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    The Gleason-type argument tacitly assumes noncontextuality. — Carmelics
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    The Gleason-type argument tacitly assumes noncontextuality.

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    1 reason for
    2 reasons against

    Reasons For

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    Reason for
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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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    Reasons Against

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    Reason against 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 against 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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    Related

    An argument that never posits definite pre-measurement values for observables ca...Gleason's theorem derives the Born rule from frame functions defined on the full...One and the same observable can belong to different commuting sets.Pitowsky and Appleby have shown that Gleason-type results can be reconstructed f...
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    Requiring the same value across different commuting contexts is an assumption of...The Gleason-type argument derives restrictions on value assignments only for set...The argument requires that the observable receives the same value regardless of ...The charge of tacit noncontextuality conflates the operational content of quantu...The continuity and additivity constraints in Gleason's proof are structural feat...Therefore the noncontextuality in Gleason's argument is a theorem consequence, n...

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    SEP: kochen-specker
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    After having offered his variant of the argument against HV theories from Gleason’s theorem, Bell proceeds to criticise it. His strategy parallels the one against von Neumann. Bell points out that his own Gleason-type argument against arbitrary closeness of two opposite-valued points presupposes non-trivial relations between values of non-commuting observables, which are only justified given an assumption of noncontextuality (NC). He proposes as an analysis of what went wrong that his own argume
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    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit