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Hidden Variables and Quantum Mechanics

  1. Jul 8, 2014 #1
    I'm reading up on interpretations of quantum theory, and I just came across Bell's theorem, which is confusing me. My main concern is this:

    Why would quantum mechanics predict something different than hidden variables?

    I hope that question is coherent enough. I'm not sure if I'm using the correct lingo. But basically I'm not seeing why "spooky action at a distance" would allow for different outcomes than local communication between systems, or just a situation where the values of aspects of the systems are defined, and we just can't know them.

    Thanks in advance, and I'll be happy to try and explain my confusion better if necessary.
     
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  3. Jul 8, 2014 #2

    atyy

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    At least for non-relativistic quantum mechanics, quantum mechanics does not predict something different from hidden variables.

    Quantum mechanics does predict something different from local hidden variables.
     
  4. Jul 9, 2014 #3
    It cant be local and cant be less then C , so for some of us it hidden , you shold look for back in time communication
     
  5. Jul 9, 2014 #4
    Ok, so how would quantum mechanics predict something different from local hidden variables? Does it have to do with when the collapse of the vector state happens?
     
  6. Jul 9, 2014 #5

    atyy

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    In the usual demonstration that quantum mechanics violates the Bell inequalities, wave function collapse is not needed. The parts of QM that are needed to are non-commuting observables and entanglement.

    The CHSH inequality, which is one type of Bell inequality, is presented in sections 4.1 and 4.2 of Scarani's lecture notes http://arxiv.org/abs/0910.4222v1. Those sections contain an explanation of what is meant by local hidden variables, and why violation of the inequality is indicates that local hidden variables are not possible, and a calculation that shows that quantum mechanics violates the inequality.
     
    Last edited: Jul 9, 2014
  7. Jul 9, 2014 #6

    DrChinese

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    QM does not, in and of itself, predict something "other than" hidden variables. I would say it is silent on the point. Deductions (via no-go theorems such as Bell) strongly imply that hidden variables don't exist or have extremely unusual properties ("grossly non-local").

    Experimental evidence is quite strong too (though not absolute). Despite best efforts, no one has been able to discover a root cause to random outcomes of any quantum observations on non-commuting bases.

    Finally, the idea that an observation is merely the updating of local information in an otherwise realistic world has been generally discredited.
     
  8. Jul 9, 2014 #7
    The random outcome come from part of the many worlds and the communication come from back in time allso from the many worlds , this way its statistic
     
  9. Jul 9, 2014 #8
    The rules of quantum mechanics have been developed from observations. It explains what happens - not why - and without regard for whether it can be readily envisioned or explained.

    So when two entangled particles are measured, the results are coordinated as if the particles knew what combination of measurements were going to be made before either particle reached the measuring apparatus. When the experiment is really run, that is what really happens.

    The QM rules that predict this were developed based on other experiments. One of the "real physicists" on this forum can check my assertion of what that rule is:

    The rule applies to two entangled particles that have separated and are moving away from each other. The specific rule is that when the spins of these two particles are measured and the axis of measurement is the same, the particles will always appear to have opposite spins. When the measurements are taken on axis 180 degrees apart, they will always agree. For other angular differences, compute the square of the cosine of the angular measurement difference. This will give you the portion of the time when the measurements will agree or disagree - depending on whether they are closer to 180 degrees or 0 degrees apart. The rest of the time, the measurements will be independent.

    Anyway, when that rule is applied to the experiment that Bell described, the results predicted by QM are shown (by Bell) to be inconsistent with any explanation based on local hidden variables. The results are very sensitive to being able to successfully measure a high percentage of the particles - since local hidden variables can explain the QM results if you allow those hidden value to affect the measurability of the particle. However, this experiment has been performed with ions where the measurement rates were about 99%.
     
  10. Jul 9, 2014 #9

    Alright, this is where I'm confused. In what way would local hidden variables allow for different outcomes than QM? Don't the entangled systems need to "agree" with each other in either case? If we let a particle break down into two photons that travel opposite directions, for example, how would local hidden variables cause the photons to make different "choices" than QM would? Because in both cases we just end up using conservation laws to make the photons agree, right?
     
  11. Jul 9, 2014 #10

    DrChinese

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    Nope! That is where Bell comes into play. Your analogy works as long as certain angle settings (notably the same two) are used. But it falls apart when other angle settings are used (such as 120 degrees apart). You cannot construct a data set - even one hand picked) in which the QM predictions would be matched using the logic you adhere to.

    This is why Bell is so important. You can easily see for yourself. All you need is about 10 or 20 examples that you make up yourself. You will find that (using your example) you cannot construct a result set that matches the QM prediction of a 75% match rate for 120 degrees difference UNLESS you know in advance WHICH angles you are measuring. For example, consider these 3 pairs of angles:

    0, 120
    120, 240
    240, 0

    To match QM and experiment, you must know which of the above are to be measured in each trial. This is called "observer dependent" reality. In EPR terms: reality "here" is a function of the nature of a measurement "there" (i.e. spooky action at a distance).

    If you don't know which of the 3 pairs are to be measured, your best rate is 66.6% which is simply different than experiment and therefore cannot be correct. That is for Type II entangled photon pairs.
     
  12. Jul 9, 2014 #11
    Thank you! Things are clearing up. What do you mean by "know in advance which angles you are measuring"? Like, you need to know not only the difference in the pairs of angles, but the actual values of the angles in the pair? How would the values of the angles have an impact on the experiment separate from the impact of the simple difference between the angles?

    Sorry, I don't yet have any formal education in QM, so this is all relatively new (and very strange) to me.
     
  13. Jul 10, 2014 #12

    Nugatory

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    The difference between the angles is all that you need to see the problem.

    Try this link: http://www.felderbooks.com/papers/bell.html, see if that help further clear things up.
     
  14. Jul 11, 2014 #13
    I think my lingering question is this: why would something different happen depending on when two particles "decide" what property to exhibit? For example, why would two photons deciding how to be polarized when they reach two lenses be different from them deciding how to be polarized before they reach the lenses?

    I feel like I'm overlooking something important. It seems to me like the same "options" would be available to the photons no matter when they collapse into a defined state. With QM, do they get to always pick a state where one photon definitely makes it through a polarized lens, or something like that?

    Thanks for the help, everyone. Nugatory, I am reading the page you posted now.
     
  15. Jul 11, 2014 #14
    When studying the covariance What we can write is obviously : [tex]cos(a-b)=\sum f_i(a)f_i(b)[/tex]

    With f1=cos, f2=sin it is a simple trigonometric identity.

    But this is not equivalent to writing [tex]\cos(a-b)=\int A(a,v)B(b,v)\rho(v)[/tex]

    Since [tex]\int A(a,v)\rho(v)\leq 1[/tex] whereas [tex]\sum f_i(a)=\sqrt{2}[/tex]
     
  16. Jul 11, 2014 #15
    Nugatory, the page you posted helped A LOT. Thanks!

    So, I understand now how the lack of objective reality would cause disagreements with Bell, but why would faster-than-light communication between particles do this? Using the example from that page (http://www.felderbooks.com/papers/bell.html), the electrons are released, the detectors are the same, one electron reaches its detector first and makes a decision, and this decision causes the other electron to make the same decision, right?

    So, wouldn't a) the second electron carry on through its detector with that property or b) the second electron has changed by the time it gets to its detector, in which case what we care about wouldn't be spooky action at a distance, but the lack of a defined state for the electrons at any time other than when one or both of them are being measured?

    I hope that makes sense. I will try to clear it up if need be.
     
    Last edited: Jul 11, 2014
  17. Jul 11, 2014 #16

    DrChinese

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    No one really knows why, and no one really knows how. That is why it is something of a mystery, which makes it all the more interesting.
     
  18. Jul 11, 2014 #17
    So we do at least know that the data we actually collect disagrees with Bell's theorem, right? Then we make a conclusion that "spooky action at a distance" is at play. I can see why rejecting objective reality would make our worldview fit with the experimental results better, but why exactly do the results lead us to the conclusion of faster-than-light communication?
     
  19. Jul 11, 2014 #18

    DrChinese

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    Technically you only need to accept one or the other (reject realism or reject locality). Although sometimes it is difficult to draw a distinction.
     
  20. Jul 11, 2014 #19

    Nugatory

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    To be precise, we know that the data that we collect disagrees with Bell's inequality. Bell's theorem shows that any theory in which the results of a measurement are determined by local and realistic properties (but see the note below) of the thing being measured must agree with Bell's inequality. Therefore, no such theory can be correct.

    [note: Actually Bell's theorem does not speak of "local and realistic properties" - that phrase is rather too slippery to use in a mathematical proof. Instead Bell starts with a mathematical assumption about what variables could affect the results of a measurement

    Again, that's not quite right. Bell's inequality applies to theories that are both local and realistic; a theory that is local but not realistic, or realistic but not local, or neither realistic nor local, can violate the inequality. Thus experimental results that show that the inequality is violated can be explained either by a faster-than-light influence traveling from the site of one measurement to other (that is, not local) or by abandoning the idea that a property not measured must still have a definite value (that is, not realistic).
     
  21. Jul 12, 2014 #20
    And I understand why the lack of realism would violate the inequality. But what's unclear to me at this point is exactly HOW faster-than-light influences would violate it as well. I'm still missing something...
     
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