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Proof of non-locality indep. of conservation law

  1. Nov 13, 2005 #1
    EPR argument makes use of conservation of momentum between two outgoing particles. Einstein boxes argument makes use of conservation of particle numbers. Anybody can tell me an experiment which proves that QM is non-local without invoking conservation law?
     
  2. jcsd
  3. Nov 13, 2005 #2

    DrChinese

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    Entanglement is due to a shared wave function between two or more particles. Conservation is involved because the input particles must have the same totals as the output particles (momentum, spin, etc.), and I cannot think of any EPR/Bell tests that don't make use of this fact.

    As to whether QM is non-local, that is an entirely different subject and one that has recently generated a lot of discussion. :smile:
     
  4. Nov 14, 2005 #3

    Tez

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    No conservation law is "invoked" in the EPR tests done with polarized photon pairs. In as much as the physical processes producing particles will obey conservation laws there will likely always be something conserved lurking around in the production process - but this doesnt necessarily have anything to do with the correlations, as is contained in the original EPR argumentation...

    By using the tricks in:
    http://xxx.lanl.gov/abs/quant-ph/0302111
    one can go further and to Bell/GHZ tests with spin-1/2 particles where the local parties do not even need to agree on a rotational frame of reference, showing that conservation of angular momentum isn't important to the "nonlocal magic" as it were...
     
  5. Nov 14, 2005 #4
    There lies my concern. If such entanglement results can be explained by the fact that conservation law has already imposed a constraint on the possible outcomes we can obtain, why are we still so mystified by such results?

    Is the concept of non-locality invoked just to reinforce (or fill in the loop-holes?) the 'wavefunction is a physical reality' interpretation? In order words, if we dun invoke non-locality, we cannot have the quantum object as a wave interpretation.
     
  6. Nov 14, 2005 #5
    will check this out. if you have a good reference for this, dun mind quote me.
     
  7. Nov 14, 2005 #6

    jtbell

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    But the results of experiments such as Aspect et al. cannot be explained simply by the constraints imposed by conservation laws. It sounds like you're thinking e.g. of the two-particle experiments where the total angular momentum is zero and the two analyzers are aligned in the same direction so that one particle must register "spin up" and the other "spin down". The interesting results come from experiments where the two analyzers are not aligned in the same direction, so that there is some probability for both particles to register the same spin orientation along their respective (different) analyzer directions.

    For a simple thought experiment that illustrates what the "problem" is, see

    http://www.ncsu.edu/felder-public/kenny/papers/bell.html

    You'll probably find it easiest to interpret his results if you assume that one of the analyzers in his setup is wired "backwards" so that both particles produce the same (not opposite) results when the analyzers are aligned in the same direction.
     
    Last edited: Nov 14, 2005
  8. Nov 14, 2005 #7
    Thanks! Let me digest Aspect and Kenny first..
     
  9. Nov 14, 2005 #8

    jtbell

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    For an example similar to Felder's (and which I think was the inspiration for Felder's version), see the following magazine article:

    N. David Mermin, "Is the moon there when nobody looks? Reality and the quantum theory", Physics Today, April 1985, p. 38.

    It's not freely available online, but if you have access to a university library, you might be able to find Physics Today there.
     
    Last edited: Nov 14, 2005
  10. Nov 14, 2005 #9

    DrChinese

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    Try this link:

    "Is the moon there when nobody looks? Reality and the quantum theory"
     
  11. Nov 14, 2005 #10

    DrChinese

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  12. Nov 15, 2005 #11

    Tez

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    Apart from the vague "neighboring measurement" comment in (b) on that page, I think its a bit unclear that you are talking about two separated photons! You may then also want to make it a bit clearer why the two photons have the same value of the hidden variable for the same setting (i.e. the [AA],[BB],[CC] cases). Also saying "at A" and "at B" makes them sound a bit like locations rather than settings (I realise thats pedantry - basically I'm just trying to see how you can ensure the maximum number of people "get it" as it were..)
     
  13. Nov 15, 2005 #12
    Thanks for both the links. Your write-up looks cool, will take a look later. But i had already read Mermin paper. It a pretty easy read. i think i finally have an appreciation of the problem..
     
  14. Nov 15, 2005 #13

    DrChinese

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    Thanks, Tez, I will make these adjustments. Let me know if you have more suggestions... I am trying to create a page that is very easy for someone new to the subject to follow the logic with the fewest possible steps - and the least complicated math too!
     
  15. Nov 15, 2005 #14
    OK, let me summarize my thoughts here...

    1) i previously tried to understand the QM problem from the EPR and Einstein box arguments. The papers i read overstressed the correlation feature which i feel may undermine the true essence of the problem. As Born's explanation to Einstein said: "objects far apart in space which have a common origin need not be independent. i believe this concept cannot be denied and simply has to be accepted. Dirac has based his whole book on this." (is he refering to Dirac's formulation of this two correlated particle problem with the tensor product of two Hilbert space?) In order words, conservation laws has already placed a contraint on the possibles particle states; the correlated result is hence solely derived from this. Nothing else. So whats the big deal? The big deal lies in the reasoning that to obtain such correlated result in experiment, the two particles must in the first place have an instruction set (or reality as coined Einstein) before measurement. Else it will require non local effects to communicate the measurement result of the first particle to the second particle state. Now, before knowing Bell's result and Aspect experiment, i can stick to the conviction that the particles must themselves have an instruction sets. Of course, by holding on to this conviction, i have wrestle with the dilemma as to whether i should regard the probability wave as a state of reality or that it is just a statistical description of the possible result which has already been predetermined before measuremnt. But since i am reluctant to embrace non-locality, i have to go with the latter view.

    2) OK, then here comes the crunch. Bell derived the inequality that must be satisfied for measurements of particles each with an instruction set. And the experiment was conducted by Aspect and has been shown that Bell inequality was not obeyed. Now, i have not really go through the details of Aspect experiment. But even without Aspect experiment, i knew that Bell inequality will not be obeyed. The reason being that Bells derivation of the inequality is based on the context that the instruction set is a one-to-one mapping with the measurement outcomes. Whereas in the experiment using polarization of light, the polarization of the photon and the measurement outcomes is a one-to-many mapping. This is due to the fact that a photon of a given polarization can be projected to more than one possible outcomes (depending on the number on polarization measuremnet axes). Therefore Bell inequality was naturally not obeyed. So now i think i need to understand the physical mechanisms of how a polarization can be projected onto another polarization axis. One should not argue this result independent of the physical mechanism of polarization measurement.

    Am i making any sense here?
     
  16. Nov 15, 2005 #15

    DrChinese

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    Keep in mind that there is no (local) "instruction set" since Bell's Inequality is violated. Also, there is nothing different about photons than other particles. Any non-commuting observables for any particles - position and momentum for example (i.e. where PQ is not equal to QP) - will also lack an "instruction set". The spin characteristics (for photons or electrons) are most easily adapted for creation of a Bell Inequality. However, other similar relations can be seen with other observables.
     
  17. Nov 16, 2005 #16
    Entanglement results can't be explained by conservation laws. (Afaik, there is no 'explanation' for entanglement results.) In the EPR scenario, where the detectors are aligned, then the correlated results would be explained by classical mechanics using the conservation law. But quantum theory treats the situation differently. The combined angular momentum is an interference property of the combined wave functions. (Quantum theory does incorporate the classical conservation laws, but they're not used to calculate the results of correlation experiments ... at least afaik.)

    The 'quantum object' can be interpreted as a wave as long as definite phase relations between different parts of the wave function exist. These exist, and interference is possible, as long as no measurement takes place.

    What happens on detection at A or B is that the system changes from having a definite combined angular momentum and an indefinite value of the spin component for each particle to having a definite value of the spin component for each particle and an indefinite combined angular momentum.

    In qm the combined wave functions interact (via the principle of linear superposition), but once a particle is produced via measurement then definite phase relations are destroyed and no such interaction is possible. The 'collapse' of the wave function following a measurement leaves open, for some, the possibility of non-local 'communication' between A and B.
    But, the correlations don't imply that either A or B is affected by the other on measurement. If you evaluate the mean value of any function of the spin variables of, say, particle B, with the wave function before a measurement, then it's the same as what you'll get after a measurement is recorded at A.


    You want to "understand the physical mechanisms of how a polarization can be projected onto another polarization axis." Well, so would everybody else it seems. :-) Unfortunately, quantum *mechanics* isn't a very mechanical description of nature. (Some have suggested that perhaps it should be called "quantum nonmechanics".) There *is* a justification of sorts for the 'projection' postulate -- but, I'm not sure I understand it well enough to discuss it. Maybe some of the mentors/advisors can give us their versions of the reasons for it.

    I think that the correlations in, say, experiments involving polarizers, have more to do with the phases and amplitudes of paired, incident disturbances than with their polarization, per se. Anyway, I'm just a beginner. I hope you don't mind me offering my two cents worth wrt your questions. I like to jump into these threads with my sketchy knowledge because it makes me think and read a bit more than I probably otherwise would. The questions you're asking indicate that you're ready to get into a quantum theory textbook if you haven't done so already. (Then, in probably a relatively short time, you can join with others in explaining this stuff to me.)
     
    Last edited: Nov 17, 2005
  18. Nov 17, 2005 #17
    From the article you referenced:
    Our communication scenario consists of two parties that have access to a quantum channel but do not possess a SRF. For simplicity, we consider a noiseless channel that transmits qubits (our results can be extended to noisy channels or higher-dimensional systems). Such a channel defines an isomorphism between Alice’s and Bob’s local experimental operations. ... We define the lack of a SRF as a lack of any knowledge of this isomorphism.
    Is the 'trick' that they actually share a rotational reference frame, but are unaware of it? If so, then does this mean that there actually is a definite combined angular momentum, so that measurements by Alice and Bob are correlated in such a way that the sum of any pair is 0?
     
  19. Nov 18, 2005 #18
    Lets put it this way, if we use the Einstein box argument, then the conservation of particle number can be used to predict the explain accurately i.e. if the particle is in box A, then there must be no particle in box B etc. The quantum weirdness comes in when we set up measurement apparatus that allows a state to project itself into more than a unique outcome. For e.g. the polarization can be projected onto two orthogonally aligned polarizer. So thats why i said that how a polarization can be projected into two orthogonally aligned polarizer is the reason why Bell inequality was not obeyed.


    Yes! What exactly is the whole physical mechanisms for a polarization to be projected onto another polarization. There got to be a rigorous explanation from atomic/molecular theory right? Oh, i already completed my fundamental QM courses and now taking a field theory course. But it seems that what we learn is mostly the technical aspect and not the philosophical. So i hope to make up for these deficiency from a forum discussion. :biggrin:
     
  20. Nov 18, 2005 #19
    OK, now lets say my photon polarization are either horizontal or vertical. And my detection apparatus at the two ends are polarizer to detect either horizontal or vertical ONLY. Now, will Bell inequality still be obeyed?
     
  21. Nov 18, 2005 #20
    Ok.
    It would be nice to get an explanation of this from a forum discussion. Especially if it were in a simple enough form that *even I* could understand it *right now*. Unfortunately, that doesn't seem likely to happen.
    As Heisenberg says in, The Physical Principles of the Quantum Theory, This assumption is one of the formal postulates of quantum theory and cannot be derived from any other considerations.
    As far as I've been able to find out, there isn't any *physical mechanism* for, as you put it, "a polarization to be projected onto another polarization".
    One approach is to go back to the beginning and try to follow the line(s) of reasoning of the original developers of the theory in deviating from a course that would have allowed a geometrically visualizable formulation.
    I got a book, Classics of Science, Volume Five -- Sources of Quantum Mechanics , published by Dover (it's relatively cheap) that has 17 of the seminal papers (translated into English where necessary) in the development qm published between 1916 and 1926. The answer to your question, or rather, the reason why your specific question (about what is exactly the whole physical mechanism involved) *can't* be answered, might be in some of those papers (especially in the papers by Heisenberg, Born and Jordan).
     
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