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The EPR Paradox

  1. Jul 1, 2003 #1

    FZ+

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    Can someone inform me a bit on the background of this problem, it's experimental testing and it's implications?

    If I have it right, it involves two particles which are involved in a singular event. If you measure the momentum of the first particle, you not only create uncertainty in it's position, but also uncertainty in the position of the second particle.

    Am I right? So how has this been experimentally tested?

    And don't we get a problem as the entire universe can be described as caused in a single event - the big bang?
     
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  3. Jul 1, 2003 #2

    chroot

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    It's usually manifest in quantum entanglement situations. Let two particles interact and then fly far apart. When you measure some property (say spin) of one particle, the other particle's state is instantaneously determined -- no matter how distant the other particle is. The information about the measurement of the near particle does not have to propagate at subluminal speed to the distant particle. The collapse of the wavefunction describing the two-particle system occurs instantaneously for the entire system.

    This is a paradox, but not an "unrecoverable" one. No information or energy is transmitted by this process, so our laws of physics are not assaulted. I generally just think of it as an example of the deep incompatibility of relativity and quantum mechanics -- despite the successes of relativistic quantum field theories like QED, the two theories are not deeply compatible. We'll have to wait for a GUT to fully understand the EPR paradox.

    - Warren
     
  4. Jul 2, 2003 #3

    Ivan Seeking

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    What about in the case of so called photon teleportation. Don't we teleport information in this case? (I'm asking not asserting). Also, how is this statement consistent with the premise that no unique state exists until measured? I have never been clear on this point. It seems to me at least information must somehow be transferred. Or do you escape this problem with the wholeness in time concept - to be described accurately by some higher dimensional model? Also, as per the solution to the Maxwell's Demon paradox, if information is transferred, then so is energy.

    Enlightenment?
     
  5. Jul 2, 2003 #4

    jcsd

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    It's easily resolved, you just have to view the two particles as one quantum mechanical system even though they may be seperated by large distances in space.

    Using quantum teleportation the actual information still needs to be sent by classical means (i.e. not at superluminal speeds), the information then allows you to reconstruct the state of the other particle using it's entangled brother.
     
  6. Jul 2, 2003 #5

    Ivan Seeking

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    I'm not sure if I am getting the flavor here [pun]. I grant you that this is no problem mathematically, but what about philosophically and mechanically? How does the information get there? Perhaps by your answer we assume that a higher dimensional model will resolve any paradoxes? To me, this still wreaks of paradox; yet most physicists seem to act otherwise. What's the scoop?


    Ah. I will have to review how these experiments work.
     
  7. Jul 2, 2003 #6

    jcsd

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    Well the result of the measurement of one particle must determine the result of the measurment of the other particle.

    Using an analogy, imagine you have two cards face down one was the King of Diamonds and the other the Queen of clubs but you don't know which is which. If you turn up the first card and find it's the King of Diamonds the other one must necessarily be the Queen of Clubs. It's just in quantum mechanics neither card (though obviously this is just an analogy as quantum mechanics doesn't really apply to large systems like this) has a seperate identity until it is turned up (Bell's theorum disproves local hidden variables) but they cannot both be the same card so measuring one determines the value of the other.
     
  8. Jul 2, 2003 #7

    Ivan Seeking

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    OK. How?

    Edit: I thought that this question has no known solution/answer. Many people seem to imply that it does, but I don't hear the core of the paradox being addressed: How? I thought that this is one question that M Theory seeks to address. Sorry if I'm just being thick headed
     
    Last edited: Jul 2, 2003
  9. Jul 2, 2003 #8

    jcsd

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    You'd have to ask an M-theorist about M-thory my knowledge of physics doesn't extend that far.

    I'll write out the mnathematics for you but I don't think it makes it any clearer than the above explanation, it's not a ture paradox because it's self-consistent.

    This is the spin part of the wavefunction for two entangled particles:

    psi(1,2) = 2(-1/2)[alphaz(1)*betaz(2) - betaz(2)*alphaz(2)]

    where alphaz(i) and betaz(i) represent particle i with a postive and negative spin component relative to the z axis

    Now from this you can see that the direction of the spin of either individual particle is not known, but when a measurment is made:

    psi(1,2) = alphaz(1)*betaz(2)

    and as the direction of the spin one particle is now known the other can be determined without measuring it from this.
     
  10. Jul 2, 2003 #9

    Ivan Seeking

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    Yes I think I understand this. Is it clear that I am asking: By what mechanism is this mathematical model made possible in the physical world? Equations on a page tell me what happens. It seems that we have nothing to say about how it happens. We have no way to explain how the condition is satisfied if no hidden variables exist. Isn't this the whole reason for the hidden variables argument - to avoid the need for a means of propagation of the information from the measured to the unmeasured?
     
  11. Jul 2, 2003 #10
    Because we don't know. It's still a mystery although it happens. And remember, imformation is not exceding c. You still have to communicate the information of the state to the reciever to verify that there are a state change of so-so or the recieving end would not know whether a state change that occured correlated with the EPR effect because you don't know the polarization outcome of the other measured particle.
     
  12. Jul 2, 2003 #11
    the experiment that was perfomed is called Aspect experiment.
     
  13. Jul 2, 2003 #12
    If you and your particle were to slip past the event horizon of some giant black hole and you measured its spin, would the information still reach its distant partner? Or does going into a black hole snap the bond, so to speak?

    If I understand correctly, the reason you know the other particle has to have a certain spin once you measure the one you've got with you is that conservation laws apply (and maybe that's not it). But do those still apply when it's impossible in principle to make sure the rules are satisfied?
     
  14. Jul 2, 2003 #13

    selfAdjoint

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    It's really not necessay to bring in event horizons and M-theory. The subject is really part of ordinary quantum mechanics.

    EPR stands for Einstein, Podolski and Rosen. They published a paper in about 1940 with the idea of entangled particles and the assertion that this would violate relativity and the uncertainty principle.

    Next we have the Bell inequalities, devised by John Bell who was a physicist at CERN in the 1960s. By a simple combinatorial argument he showed that if two systems are truly separated so no influence can pass from one to the other, then there was an upper bound on the frequancy of coincidences between them. And he showed that in quantum mechanics that limit of coincidences would be exceeded for entangled particles.

    Alain Aspect, in Paris, then did an experiment which is viewed by the physics community as proving Bell's assertion about quantum mechanics, although there are a few dissenters.

    Quantum mechanics has no problem with this as stated in previous posts; the particles form an extended state and when you measure either one you collapse the state and end the entanglement. In order to find out whether a remote particle has collapsed you are limited by relativity, and relativity of simultaneity means you will never be able to know which particle "drove" the other. So all that survives is a correlation between the particles, a la Bell, not a causal connection.

    Hidden variable theories (but not Bohm's) have a problem since they want everything to be classical and relativistic, and Bell's theorem and Aspect's experiment show they can't.

    There are endless sites on the web that try to use EPR or entanglement as a refutation of relativity or a source of mysticism but none of them is correct!
     
  15. Jul 2, 2003 #14

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    Thanks folks. Very helpful.
     
  16. Jul 3, 2003 #15

    Ivan Seeking

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    It may not be useful information to us, but perhaps it is to the entangled particle. That this statement does not violate our basic concepts from relativity to me has always seemed a flawed. We don't know that the information travels at < C, we only know that we can't make use of this information without this limitaion. Correct?
     
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