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Bell's Theorem and Counterfactual Definiteness

  1. Dec 7, 2009 #1
    Bell's Theorem and "Counterfactual Definiteness"

    Bell's Theorem and Aspect's experiments pretty much show that quantum theory is nonlocal--the violation of Bell's inequalities show that somehow the wavefunction is acting on the entangled particles faster than c.

    However, I've heard that Bell's inequalities violate either locality or "counterfactual definiteness."

    Now I'm very confused about what that means. Is that complete garbage or is there some possibility that quantum theory is local and we just need to abandon "counterfactual definiteness" instead? I thought quantum theory was already counterfactually non-definite, being as though you can't simultaneously measure complementary properties (like position and momentum) due to the Heisenburg uncertainty principle.

    What does "counterfactual definiteness" mean in that context?
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  3. Dec 7, 2009 #2
    Re: Bell's Theorem and "Counterfactual Definiteness"

    Actually, I thought Bell's theorem at best showed that a hidden variable theory which reproduced the results of QM would be non-local.

    I was under the impression that QM, as it stands, is compatible with locality - though there are some difficult issues about whether all interpretations of QM (in particular those with wave function collapse) are indeed non-local
  4. Dec 7, 2009 #3


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    Re: Bell's Theorem and "Counterfactual Definiteness"

    No, it shows that theories that are both local and realistic can not be correct.

    I am pretty sure that "counterfactual definiteness" refers to what is commonly knowns as "realism", realistic theories/interpretations basically assume that objects exist and have properties even when they are not measured.

    Hence, a violation of Bell's inequality is still compatible with local theories, as long as you give up realism. Of course it is also compatible with non-local, non-realistic theories (which some claim are supported by experiments)
  5. Dec 7, 2009 #4
    Re: Bell's Theorem and "Counterfactual Definiteness"

    Accepting the Wikipedia version of "counterfactual definiteness," this sounds correct. http://en.wikipedia.org/wiki/Counterfactual_definiteness:
    Compare this to the EPR criterion for reality, which is most likely where we get the physics/QM version of the term "realism" from:
    The two are equivalent because taking an actual measurement would disturb the system. To meet the EPR criterion, you must be able to speak about what the result of a measurement definitely would be if it were taken - you need counterfactual definiteness. Of course, actual reality may not necessarily conform to Einstein's view of what realism is, so be careful not to read too much into the terminology. Everyone thinks that the job of physics is to describe reality, or at least to model it as best as possible, even those who deny "realism."
    Last edited: Dec 7, 2009
  6. Dec 7, 2009 #5


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    Re: Bell's Theorem and "Counterfactual Definiteness"

    Alll of the above replies are correct, as is your viewpoint. The issue is the language more than anything. Some people don't like the term "realism" and prefer "counterfactual definiteness" instead. You could use the term "Is the moon there when no one is looking" and get the same effect (Einstein used this analogy). Any way you describe it, it has 3 characteristics: a) the specific observable is NOT measured; and b) it should have a specific value; and c) the probability of it having that value should be between 0 and 1.

    A lot of people assume QM must be non-local because of Bell; however, as you point out, simply accepting reality as matching the HUP avoids having to discard locality. Most folks think these positions are a matter or personal choice.
  7. Dec 7, 2009 #6
    Re: Bell's Theorem and "Counterfactual Definiteness"

    No, they don't show this.

    The locality condition (manifested as factorability of joint, entangled state representation) in Bell-type lhv formulations contradicts the statistical dependence between the separated data accumulations. However, this statistical dependence (which is a necessary byproduct of the pairing process) is entirely due to local transmissions/interactions vis, eg., coincidence circuitry.

    The Bell locality condition is also incompatible with standard qm formulation (not factorable, nonseparable) of joint, entangled state.

    But this doesn't make standard qm a nonlocal theory any more than violations of Bell-type inequalities indicate that Nature is nonlocal.
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