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Easy (I think) quantum non-locality question for the experts

  1. Aug 21, 2008 #1
    Hello All,
    I've recently become interested in learning more about the concept of quantum non-locality, and have a quick question I hoped someone might be able to shed some light on for me.

    My question is this: How do we know that Einstein was wrong that some "local hidden variable" accounts for the fact that the respective spins of two once "entangled" but now distant photons, to take a classic example, will always be oppossite?

    In other words, what is it about modern-day experiments that "proves" that these distant photons are actually engaging in some kind of instantaneous communication, as opposed to the much simpler (and thus arguably more likely) conclusion that these two photons always had, and always will have, opposite spins. Doesn't this simpler explanation (which I believe was Einstein's explanation) account for the fact that the spins, once measured, will always be oppossite (i.e., they are opposite because they started out like that and will always be like that, and thus, the measurement is not determining the spin, but only recording it).

    I know the answer relates to Bell's Inequality Theorem and experiments that prove it, but I've yet to come accross an easily understandable (for a layperson) explanation of how we know that distant particles are in fact RESPONDING to measurements taken of the other, as opposed to just continuing to exist in their original state?

    It seems to me that to prove that there truly is an instantaneous response to measurements to or impacts on one of these photons, we would have to change the spin, and see if the spin of the corresponding photon also changes. Have any experiments to this effect been conducted.

    Thanks in advance for any resposnses. Scott.
  2. jcsd
  3. Aug 22, 2008 #2
    If I understand your question exactly, here's my view on it:
    Think of the entangled particles in one wave packet, so when it is 'observed' - at either end - the whole packet collapses at once. So nothing is actually sent from one end to the other in the sense that you mean. At both ends it is unsure the states for both particles, but when collapsed probability decides instantly for both.
    QM says as a fundamental postulate that their states must correlate, but we are unsure exactly the mechanism the Universe uses to achieve it - especially when it occurs over large separations.
    What do you think?
  4. Aug 22, 2008 #3
    This is my first answer here and I’m no physicist. But I’ve been trying to think of an easy way to explain this. So I’d love feedback from all.

    First of all, forget the instantaneous thing for a while. It will only cook your noodle. There are modern theories for this that avoids a paradox. Some don’t include instantaneous either.

    Another important point is that QM results are based on statistics. So an individual measurement might not give you the results that you think QM predicts. That doesn’t stop physicists from talking about them that way. It’s just easier.

    Now for this entanglement business. If you measure the spin of entangled particles from the same direction then, yeah, the results are opposite. Let’s call that a 100% agreement. If the spin is fixed at the time of entanglement then it doesn’t matter what direction the detectors are in as long as they’re both in the same direction.

    But if the spin is set at the time of entanglement then it must be set in all directions. So now let’s try setting the detectors at right angles to each other. In this case, one measurement tells you nothing about the other. Let’s call that a 50% agreement. It’s random like flipping a coin.

    But what if the measurements were taken at 45 degrees from each other? Just as a silly example, try drawing pictures of two baseballs spinning the exact same direction. I know, I know. Photons and electrons are nothing like baseballs. But you can easily imagine measuring their spin. So the spin is exactly the same but the detector on one is 45 degrees off from where the other one is on the other baseball. Play with this for a while and you’ll realize that the agreement should be 75%, right in between 100% and 50%. You can think of this as the hidden variables theory described in the EPR paradox. Do this again for a few different angles and you’ll get a nice linear graph from 100% to 50%.

    This is not what Bell’s Theorem predicts. Instead the graph is a nice round curve from something like the Pythagorean equation (a^2 = b^2 + c^2). So measurements at 45 degrees have an 85% agreement. If the experiments average out to something like this (which they do), then we need a better explanation than fixing the spin at entanglement time. This is where crazy ideas like wave collapse and instantaneous come from. But you’ll get over that as you ask more questions.

    OK, so, how’s that from a total non-physicist?
  5. Aug 22, 2008 #4
    Wow guys, thanks for the quick and thoughtful responses. Thenewmans, that is a great answer for a layperson. I need to noodle it a bit more, but I think your response has materially advanced my understanding of why these experiments are so important, and how they prove (or nearly prove) the concept of non-locality.

    Lasermind, your example was very useful as well. Your answer has given some context to various statements I've heard or read to the effect that if in fact "space" for lack of a better term, is comprised of many dimensions, some of which are are folded/curved/nonlinear, perhaps on some other plane or "manifold" these particles are not so far apart--even though they appear as such due to our limited perspective (i.e., limited in the sense that we don't physically percieve these other dimensions). Thanks guys.
  6. Aug 23, 2008 #5
    This explanation is a good attempt but you have not got the idea. You are trying to conceptualize classically (baseballs etc) and it does not quite hang together - in QM we need complex vector analysis - orthogonal states, operators, observables, normalization, basis, bras and kets, Hibert Space, inner products, amplitudes, fourier transforms etc - I suggest Leonard Susskind on youtube. He is a professor at Stanford and walks you through the mathematical abstractions, you need some school math (complex numbers, sine, cosine, exponentials).
    You will not get anywhere in QM without this mathematics.
    Last edited: Aug 23, 2008
  7. Aug 23, 2008 #6
    Absolutely, I agree. Such a cheesy metaphor runs the risk misleading the reader. Hopefully, ScottArizona knows photons aren't like baseballs particularly since baseballs give a result more like hidden variables than Bell's theorem. My intention is not to give a metaphor for photons but to explain the experiment. After all, the question is: What modern-day experiments prove hidden variables wrong? Hopefully, I did a half decent job at that. All that other stuff (bras, kets, hibert, bla bla) will take a little longer.

    PS: Thanks for the Susskind videos suggestion. I plan to watch all of them!
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