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B How does Bell's inequality rule out realism?

  1. Jun 27, 2016 #1
    I understand Bell's inequality, and I can see how removing locality can produce the observed statistical correlations. However something that I often read is that eradicating realism can also generate the correlation observed in entanglement. I don't see how a particle not having definite properties prior to measurement will produce the correlations. Can I have someone clear this up for me?
     
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  3. Jun 27, 2016 #2

    jfizzix

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    When a Bell inequality is violated, one rules out that the correlations between the particles can be explained by information in their shared past (i.e., locally).

    This implies either that the correlations are explained non-locally (so that there is some manner of instantaneous information transfer), or that the correlations are simply not explainable, which would deny that the measurement results can be predicted with enough information about it.
     
  4. Jun 27, 2016 #3

    DrChinese

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    Removing realism does not "generate" anything any more than removing locality does.

    On the other hand: there are interpretations of QM in which things like causality are not present. Such an interpretation does not inherently violate the Bell limits. Further, they don't violate locality, which is their "selling" point.
     
  5. Jun 27, 2016 #4

    gva

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    Isn't removing realism like saying it is the equations that are non-local and they connect the entire universe into one instantaneous whole?
     
  6. Jun 27, 2016 #5
    Thanks for the response. I continually heard that bell's inequalities proved that either locality or realism (also referred to as counterfactual definiteness) was wrong. From my understanding now, removing realism is just another way of saying that we don't know what's happening?
    In other words, probability doesn't work in the same manner in the quantum level as it does in the classical way?

    Also, when you said,
    "removing realism doesn't generate anything more than removing locality does" this confused me.
    Removing locality, at least in the way that I've been told, permits for one entangled particle to "tell" the other entangled particle what state to be in
     
  7. Jun 28, 2016 #6
    (Quantum) realism, as far as I understand it, signifies the existence of quantum properties independent of whether we examine them.

    How this fits into the entanglement picture remains a mystery to me...
     
    Last edited: Jun 28, 2016
  8. Jun 28, 2016 #7

    Demystifier

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    See https://arxiv.org/abs/1112.2034
     
  9. Jun 28, 2016 #8
    Thanks for the paper. I don't have time right now to read the entire thing but I did read the first page. It says, "...[some say] that nature is local but objective reality does not exist." I'm merely asking for the explanation of this. How can removing objective reality retain locality and also not violate Bell's inequality? Thank you.
     
  10. Jun 28, 2016 #9

    Simon Phoenix

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    I'm guessing here that what you're after is some kind of intuitive view for why the failure of realism helps us understand things. After all, as you said, if we have a hidden (or extra) variable model then intuitively we can see that one way to get a violation of the inequality is to have some kind of 'information' transferred between the two measurement devices; put those devices far enough apart and we would have to suppose that this 'information' gets from A to B faster than a light signal can propagate between the two devices.

    So I think what you're asking is whether there is a similar kind of explanation for why the failure of realism allows the inequality to be violated (if we assume everything is hunky-dory in the locality department).

    So what does the assumption of 'realism' buy us? What do we get from it? Well if you've read some of the literature you'll see that this issue generates a whole slew of metaphysical musings, often expressed in some quite sophisticated terminology. For me, the essential point is that in classical physics it is meaningful to talk of properties we might have measured - "we measured the position of the particle, but IF we'd measured the momentum we would have got this result" - kind of thinking. Just writing down the state of a classical particle with its 3 position variables and 3 momentum variables is making this assumption. This gets called 'counterfactual definiteness' but in my view this is just a shorthand for saying 'classical physics' because it's implicit in all of classical physics.

    In the usual 'textbook' derivations of the BI where this assumption gets used is in the manipulation of the conditional probabilities - essentially we replace a probability representing the result of something that WAS measured with a result probability of something that MIGHT have been measured. It's a completely legitimate operation in a classical world - but somewhat less legitimate in a quantum world. In a hand-waving way we can think of the uncertainty principle preventing us from doing this in any meaningful way within a quantum perspective.

    But I agree with you that it's more difficult to get a picture of why this messes things up. I go back to Feynman's path-integral paper where in the introduction he makes a very powerful point on this issue (I urge you to read it - there is no way I could match Feynman's clarity and insight). Here's his argument sort of simplified :

    Let's suppose we have some object prepared in some state A. We're going to measure some property and suppose we obtain the result C. We're going to further suppose that we can 'get' to C from A via 2 intermediate states B1 and B2. Classically then we would write the conditional probability P(C|A) as
    P(C|A) = P(C|B1)P(B1|A) + P(C|B2)P(B2|A)
    So the classical view would tell us we can get to C either by going along B1 or B2 - we just don't know which of these paths, but we assume classically that in getting from A to C the object did indeed go via one of these paths.

    But the quantum rules are different - to get the conditional probability P(C|A) if we don't know which path we must work with the amplitudes and the probability is then
    P(C|A) = | a(C|B1)a(B1|A) + a(C|B2)a(B2|A) |2
    where here the a are the amplitudes.

    So in a nutshell if we make the assumption that the object really did go on one of these paths (we just don't know which) then we just use the classical conditional probability formula - but this gives us the wrong prediction according to QM. In other words assuming some 'real' property gets us into trouble. It's really just the 2 slit issue (and we note that the issue of commutativity vs. non-commutativity that is central here - as it is in the derivation of the BI where we effectively assume commutativity in making our 'counterfactual' argument)

    I've tried here to present a bit more 'intuition' about what might be different in QM in hopefully plain terms and undoubtedly I've glossed over a lot of technical things, but I hope it's given a bit more of a feel for what the issues might be. I'm sure others will help flesh out the technicalities better than I can.
     
  11. Jun 28, 2016 #10
  12. Jun 28, 2016 #11

    gva

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    Reading this makes me realized that the realism is about particles only.. there is still the field even if no particles.. so in the double slit experiments.. even if there are no solid particles.. there is still detection.. sometimes anti-realism feels like there would be no detection and just nothingness which is not the case at all.
     
  13. Jun 28, 2016 #12

    gva

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    But for Aspect experiment, the field has to be instantaneous billions of light years away... hope Simon can explain what occurs in this scenario.
     
  14. Jun 28, 2016 #13
    @Simon Phoenix
    Thanks for the post. That was really insightful. If I understand you correctly, if we remove realism, then we don't have to go through some state to reach a final outcome. In your example you used B1 and B2 as the states between A and C. This produces a separate way of approaching probability in quantum mechanics than in the classical manner. If we approach it in this way, does it result in the probability observed through entanglement? Also, in the real world, what is the manifestation of states A and C?
     
  15. Jun 28, 2016 #14

    Simon Phoenix

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    I'm not sure I would agree with that gva. If you look at one of the clearest papers ever written on the Bell Inequalities by the master himself (John Bell)

    https://cds.cern.ch/record/142461/files/198009299.pdf

    Then you'll see mid-way through that paper there is a very general model of the experimental situation that is used to derive the inequality. We have 2 measurement devices that measure 'something' and the results of the measurement are yes/no (or 1/0 or up/down - whichever takes your fancy). We can also adjust the setting on the measurement devices. If we let A and B stand for the measurement results and a and b stand for the measurement settings of the respective devices then many runs of the experiment will allow us to measure P(A,B | a,b).

    The idea is to explain any correlation between the results by some extra variables - something is assumed to be happening behind the scenes, so to speak, that gives rise to the correlations. So, it is assumed, what we actually have is P(A,B | a,b, {hv}) where hv is this collection of 'hidden' variables.- which if we only knew them we could use to explain the measured statistics. Bell takes very great care to stress that no assumption is made about the nature of these hidden variables - or even the thing we're measuring - so we could have particles, fields or something hybrid entity. The hidden variables could be a collection of discrete things or functions - or even wavefunctions! No model of physics is assumed - in particular no quantum assumptions are used.

    If we then make some (on the surface) very reasonable assumptions about the properties of those variables then it can be shown that there is a constraint on the correlations. Since these are things we can directly measure we can test this if we can find a physical system that gives us these yes/no answers that might have correlations.

    These 'reasonable' assumptions are the realism and locality conditions which might be loosely expressed as :
    - things have properties independent of measurement
    - statistics 'here' are not influenced by settings 'there'

    Using these assumptions we get the constraint on the correlations that have to be satisfied by probabilities of the form P(A,B | a,b, {hv}) - and this is the celebrated Bell inequality.

    It is important to note that absolutely no assumption is made about particles or fields or the nature of the extra variables (other than these 2 reasonable assumptions). I have heard it argued that Bell makes the implicit assumption that we have particles - but I don't understand this myself since all we're connecting is measurement results using pretty straightforward probability models. The detectors just go 'ping' or 'ding' - and we just model the statistics of the pings and dings using good old probability functions. What causes the pings or dings is of earth-shattering irrelevancy.

    There is an implicit assumption - and that is that it is possible to make truly random choices of the measurement device settings.
     
  16. Jun 28, 2016 #15

    gva

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    Thanks for this very clear presentation.. the violations of Bell's Inequality means either realism or locality is wrong. If we assumed realism was wrong, then
    - things have no properties independent of measurement

    but the following can't be right

    - statistics 'here' are not influenced by settings 'there'

    I think the OP was saying both had to be wrong.. that is if realism was wrong, it didn't mean locality was right.. it's because the correlations can only occur if there are "non-local" influence. Or was it about semantics where locality is defined as the particles having objective properties and "non-locality" means they are communicating by signals? But non-locality can also mean the equations are non-local and causing the correlations. Are we being constraint to use the precise meaning of locality and limit the possibilities (trying to push us in one thought only)?
     
  17. Jun 28, 2016 #16

    Simon Phoenix

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    Well if we derive something using assumption X and assumption Y - and then we do an experiment and find our prediction doesn't match, then it means that at least one (and maybe both) those assumptions can't be correct.

    In the case of QM it is possible to set up a 'realistic' theory that reproduces the predictions of QM - but this theory (de Broglie/Bohm theory) is non-local in that the results of experiments in your lab depend on the configuration of everything in the universe, at least as I understand it. So dBB theory keeps 'realism' at the cost of discarding locality. In dBB theory we have a real particle with real properties (as I understand it) that is 'guided' by some mysterious complex-valued potential associated with it. The potential is constructed so that it agrees with the results obtained from the Schrodinger equation. I'm not a big fan of the dBB approach myself (although John Bell did seem to be) but it does give the same answers as standard QM as far as I can tell.

    Locality is one of those words that get used in different ways. In the context of Bell's inequality I like to think of it in the following way.

    Suppose we set up an experiment in lab A and another experiment in lab B. If the guy in lab B can set his device to measure x or y, then the results obtained in lab A should not depend on the choice of the setting x or y. This is how I define locality in the context of the BI.

    I think we would live in a very strange world indeed if that were not true - but some people do prefer some kind of non-local influence as an explanation of nature, rather than dispense with 'realism'. Dispensing with 'realism' is admittedly a bit odd too :-)

    If we define 'locality' in the above fashion then (standard) QM is a fully local theory. Results of measurements in (standard) QM do not depend of the settings of remote devices.
     
  18. Jun 28, 2016 #17

    Nugatory

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    You are trying to find more in Bell's theorem than is there. Bell starts with two assumptions (which are sometimes called "locality" and "realism", but are more precisely and mathematically stated in the proof) and derive an inequality. Experments show that this inequality is violated, so we can conclude that one or both of the assumptions is invalid.

    But that's all that we can ever learn from the theorem - it cannot tell us which of the assumptions are wrong. To do that we'd need to propose and experimentally confirm a theory of what is going on, and all that we'll ever get from Bell's theorem is a constraint on what properties that theory might have.
     
  19. Jun 28, 2016 #18

    gva

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    Results of measurements in (standard) QM do not depend of the settings of remote devices? But since Bell's Inequality is violated, then shouldn't it mean "Results of measurements in (standard) QM DEPEND of the settings of remote devices"? Or does anti-realism mean there is no remote devices in the first place? But standard QM is about anti-realism (no counterfactual definiteness). What is your idea about dispensing with realism? Hope someone can standardize what is the case about settings of remote devices and locality, realism label because different people have different semantics and some of us may be quite confused. Thank you.
     
  20. Jun 28, 2016 #19

    DrChinese

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    I can give you some examples of non-realistic interpretations. There are several classes of such. First, keep in mind that the opposite of objective realism is subjective realism. This is realism which is observer dependent. In other words, the observer is a part of the overall measurement context. In the classical world, there is objective realism. But not so in the quantum world. The observer's choice of measurement basis is relevant to the correlated outcomes.

    A. Many Worlds Interpretation (MWI) is non-realistic. Any measurement causes a "splitting" of worlds. This is a fairly popular interpretation.
    B. Time symmetric / retrocausal / acasual interpretations are non-realistic. There is not strict causality. In other words, the future and the past are part of an overall context that describes outcome probabilities. While this seems strange and counterintuitive, there are a number of experiments for which this is actually a very apt descriptive interpretation.

    Don't ask me HOW any of the above work mechanically; I have no clue and I doubt anyone else does either. :smile:
     
  21. Jun 28, 2016 #20

    DrChinese

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    There is a lot of semantics involved. In entangled state statistics, generally: Predictions for correlated results of measurements in (standard) QM DEPEND of the settings of remote devices (in the sense that the measurement context is not limited to a local region).
     
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