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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that The Gleason-type argument tacitly assumes noncontextuality.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Gleason's theorem derives the Born rule from frame functions defined on the full Hilbert space lattice, not from value assignments to commuting sets.
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    • 2.The continuity and additivity constraints in Gleason's proof are structural features of the lattice, not assumptions about how a single observable behaves across contexts.
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    • 3.Therefore the noncontextuality in Gleason's argument is a theorem consequence, not a tacit premise smuggled in through measurement context selection.
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    Reason for 2 of 2
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    • 1.Pitowsky and Appleby have shown that Gleason-type results can be reconstructed from purely measure-theoretic constraints without invoking hidden-variable value assignments at all.
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    • 2.An argument that never posits definite pre-measurement values for observables cannot be said to assume noncontextuality, since noncontextuality is a constraint on such pre-existing values.
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    • 3.The charge of tacit noncontextuality conflates the operational content of quantum probability with the metaphysical commitments of hidden-variable reconstructions.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.The Gleason-type argument derives restrictions on value assignments only for sets of compatible observables.
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    • 2.One and the same observable can belong to different commuting sets.
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    • 3.The argument requires that the observable receives the same value regardless of which commuting set it is considered in.
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