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    Parameter dependence is a necessary and sufficient condit... — Carmelics
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    Home/Modality & Possibility
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    Parameter dependence is a necessary and sufficient condition for controllable probabilistic dependence in models where measurement outcome probabilities depend only on the pair's state and apparatus settings

    Modality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.In such models, the probability of a distant measurement outcome depends only on the pair's state λ and the settings of the measurement apparatuses
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    • 2.Parameter dependence is defined as the dependence of the probability of the distant measurement outcome on the setting of the nearby measurement apparatus
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Outcome dependence can generate controllable probabilistic dependence even without parameter dependence, as Jarrett's original 1984 decomposition shows.
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    • 2.In models where outcome probabilities depend on distant outcomes (not just settings), signaling constraints are violated by outcome dependence, not parameter dependence alone.
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    • 3.Therefore parameter dependence is not necessary for controllable dependence, since outcome-dependent models can permit statistical correlations exploitable for signaling.
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    Reason against 2 of 2
    ?
    • 1.Shimony's distinction between parameter and outcome dependence presupposes a sharp separation that contextual hidden variable models, like those of Bohr, systematically blur.
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    • 2.In contextual models, apparatus settings and outcomes are not cleanly separable variables, making the probability function's domain ill-defined for the parameter/outcome distinction.
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    • 3.The sufficiency claim therefore fails because the model class it targets—where probabilities depend only on λ and settings—excludes precisely those contextual models where the condition's behavior is most contested.
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    Modality & PossibilityCausation

    Key Terms

    Apparatus settings(in experimental physics)
    The configuration or adjustable properties of the equipment or instruments used in an experiment.
    Measurement outcome(in physics and empirical science)
    The result you get when you perform an experiment or test—the actual number or observation you record.
    Necessary and sufficient condition(in logic and philosophy)
    A necessary condition is something that MUST be true for something else to happen; a sufficient condition is something that GUARANTEES it will happen. Together, they mean one thing absolutely requires and completely determines another.
    Pair's state(in quantum mechanics and physics)
    The complete description or condition of two related things (like two particles) at a given moment.
    Parameter(in physics and mathematics)
    A variable or setting that you can adjust or change in an experiment or model—like the knobs on a machine that affect what happens.
    Probabilistic(describing the method used)
    Dealing with likelihood and chances rather than certainty; things that are probably true based on odds and statistics.
    controllable probabilistic dependence(EPR/B experiment models)
    A condition that obtains when, for some pairs' states λ, L-setting l, R-setting r, and local physical quantities α and β, the conditional probability of the R-outcome given λ, l, r, α, and β differs from the conditional probability given λ, l, r, and β alone — i.e., Pλlrαβ(yr) ≠ Pλlrβ(yr)
    parameter dependence(EPR/B experiment models)
    The dependence of the probability of the distant measurement outcome on the setting of the nearby measurement apparatus

    Connections

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    Philosophy of Language1 linked

    Related

    In contextual models, apparatus settings and outcomes are not cleanly separable ...In models where outcome probabilities depend on distant outcomes (not just setti...In such models, the probability of a distant measurement outcome depends only on...

    Source

    AI-extracted1/3 agreementValid
    SEP: qm-action-distance
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    Four comments: (i) In controllable probabilistic dependence, the term 'probabilities of measurement outcomes' refers to the model probabilities, i.e., the probabilities that the states λ prescribe for measurement outcomes. (ii) Our discussion in this entry focuses on models of the EPR/B experiment in which probabilities of measurement outcomes depend only on the pair's state λ and the settings of the measurement apparatuses to measure certain properties. In such models, parameter dependence
    Extraction notes

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    Outcome dependence can generate controllable probabilistic dependence even witho...
    +4 moreShow less
    Parameter dependence is defined as the dependence of the probability of the dist...Shimony's distinction between parameter and outcome dependence presupposes a sha...The sufficiency claim therefore fails because the model class it targets—where p...Therefore parameter dependence is not necessary for controllable dependence, sin...

    Similar

    Parameter dependence is not a necessary condition for controllable pro...89%Parameter dependence is defined as the dependence of the probability o...89%If controllable probabilistic dependence is not washed out in such ens...82%In any empirically adequate model of the EPR/B experiment where the pa...82%
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