Bell's theorem proof. Does it really proofs anything?

  1. So here is this thing that i really really can not agree with (regarding experiments)! What Bell's theory states (correct me, if i am wrong) and experiments with SPOT detector tend to prove is, that measurement of spin of one twin-light photon affects spin of other. Well - if we assume that then results of this experiment agree with predicted results of theory. However - i see no way how this theory rules out theory of "hidden variable".

    One can also assume, that both twin-photons have defined spin from very beginning. If we describe spin not as "angle" but as most-highest spin direction, then these test results would also describe theory in which photon carries more information than just it's spin (as angle). In such case this measurement with angles 60 degrees made of -30 and +30 (50% and 50%) actually is same measurement as 0 and 30 degrees so as expected, error is 25% (100 - 75%).

    Said that - this experiment proves NOTHING about measurement of spin impacting spin of other photon.

    http://quantumtantra.com/bell2.html

    Please help me out with this!

    Sincerely,
    Beef
     
  2. jcsd
  3. I think you should stop worrying about angles. Looking at the diagram showing the 4 different measurement possibilities, there is nothing which says the properties of the photons are represented as angles. It's the detectors which have different possible angle settings. But even then the angles are not vital to the argument. Alice could have a detector with settings marked 0 and + and Bob with - and 0. Then the 4 possible settings and the difference between results are:

    AB : Difference
    00 : 0%
    +0 : 25%
    0- : 25%
    +- : 75%


    Assuming locality, the difference for +- can't possibly be more than the sum of the differences for +0 and 0-
     
  4. Please be more "specific". I really did not understand your idea. What i see is - this could be easily explained by photons having "angle vector" not by detectors by any means affecting measurement results.

    I see this experiment results - conclusions as misintrepreation of cause and effect.

    Beefs
     
  5. DrChinese

    DrChinese 5,664
    Science Advisor
    Gold Member

    The problem you face is that there is NO data set which you can provide which will match experimental results. I think if you attempt to produce one, you will quickly see the problem. Any rule set you provide - in which the hidden values are independent of the measuring device settings for Alice and Bob - will not be able to match the predictions of QM.

    So that means that either there are no predefined values, or there is FTL communication between the twins.
     
  6. I strongly disagree! In fact - there is data set and rulles, that i can apply, which will exactly match experiment results! Could you please describe experiment results, because ones provided in that web page i just posted seems too trivial to work with. Any normal distribution function for spin value would predict these results!

    Edit: In fact - to work properly with these results one would also need exact placement of sensors used in this experiment. As well - one would need exact knowlege of crystal used for directing polarized light. What i see from these results - NOTHING! And i mean - NOTHING! I see two photons with same spin being analyzed twice! I see big misinterpretation of data. And i see BIG BIG problems with logic used there. Either i am totaly stupid or something is very wrong here! (btw - i am not THAT stupid)
    Sincerely,
    Beef
     
    Last edited: Dec 6, 2010
  7. Cthugha

    Cthugha 1,703
    Science Advisor

    Well, the first thing that comes to my mind is, that it might not be the best idea to discuss Bell's theorem based on the information on a page entitled quantum tantra, run by a guy who claims quantum tantra to be a brand new way of doing science and who also claims to be the author of books with high credibility titles such as "Quantum Reality", "Faster Than Light" and "Elemental Mind". I suggest you learn a bit about Bell's theorem from a more credible source (the link in DrChinese's signature for example will take you to one) and then return to discuss based on the complete story.
     
  8. Yes! Exactly!
    But anyway - i see this as simplified explanation. Problem is - i am not willing to accept this on results based on that page. How i see photon is (lets look at it from front) as wave front traveling through space. Polarized wave would mean, that this round wave is "cut". If so - these experiments can be explained by "hidden variable" which is "polarization" strength for different angles. Are there any experiments which prove, that photon has single polarization direction (thus - it is not field where polarization actualy is vector of many summs?)

    Please help me out since this makes NO sense to me at all!
    Beef
     
  9. JesseM

    JesseM 8,491
    Science Advisor

    From an old post, a simple analogy I came up with illustrating why assuming pre-existing values for the variables doesn't work:

    Suppose we have a machine that generates pairs of scratch lotto cards, each of which has three boxes that, when scratched, can reveal either a cherry or a lemon. We give one card to Alice and one to Bob, and each scratches only one of the three boxes. When we repeat this many times, we find that whenever they both pick the same box to scratch, they always get the same result--if Bob scratches box A and finds a cherry, and Alice scratches box A on her card, she's guaranteed to find a cherry too.

    Classically, we might explain this by supposing that there is definitely either a cherry or a lemon in each box, even though we don't reveal it until we scratch it, and that the machine prints pairs of cards in such a way that the "hidden" fruit in a given box of one card always matches the hidden fruit in the same box of the other card. If we represent cherries as + and lemons as -, so that a B+ card would represent one where box B's hidden fruit is a cherry, then the classical assumption is that each card's +'s and -'s are the same as the other--if the first card was created with hidden fruits A+,B+,C-, then the other card must also have been created with the hidden fruits A+,B+,C-.

    The problem is that if this were true, it would force you to the conclusion that on those trials where Alice and Bob picked different boxes to scratch, they should find the same fruit on at least 1/3 of the trials. For example, if we imagine Bob and Alice's cards each have the hidden fruits A+,B-,C+, then we can look at each possible way that Alice and Bob can randomly choose different boxes to scratch, and what the results would be:

    Bob picks A, Alice picks B: opposite results (Bob gets a cherry, Alice gets a lemon)

    Bob picks A, Alice picks C: same results (Bob gets a cherry, Alice gets a cherry)

    Bob picks B, Alice picks A: opposite results (Bob gets a lemon, Alice gets a cherry)

    Bob picks B, Alice picks C: opposite results (Bob gets a lemon, Alice gets a cherry)

    Bob picks C, Alice picks A: same results (Bob gets a cherry, Alice gets a cherry)

    Bob picks C, Alice picks picks B: opposite results (Bob gets a cherry, Alice gets a lemon)

    In this case, you can see that in 1/3 of trials where they pick different boxes, they should get the same results. You'd get the same answer if you assumed any other preexisting state where there are two fruits of one type and one of the other, like A+,B+,C- or A+,B-,C-. On the other hand, if you assume a state where each card has the same fruit behind all three boxes, so either they're both getting A+,B+,C+ or they're both getting A-,B-,C-, then of course even if Alice and Bob pick different boxes to scratch they're guaranteed to get the same fruits with probability 1. So if you imagine that when multiple pairs of cards are generated by the machine, some fraction of pairs are created in inhomogoneous preexisting states like A+,B-,C- while other pairs are created in homogoneous preexisting states like A+,B+,C+, then the probability of getting the same fruits when you scratch different boxes should be somewhere between 1/3 and 1. 1/3 is the lower bound, though--even if 100% of all the pairs were created in inhomogoneous preexisting states, it wouldn't make sense for you to get the same answers in less than 1/3 of trials where you scratch different boxes, provided you assume that each card has such a preexisting state with "hidden fruits" in each box.

    But now suppose Alice and Bob look at all the trials where they picked different boxes, and found that they only got the same fruits 1/4 of the time! That would be the violation of Bell's inequality, and something equivalent actually can happen when you measure the spin of entangled photons along one of three different possible axes. So in this example, it seems we can't resolve the mystery by just assuming the machine creates two cards with definite "hidden fruits" behind each box, such that the two cards always have the same fruits in a given box.
     
  10. No!
    That would not be violation at all! In fact - there are rulles! You can not seperate those two systems! There is no violation! There is ERROR in logic!

    So you say - when they picked different boxes, they found out that they only got same fruits 1/4 of time? But of course! Because it is a rule that same boxes have same card on them! BUT also it is a rule, that two boxes have different card on them! Lets quickly go through all possilbe combinations -
    (aa), ab, ac, ba, (bb), bc, ca, cb, (cc). 9 options. 1/3 of them has same card (match). But we have to take out these matches since we are not looking at them.
    So we are left with (ab?, ac?), (ba?, bc?), (ca?, cb?) - so - one would expect, that we should get pretty good chance that either of them maches. HEY - but we have FORGOTEN about another rule! There allways are two different pairs because of nature of photons!
    (next post)
     
  11. DrChinese

    DrChinese 5,664
    Science Advisor
    Gold Member

    Your problem begins with the fact that such explanation does not match experimental results. You will see this as you answer a series of questions.

    If a photon is polarized at 0 degrees, what is the likelihood that it will pass a polarizer at 45 degrees? Is that too pre-determined (even if we do not whether it will or won't) ?

    -------------------

    By the way, your ongoing commentary about "Either i am totaly stupid or something is very wrong here!" is out of place. It is common courtesy to post politely while you are learning about a subject. The fact is, Bell's Theorem has attracted the interest of many professional physicists. Over 1000 papers are written about it annually, many involving complex experiments as well.
     
  12. I am totaly sorry about "Either i am totaly stupid or something is very wrong here!". It seems i have "missed" Ballmer's peak!
    I am really open minded so i allways tend to disagree. This is how i work! I will provide my proof by writing experimental programm so you can see what i mean!
    Please be patient!
    Beef
     
  13. Cthugha

    Cthugha 1,703
    Science Advisor

    You will notice that this "easy" explanation will fail as soon as you consider putting polarizers in at arbitrary angles. There is a difference between what you would expect if there was a predefined value of the polarization as compared to having none for testing several combinations of polarizer settings.

    One thing to consider beforehand, as it might save you some time. It is easy to construct a classical HV explanation for some polarizer setting matching the experimental results. However, it is impossible to do the same when trying to match the experimental results using the same initial state, but many different polarizer settings. But you will soon find out yourself, which is a good way to learn stuff.
     
  14. BTW - before i go on with program - can i assume that A B and C were ment 0 +30 and -30 measurements?
    Beef
     
  15. JesseM

    JesseM 8,491
    Science Advisor

    If the boxes on each card were printed with different fruits hidden behind them, then there would be a nonzero probability that Alice and Bob could pick the same box but get different results. But as I said at the beginning of the example, that never happens:
    The point is that if we assume each box had a pre-determined fruit behind it (and that the machine printing each pair of cards didn't know in advance whether Alice and Bob would choose to scratch the same box or different boxes), then these two observations are inconsistent: 1) on the trials where they randomly choose to scratch the same box, they always see the same fruit, and 2) if they randomly choose different boxes (equal probability of each one), then they only see the same fruit on 1/4 of the trials. 1) or 2) could be true individually, but the "pre-determined fruit" theory cannot possibly explain how both could be true simultaneously.
     
    Last edited: Dec 6, 2010
  16. DrChinese

    DrChinese 5,664
    Science Advisor
    Gold Member

    Sure, those are 3 good angle settings to use. Don't forget there are other requirements too. Such as same answer for identical settings at ANY angle if the pair is polarization entangled.

    So you should have Entangled State statistics for polarization entangled pairs (cos^2 rule) and Product State statistics for non-polarization entangled pairs (entangled pairs where the polarization is known). This second group may not seem possible, but each Type I PDC crystal actually produces this second group (Product State). You get the first group by combining the outputs of 2 Type I crystals oriented 90 degrees apart.

    Now, using your logic, you should not be able to combine known output streams - with their predetermined and known values which never exceed 75% matching (averaged) - and get something that exhibits qualitatively different behavior. That being 100% matching. That is because superpositions do not follow ordinary rules. So I am just warning you, there are a lot of hoops to jump through and you have not fulfilled any yet.
     
  17. DrChinese

    DrChinese 5,664
    Science Advisor
    Gold Member

    You can just describe what you are doing rather than writing a program. I doubt anyone is going to literally walk through the code with you. Although JesseM might.

    There are teams out there that have attempted such programs and I have worked with the code of the foremost team in that area (in my opinion). They have needed to go outside of the Bell Theorem to find an angle of attack. Specifically: exploiting the fair sampling assumption. So again, I urge you to learn more before you come to firm conclusion.

    You seem to be operating in reverse in that you form an opinion prior to obtaining suitable information. And then you defend your entrenched position. That is NOT being open minded!
     
  18. Ok - about program - it actually would be very simple. It would generate those ABC random pairs (same) and give them to Bob and Alice. Bob and Alice would then pick random and different "axis" to compare and come to conclusion, that error rate is 50%.

    On second scenario same program would again generate pairs of ABC and give to both Bob and Alice, but this time program would follow rule so that at 75% of all cases B would match A and another rule that in 25% of cases C would match A (and in other cases it wont). Second run would show very different results and we would see them match with predicted by experiment. BECAUSE C and B are dependent on A, not randomly chosen! (or vice versa).

    How i see this is - lets assume we got statue of rectangular cuboid (matchbox). Actually - this statue could also be a cube.

    Lets have two observers at same distance but at different angles. We ask them question - what does it look like more - matchbox or cube? The further (angle) one observer moves from another, the more different figure he "might" observe. But still - both observations (especially if at angle 45%) would only complement each other, not "somehow" change statue it self.

    So - where is the catch?

    Sincerely,
    Beef
     
  19. DevilsAvocado

    DevilsAvocado 1,665
    Gold Member

    DrChinese & JesseM are right. You have probably missed something crucial in EPR-Bell.

    This is nothing to be 'upset' or 'ashamed' of; I did the exactly same thing, when I first heard about this paradox – "Haha! They are missing the obvious! I can solve this easily!"

    But I was dead wrong (of course :smile:)...


    As novice it’s easy to forget these crucial facts:
    • The two polarizers at Alice and Bob are set independently and randomly.

    • The two polarizers at Alice and Bob are separated spatially with no possibility to communicate the settings of the polarizers (at the speed of light between Alice and Bob).

    • Consequently - nothing that happens at Alice can affect the outcome at Bob, and vice versa.

    If you accept these three points, then it’s very hard to refute this:
    When both polarizers are set to , we will get 0% discordance.
    [​IMG]

    Next we set first polarizer at +30º, and the second polarizer at :
    [​IMG]
    The discordance is 25%, according to QM and experiments.

    Next we set first polarizer to , and the second polarizer to -30º:
    [​IMG]
    This discordance will also naturally be 25%.

    Now let’s ask ourselves:

    – What will the discordance be if we set the polarizers to +30º and -30º?
    [​IMG]
    If we assume a Local Reality, that NOTHING we do to one polarizer can affect the outcome of the other polarizer, we can formulate this simple Bell Inequality:

    N(+30°, -30°) ≤ N(+30°, 0°) + N(0°, -30°)

    The symbol N represents the number of discordance (mismatches).

    (The "is less than or equal to" sign is just to show that there could be compensating changes where a mismatch is converted to a match.)

    We can make this simple Bell Inequality even simpler:

    50% = 25% + 25%

    This is the obvious Local Realistic assumption.

    But this is wrong! According to QM and physical experiments we will now get 75% discordance!

    sin^2(60º) = 75%

    Thus John Bell has demonstrated by the means of very brilliant and simple tools that our natural assumption about a Local Reality is by over 25% incompatible with the predictions of Quantum Mechanics and physical experiments.

    To learn more, check out DrChinese’s site and these:

    If you do get some spare time, you can always check out this thread on PF; Is action at a distance possible as envisaged by the EPR Paradox, to realize that most have probably already been said in the 1,500 replies and +58,000 views!! :rofl:


    Good luck! :wink:
     
    Last edited: Dec 7, 2010
  20. No! I disagree!
    Setting polarizers at angle -30% and +30% is same as setting polarizers at angle 0 and 60! But setting polarizers at 0 and 60% gives same result as setting at -30% and 0 (reverse sign).

    Let look at same example, but take different angles - say - -45 and + 45. This will give 100% error (what actually means, that we receive 100% hit only reverse sign). Same as 0 and 90!

    From the other perspective (this wrong one) 45 and 45 gave 50% error which should end up having same 50% error (50% error -> total random and total random x2 is still total random).

    This explanation is against logic (because you operated with absolute values, whilst relation between measurements is clearly relative)
    Beef
     
  21. DevilsAvocado

    DevilsAvocado 1,665
    Gold Member

    Hehe, relax...

    Next advice: Think, at least, twice before you are certain that you have discovered something that thousands of professors missed completely.

    Correct:
    sin^2(0 + 60) = 75%
    sin^2(30 + 30) = 75%

    Wrong:
    sin^2(0 + 60) = 75%
    sin^2(-30 + 0) = 25%

    I will not get into 45º or "Boxes" or "Doctors in Africa", or anything else. The example I gave you is 100% sufficient, if you want to understand what EPR-Bell is all about (in fact John Bell himself used this example when explaining EPRB to the public).
     
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