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I State Separability & CFD

  1. Jun 20, 2017 #1
    I am thinking of the usual "Alice and Bob" type scenario.

    If I choose to view the measuring instruments of Alice and Bob as "classical objects in spacetime", am I not then forced to say the following as well?

    1) The joint-state of the measuring instruments is separable throughout the whole of spacetime.

    2) The principle of CFD applies (validly) to the outcomes which those instruments can register.
     
  2. jcsd
  3. Jun 20, 2017 #2
    Of course, in the above, I assume NO retro-causality.
     
  4. Jun 22, 2017 #3
    I will improve upon the expression of my query, and answer it ... then add a little more.

    Consider the four conditions below:

    1) Alice and Bob have free choice of their instruments' settings.

    2) All influences which propagate within spacetime are limited by c.

    3) There are no retro-causal influences propagating within spacetime.

    4) The joint-state of the measuring instruments of Alice and Bob is separable throughout the whole of spacetime.

    Are these conditions sufficient to allow for CFD to apply (validly) to the outcomes which those instruments can register?
    ____

    I think the answer to the question is "No", because it is still possible to say:

    Although the joint-state of the instruments is 'separable', nonetheless, the outcome that each instrument registers (for the paired events) is 'nonseparably linked' to the setting of other instrument.

    I am making this statement on the basis of what @RUTA wrote not long ago:

    CFD - Counterfactual Definiteness, post #105
    ____

    Moreover, I would add this also:

    The above four conditions imply 'nonlocality' in the FTL sense.

    I think RUTA concurs on this:

    CFD - Counterfactual Definiteness, post #113
    ____

    ... Any comments?
    ____
    ____

    ASIDE:

    All four of the above conditions, as well as CFD, hold true in BM ... correct?

    (I'm sure @Demystifier can answer this.)
     
    Last edited: Jun 22, 2017
  5. Jun 23, 2017 #4

    As far as I can tell your condition 1 (free choice) has no justification in any theory, classical or quantum. BM is no exception. According to the theory once you specify the state of Alice and Bob some time before the experiment, their "choices" are predetermined, so you have no choices whatsoever.

    Andrei
     
  6. Jun 25, 2017 #5
    Thanks for that, Andrei. I should not have included "free choice" in the ASIDE.

    Let the ASIDE be restricted to conditions 2,3,4 only.
     
    Last edited: Jun 25, 2017
  7. Jun 25, 2017 #6
    Consider an interpretation for which

    the above four conditions hold true

    but

    the "principle of CFD" is invalid.

    Then

    according to that interpretation one must say

    Alice's outcome has an intrinsically 'nonseparable' dependency upon Bob's setting, and vice versa.

    ... Does anyone have anything to say about this statement?
     
  8. Jun 26, 2017 #7
    Okay, now I see what my problem is.

    The required conjunction is this:

    The joint-state of the measuring instruments of Alice and Bob is separable throughout the whole of spacetime;

    AND

    Alice's outcome has an no dependency upon Bob's setting, and vice versa.

    These two conditions, when taken together, are then sufficient conditions for one to be able to derive a Bell Inequality.
    _____

    Shortly, I will start a new thread.
    _____
    _____

    EDIT: The new thread is Seeing the essence of Bell.
     
    Last edited: Jun 26, 2017
  9. Jun 26, 2017 #8
    No. There is no CFD in BM. Or, more accurate, there is also a very restricted CFD in BM, namely the configuration is defined even if not measured. Everything else is contextual, that means, what is measured is not predefined by the system alone, but depends also on the configuration of the measurement device, thus, experiments which are not done have no result - the result would have to depend on a non-existing configuration of the non-existing measurement device.
     
  10. Jun 26, 2017 #9

    PeterDonis

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    That is not necessary, nor is it desirable.

    Which I have closed and deleted. Please keep the discussion here.
     
  11. Jun 26, 2017 #10
    But that thread was not about an exploration of the relationship between the notions of "state separability" and "CFD".

    It was about a particular perspective from which a Bell Inequality can be derived.

    The two topics are very distinct (but, of course, related).

    ... Are you sure you'd rather keep both topics in one thread?
     
  12. Jun 26, 2017 #11

    PeterDonis

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    They might seem that way to you, but to me they look close enough that they can happily coexist in the same thread.
     
  13. Jun 26, 2017 #12
    Let it be so.
    _____
    _____

    By hypothesis (in the thought experiment about "Alice and Bob"), the following is true:

    If Bob's setting would have been b' instead of b,

    then

    each of Alice and Bob would have obtained a definite outcome.

    _____

    Consider the following two conditions:

    1) The joint-state of the measuring instruments of Alice and Bob is separable throughout the whole of spacetime;

    2) Alice's outcome has no dependency upon Bob's setting, and vice versa.

    If both conditions, 1 and 2, hold true (in a given interpretation), then (according to that interpretation) the following principle is valid:

    α) It is 'admissible' to suppose that Alice's outcome for (the hypothetical setting) b' would have been the same as that for (the actual setting) b.

    Also, there is an axiom:

    β) It is 'admissible' to apply the theory to any 'admissible' scenario.
    _____

    The above two principles, α and β, can then be used to derive a Bell Inequality (when the theory in question is QT).

    THEREFORE (for any correct interpretation of QT):

    If condition 1 holds true,

    then

    condition 2 holds false.
     
  14. Jun 27, 2017 #13

    morrobay

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    You could check the validity of condition 2 ( locality + CFD ) : Given P ++ , P-- = 1/2(sin a-b/2)2 :
    Measure a stream of entangled particles with settings A = a and B = b. alternating A = a and B = b'. If outcome at Alice does not vary as B setting varies then Alice outcome is independent of setting at Bob
     
  15. Jun 27, 2017 #14
    Alice will obtain an apparently random sequence of spin up and spin down. Even if the individual values Alice gets are influenced by Bob's setting you cannot observe it.
     
  16. Jun 27, 2017 #15
    This makes no sense.

    Compare B = a and B = -a. The average outcome at Alice would be the same 50% up and 50% down. But in the first case this would be perfectly anticorrelated, in the second perfectly correlated. To think that in such a situation of perfect correlation/anti-correlation there is independence makes no sense.
     
  17. Jun 27, 2017 #16

    morrobay

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    Reread my post. I made no such reference to a = b or a = -b
     
  18. Jun 27, 2017 #17
    So what? These are particular examples of your more general case, not?
     
  19. Jun 27, 2017 #18
    Condition 2 is not the same as "locality + CFD". From the latter, one can derive a Bell Inequality. Condition 2 alone is insufficient.

    It is the conditions 1 and 2 together that are sufficient to establish a derivation of a Bell Inequality.

    But there is an important difference between the pair 1 + 2 versus the pair "locality" + "CFD". Each of 1 and 2 can stand on its own as a well-defined concept, whereas each of "locality" and "CFD" cannot. One parsing is 'clean'. The other is 'dirty'.

    Only when you think in terms of "particle properties" (as opposed to "measurement outcomes") does "CFD" become a well-defined concept.
     
  20. Jun 27, 2017 #19

    PeterDonis

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    These are stated in vague ordinary language. You should state them using precise math. What is a "joint state"? What does "separable" mean? What does "no dependency" mean?

    The great virtue of Bell's papers was that he gave explicit, precise mathematical conditions instead of vague ordinary language ones.
     
  21. Jun 28, 2017 #20
    Agreed.
    Let us see just how sharply those concepts can be defined, and then look back to see what will stand, what will fall, and what (if anything) will remain fuzzy.
    _____

    Begin with the notion of 'separability'.

    Let X and Y be two systems with associated state spaces SX and SY.

    Now, consider X and Y together as a single system and designate this (combined) system as the "joint-system" consisting of X and Y.

    Then, the "joint-system" is said to be 'separable' with respect to X and Y iff

    a) The state space of the joint-system is given by

    SX x SY (Cartesian product);

    and

    b) The "state of X" is u and the "state of Y" is v

    iff

    the "joint-state of X and Y" is (u,v).

    This "joint-state" is said to be 'separable' with respect to the subsystems X and Y.
    _____

    Let the state space of Alice's instrument be given by the Cartesian product of the set of unit vectors in R2 with the set {0, U, D}.

    The unit vector represents the 'setting'.

    The elements of the other set represent the 'values':

    0 - ready for registration ,

    U - an "up" has been registered ,

    D - a "down" has been registered .

    Likewise, for Bob's instrument.
    _____

    ... I will stop here for any comments and to think more about the next stage of clarification.
     
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