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Quantum entanglement, not that weird.

  1. Dec 11, 2009 #1
    I'm fairly new to my readings in Quantum mechanics, so my apologies for any mistakes in interpritation of the theory.

    I've read that Einstein could not come to terms with entanglement and in general most entries describe it as a really weird affect, but it really doesn't seem that way to me. Am I missing something?

    A laser is shown into a crystal and a photon can split into two, of these two one must have a horizontal polarization, and the other must have a vertical polarization according to the law of conservation of angular momentum.

    Now when articles talk about this they make it seem like when you measure the polarization of the particles it affects the other particle some how, but one is horizontal and one is vertical so of course when you measure one you know properties of the other, but that doesn't mean they are some how communicating with each other saying "Hey he measured me you have to be this", yet articles on entanglement make it seem so.

    I guess what I'm getting at is, is there a weird part of entanglement I have missed, or do people like to make it seem weirder than it is.

    Thanks.
     
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  3. Dec 12, 2009 #2

    JK423

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    In order to understand quantum entanglement you must first understand the superposition principle. (According to Copenhagen interpretation:) When a particle is in a superposition of states (state=polarization orientation for example) then it is somehow in both states(polarizations) until you measure it. When you make the measurement to check its state(polarization) this superposition collapses to one of the states with specific probability. That means that you cant watch a photon having both polarization orientations (vertical and horizontal) at the same time.
    You must keep in mind, that a particle in a superposition of two states -that is a particle being in two states at the same time- is not equivalent to a particle which is in one of the two states but you dont know which! These are two different things and it can be proven experimentally.
    In your example of photons now:
    The two photons are in a weird state. As i told you above, each photon is in a superposition of polarizations at the same time! But its not only that, the two photos are also entangled! That means:
    When photon_1 has horizontal polarization (HP) then photo_2 has vertical polarization (VP), and inversly, when photon_1 has VP then photon_2 has HP. But be careful, its not that each photon has a predetermined polarization before you measure it! As i told you above, each photon is in a superposition of polarizations at the same time!
    So the measurement that you perform, determines the polarization state of the photon_1 for example. But if photon_1 has HP then photon_2 must have VP! You somehow determined the polarization state of the second photon instantly, just by measuring photon_1!
    If you go and measure photon_2 you will find with 100% confidence that it`s VP! Remember! It had BOTH VP and HP before you make the measurement and by measuring photon_1 you instantly determined photon`s_2 polarization state! It`s not that it had it had VP all the time and you just didnt know!
    I hope you get it now..


    I want to make clear, that the following are DIFFERENT:
    A. The photon has a specific polarization unknown to us before the measurement and when we measure it we just.. find it out. We find HP or VP with specific probability.
    B. The photon doesnt have a specific polarization but has both polarizations - that is, its in a superposition of HP and VP. However, when we measure it, this superposition collapses to HP or VP with specific probability.
    These two situations (A and B) give two DIFFERENT results! They are not equivalent!!
     
  4. Dec 12, 2009 #3

    HallsofIvy

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    And, I might add, experiments seem to indicate that situation B is what really happens!
     
  5. Dec 12, 2009 #4

    DrChinese

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    Welcome to PhysicsForums! Just to add to what is above...

    You don't notice much difference in the 2 situations A and B when you measure the polarizations at H and V (0 and 90 degrees) for Alice and Bob. But what happens if you measure at 45 degrees and 135 degrees, or 120 degrees and 240 degrees? It turns out that superpositioned states yield different predictions than you would expect than in the classical view.

    To understand this, try to picture the classical view that Alice is simply polarized at 0 degrees and Bob is at 90 degrees. Then imagine you measure Alice at 1 degree, 2 degrees, 3 degrees, etc. Obviously, at some point - 90 degrees exactly - you get the opposite result than 0 degrees. Now, where in that range did Alice change from H to V?

    Now imagine Bob changing from 90 degrees to 180 degrees. Where in that range did Bob change from one to the other?

    After a while, you will be forced to conclude that if Alice and Bob are operating independently - the classical, Einsteinian view - then their results will NOT be exactly correlated at angles such as 1 & 91, 2 & 92, 3 & 93, etc. Do you see why? It is because when Alice is at 0 degrees, a subsequent measurement of Alice at some other angle follows the cos^2(theta) rule (Malus). Are you familiar with this rule? If you are not, I would be happy to explain the thinking in more detail.

    In fact, in a superposition, Alice and Bob DO stay correlated at any angle pair like 1 & 91, 2 & 92 etc. This is the experiementally verifiable prediction of QM that is at odds with classical reasoning. There are in fact some classical theories which can explain this particular result as well, but it turns out they fail at explaining other results. When the dust settles, there are no remaining classical theories which can explain superposition completely. See Bell's THeorem for more on that.
     
  6. Dec 12, 2009 #5
    Thanks. I was thinking of it in terms of A, but now I understand it in terms of B. Thanks to everyone for clearing this up for me.
     
  7. Dec 13, 2009 #6
    People like to make it seem weirder than it is. Entanglement occurs in all interacting quantum systems. Take any remotely interesting physical system, and its ground state will be entangled when expressed in the obvious basis.

    The obvious example is two AFM coupled spin 1/2. The singlet ground state is entangled when expressed in the basis given by the product of the separate hilbert spaces.

    There is nothing weird about entanglement, beyond the normal weirdness of the rest of QM, since entanglement is such an essential part of any QM problem.
     
  8. Dec 20, 2009 #7
    Here we have an experiment where two photons are created with entangled polarization states. The photons can be x polarized or y polarized, but if the first photon is x polarized then we know with certainty that the second photon is y polarized. We can ignore the second photon, yet still know its polarization. And, likewise, if the first is y polarized, then the second is x polarized. In quantum mechanics the photon does not have a polarization until we measure it. But, here, we know the polarization of the second photon without measuring it directly.

    The two-photon entangled state vector is |psi>=.707(|x y>+|y x>), where the first letter is the measured polarization of the first photon and the second letter is the polarization of the second photon. The eigenstate |x y> is a single entity and it cannot be factored into |x> and |y>. Likewise for
    |y x>.

    We see only two possible results: x and y or y and x. The "values" x and y, are inseparable and, together, they make up a single result of this experiment. x and y always appear together. The polarization of photon 1 is not independent of the polarization of photon 2.

    But this is not simply conservation of angular momentum as in classical mechanics. When we measure any quantum observable, we are not measuring a value that the photon already had before we make the measurement. The photons do not "get" a polarization at the moment of creation in the crystal. Rather, they "get" a polarization at the moment they are detected in the polarization measuring device. And the measured polarization is determined by the entire experimental apparatus, including the measurement device.

    Now consider a second experiment where the polarization detector for photon 1 is rotated by some angle. Now, the possible results of a polarization measurement on photon 1 are x' or y', say, polarization. Assume that the measurement device for photon 2 is unchanged. We measure photon 1 and get x' polarization, but now the polarization of photon 2 is indeterminate; when we get x' for photon 1, we sometimes get x polarization and sometimes we get y polarization for photon 2.

    The point is this: It appears that the results for photon 2 depend on what we do to photon 1! The only change we made was to the apparatus associated with photon 1. Without interacting with photon 2 in any way we have changed its state of polarization. (Actually, we haven't changed anything. Rather, we have two different experiments with different results that are mutually exclusive.)

    There is no classical explanation for quantum entanglements. Classically, particles travel independently through space-time, and looking only at particle 1 cannot have any affect on a second particle far away. Classically, there must be an interaction or communication of some sort between the two photons. Entanglement is "weird" only if we insist that the photons behave like classical particles, which they are not.
     
  9. Dec 26, 2009 #8
    Just to clarify, do the polarizers 'round' their values? A value of x will be returned if the actual angle is (well, "is" isn't quite the right word maybe "is determined to be" is better) within 45 degrees of x and y if it is within 45 degrees of y, right? And because of that what you get for the result from photon 2 depends on the angle of offset for photon 1's detector?
     
  10. Dec 26, 2009 #9

    DrChinese

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    That would be a good first hypothesis. That is not what QM predicts, however, as entangled systems illustrate. If you use 45 degrees as your benchmark (as in your example), nothing weird seems to appear. But it does appear at other angles. Bell pointed this out in 1964 in his famous paper. Keep in mind that his result was missed by many of the greatest minds in the area, including Einstein.

    If you are not familiar with Bell, check out the following or similar as this will help to bring the issue into focus.

    http://www.drchinese.com/Bells_Theorem.htm
     
  11. Dec 27, 2009 #10
    Thanks,

    So the 'wierd' effects show themselves if you unevenly divide what you call x and y?
     
  12. Dec 27, 2009 #11

    DrChinese

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    Yes. An example is as follows: Alice and Bob are entangled photons measured at 0 and 120 degrees. The QM predicted correlation (same as what is observed) is cos^2(120 degrees i.e. the difference between 0 and 120) = .25. Now, that figure is too low for what is called a realistic explanation (such as what you proposed), which will be 1/3 or .333 at a minimum. Because you have to have a rule for your explanation that provides a continuous range of predictions for all possible angles. You will find quickly that the rule can't work at 45 degrees (i.e. = .5) and 120 degrees both. Because if you measure correlations at 0 and 120 degrees, then you could also measure correlations at 120 and 240 degrees; and at 0 and 240 degrees. These won't be internally consistent. I.e. you can't have each of these be .25 because there is no combination of values for 0, 120 and 240 degrees that yield correlations of .25. Yet they should be since the difference for each of these is the same... 120 degrees.

    The point being that you have postulated "realism" any time you describe something happening independently at Alice and Bob. Because if the physical mechanisms/systems are independent, then you should be able to estimate the results for any possible measurements - not just the ones actually performed. So you cannot have independence of the systems and realism both.
     
  13. Dec 27, 2009 #12
    Another question: will any pair of particles generated as a pair at exactly the same time be entangled? In other words, does every process that generates a pair of particles like the photons necissarily also produce them in an entangled state? If the wording is confusing I can try again.
     
  14. Dec 27, 2009 #13

    RUTA

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    Entanglement leads to violations of Bell's inequality which implies causal and/or constitutive non-locality. General relativity is both causally and constitutively local. Therefore, these two successful theories of physics imply incongruous ontologies. Whether entanglement strikes you as weird depends on your emotional reaction to this fact.
     
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