite spins given [1C, 2A]) + 1/6*P(opposite spins given [1C, 2B]). Given the angles above and the cosine squared formula, this works out to 1/6*(0.25) + 1/6*(0.25) + 1/6*(0.25) + 1/6*(0.25) + 1/6*(0.25) + 1/6*(0.25) = 0.25
    You're concerned with fewer "matches" than expected classically, again assuming a "match" means the spins were opposite.
     
    Last edited: May 29, 2007
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