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Entanglement, what is it?

  1. Aug 3, 2005 #1
    I am confused by the descriptions of entanglement I have read. Some seem to imply there is a superluminal transfer of information going on, while other descriptions do not. Can anyone explain this simply? I have a B.A. in Math, but am self taught in physics.
     
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  3. Aug 3, 2005 #2

    vanesch

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    One thing is sure: there is NO superluminal transfer of information. This can be shown mathematically, in that the reduced density matrix of one system is unaffected by whatever measurement is done on the other system (or even whether a measurement is done).
    All the rest depends on how you interpret quantum theory.

    What is true, is that Bell's inequalities can be violated in quantum theory. Bell's inequalities put a condition upon correlation functions under very "reasonable" hypotheses, which come down to claiming that (1) the apparent randomness of quantum events is only apparent, and that there is a deterministic underlying theory giving their outcomes, but which uses extra variables we don't know about and which are statistically distributed according to some probability law satisfying Kolmogorov's axioms and (2) that the dynamics of this underlying deterministic theory respects locality.
    Theories respecting (1) and (2) are called "local realistic hidden variable" theories, and you can show then that correlations between outcomes of such theories satisfy certain inequalities (Bell's inequalities).
    Quantum theory violates these inequalities in its statistical predictions (simply because it doesn't satisfy (1) and (2)). Experiments seem to be in agreement with the quantum predictions, although there are still people debating the validity of these experiments.
    This kills Einstein's view that quantum theory was in fact a kind of statistical mechanics and we'd find soon a theory satisfying (1) and (2) which explains the apparent randomness of quantum theory.

    Mind you that there EXISTS a theory which satisfies (1) (but not 2) and which is equivalent to QM: it is Bohmian mechanics. It contains non-local dynamics (action at a distance, which poses problems with special relativity).

    BTW, I've written up quite some stuff concerning EPR in my journal (to the left of this post).

    cheers,
    Patrick.
     
  4. Aug 3, 2005 #3
    Entanglement can be understood also as a way of conecting the states of two or more subsystems. If you cut a coin in two equal parts through a plane perpendicular to its simetry axis, and send one of this parts to person A e the other to the person B inside envelopes, when person A finds a head, he knows B had enconuntered a tail and vice versa. We know, according to classical machanics, that the states of this two parts were already well defined in the instant you sent the envelopes. There were only a statistical uncertainty, a classical statistical uncertainty. And the fact that makes this uncertainty classical is that there exists a well difined experimental method which could have been used to let us know which side of the coin you have sent to me at the moment you sent. You had a well defined intention, and ultimately you are choosing which half coin I will get. One could ask you before I receive the letter.

    In quantum mechanics there exists no material experimentally accessible source of information on which side of coin was sent to A and B. It is not just a question of not being interested or not being technically capable of pursuing this information. Quantum mechanics assumes this information does not exists until A and/or B open their letters. So, the physical reality of "the state of the piece of metal inside the letter going to A" is a bad defined issue within quantum mechanics. Although if A find tail, necessarily B will find head, i.e. although this correlation still exists, there is no well defined state of the half coin inside the letter : the two pieces of metal are ENTANGLED.
     
    Last edited: Aug 4, 2005
  5. Aug 3, 2005 #4

    DrChinese

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    Welcome to PhysicsForums!

    Entanglement is many things to different people. If you look at the 1935 EPR paper and Bell's Theorem, you will get a pretty good idea of some of the base issues. You can treat these as source documents for most of the debate. There are lot of different ways to describe entanglement and you will want to find a description that is comfortable to you.

    While particles are entangled, there is a conservation or symmetry constraint present. The constraint usually is stated in terms of spin, but also applies to other observables as well. Usually there are 2 particles, and it is possible to entangle more. The following are some pretty good things to consider:

    1. There is no superluminal information transfer (as Vanesch pointed out).
    2. The HUP is not violated.
    3. The entangled relationship extends over space and time beyond the limits implied by Special Relativity.
    4. Experiments support all of the above, and also that the separate and independent existence of the individual particle observables is not supported (per Bell's Theorem). I.e. attributes such as spin are "contextual" (are not independent of the act of observation).

    Interpreting the finer meaning of the above leads to a lot of philosophical issues. Good luck!!
     
  6. Aug 4, 2005 #5
    The analog of the entanglement is two coins. Every of the coins gives a random results - head I1> or tail I0> with the probability 1/2.
    The coefficient of correlation K of this coins is zero because we have two different random process.
    In quantum world for the entanglement we have non-zero coefficient of correlation. In the ideal case is K=1.
    You are remember but I employ the definition of coefficient of correlation K=<xy>-<x><y>. Here x and y is two random process between 1 and 0. <> is average. If the process is independent the K=0. For quantum case we are think that the processes is independent but K non-zero. It is very strange for the classical viewpoint.
     
  7. Aug 4, 2005 #6
    I must say that it seems to me that we may have entaglement with less that 1 correlation. Supose you have two DICES. One entangled state of the upper side numbers of these dices may be:

    | 2 > X N {| 2 > + | 3 > + | 5 > - | 6 >} +
    | 5 > X N {| 1 > + | 4 > + | 2 > - | 3 >} +
    N {| 1 > + | 2 > + | 3 > + | 6 >} X | 1 >

    where N is a normalization constant asd the first bra (or set of bras) always is related to dice 1 and the expression after the direct product X always has to do with the state of dice 2.

    If the first dice shows | 2 > we can expect the second dice to show 2,3,5,6 and 1.

    But if the second dice shows | 2 > we may expect the first to be 2 or 5 only.
     
  8. Aug 5, 2005 #7
    The concept of entanglement in nuclear physics is often based on a false logical premise, that is, that the "object" [O] and the "act of perception" [P] are independent. It is nonsense to say that neither A nor B as [O] exist in the envelop until [P] event occurs, likewise that [P] must exist before A or B can be realized. Both positions are false. As discussed above, experiments in quantum reality show that [O] and [P] are not separate nor independent.

    Entanglement is the "product" of the interaction between [O] and [P], thus entanglement [E] = { [O] * [P] }. Entanglement cannot be exclusively identified with either [O] nor [P]--which thus forms the third alternative of quantum reality, quantum entanglement is the integration operation process of "object [O] as perceived [P]".

    Finally, entanglement as { [O] * [P] } is preformed within [O]. Thus [E] = {([O]*[P]) * [P]}, and we see then that [E] = [O] * [P]2. Thus the concept of entanglement is the source of the metaphysical nature of reality itself. We also know this fundamental reality of entanglement by its more specific notation: E = MC2.
     
  9. Aug 5, 2005 #8

    DrChinese

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    This is not an accurate usage of the terms. Entanglement is a specialized quantum state involving 2 or more particles. Entanglement itself has nothing to do with the observer.

    On the other hand: all quantum state statistics will obey the Heisenberg Uncertainty relations, and these are affected by the observer. This element of QM is often subjected to metaphysical analysis.

    Entanglement is NOT the source of this, and it is certainly not described by E=mc^2.
     
  10. Aug 8, 2005 #9
     
  11. Aug 8, 2005 #10
    FYI, the singular of this word is "die" and the plural is "dice". I know no other English word that follows this rule ... what a crazy language!
     
  12. Aug 8, 2005 #11

    DrChinese

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    The reason this is not correct is simple. The observer plays a similarly important role an all quantum interactions, including systems where entanglement is not a feature. There is nothing wrong with your quotes per se but they don't tell the entire story.

    The reason entanglement is so associated with the observer is because it disproves the idea of local hidden variables via Bell's Theorem. That elevates the role of the observer. But it is not a feature solely of entangled systems, it is a general feature of QM. Your quote would be more consistent if you had said: "quantum reality makes no sense without observer".
     
  13. Aug 8, 2005 #12

    DaveC426913

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    Mouse/mice?
     
  14. Aug 8, 2005 #13

    ZapperZ

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    I agree with DrChinese. I don't understand why this "quantum reality" bit is only applied to entanglement and NOT to the rest of QM. If one has a problem with "observer dependent reality", then why pick only on the entanglement phenomenon? The Schrodinger-Cat type observation is a HUGE part of this and can't be separated out of any QM measurement, entangled or NOT. The fact that the system of entangled states are in a superposition of a number of possible states IS the whole reason why it is different than a simple "conservation of angular momentum" system in classical mechanics.

    Zz.
     
  15. Aug 8, 2005 #14
    To summarize what I think I am hearing about concept of entanglement from the above comments: (?):

    1. Reality-[R] exists [An axiomatic statement]
    2. Quantum-reality is a subset of Reality-[R], thus quantum-reality exists
    3. Quantum-reality makes no sense without observer [DrChinese]
    4. Entanglement is a sub-set of quantum reality [DrChinese, ZapperZ]
    5. Thus, by logic, entanglement makes no sense without observer [Vecchi paper]
    however,
    6. Non-quantum reality = Reality-[R] that is not Quantum-reality
    7. Non-quantum reality makes sense without observer
    which leads to the question
    8. Is entanglement also a state of Non-quantum reality ?
     
  16. Aug 8, 2005 #15
    Entanglement IMO is related to making ones capable of performing an interference experiment. Otherwise it has only the aspect of statistical uncertainty.
     
  17. Aug 8, 2005 #16
    I have always been confused by entanglement but recently got this gist after reading the fabric of the cosmos (brian green).

    It goes like this:

    Consider first just a single particle that can be in state A or B. Now this is the important point - when you perform a measurement it can either be in A or B, then if you perform the measurement again a little later - it can AGAIN be in A or B. Just because you measured it A say the first time it doesn't mean it will be in A the second time.

    Once you grasp that then entanglement is easy to understand.


    So, now consider 2 entangled particles.

    1 has a 50:50 chance or being in state A or B.
    2 has a 50:50 chance of being in state A or B.

    Now, release both particles in opposite directions say. The point is that when you perform the measurement they should both give RANDOM answers, but they end up correlating exactly. i.e particle 1 really is in both A and B until the measurement and then when you finish measuring it goes back to being in some superposition of A and B.

    The very fact that 1 and 2 correlate is amazing because without an observer they really are never in state A or B - just a superposition, but when an observer comes in and has a look it collapses both wavefunctions simultaneously!
     
  18. Aug 9, 2005 #17
    But this part of measuring in sequence has to do with the specific Hamiltonian which will ultimately rule the time evolution of your system. I am not sure that you can count on the fact the 50:50 pattern will come back after the first measurement.

    Best Regards


    DaTario
     
  19. Aug 9, 2005 #18

    ZapperZ

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    Is this physics or philosophy?

    What is "a state of non-quantum reality"? This is odd because entanglement came out of QM's own formulation. How can it be a "non-quantum" anything?

    You do know what mathematics represented by "entanglement", don't you? Now see if it is separable. If it isn't, you have just arrived at its definition.

    Zz.
     
  20. Aug 9, 2005 #19

    DrChinese

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    This portion of the post is not fully accurate. If you make a measurement of a particle, subsequent measurements will be consistent with the Heisenberg Uncertainty Principle (HUP). A photon with a known polarity will continue to have that polarity as many times as you care to check it. If you make a different measurement, you may then get different results, still obeying the HUP.
     
  21. Aug 9, 2005 #20
    You are too kind. :biggrin:
     
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