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    Orthogonality in R3 corresponds to orthogonality in physi... — Carmelics
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    Orthogonality in R3 corresponds to orthogonality in physical space when R3 is used to give an argument for H3.

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The same reasoning that links H3 orthogonality to physical space orthogonality applies to R3.
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    • 2.R3 can be considered in order to give an argument for H3.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.R3 is a real Hilbert space lacking the complex structure of quantum mechanics, making its geometric orthogonality physically distinct from H3 orthogonality.
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    • 2.Kochen-Specker proofs require the full unitary symmetry group of complex Hilbert space; R3's orthogonal group is a proper subgroup with fewer symmetries.
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    • 3.Mermin and Peres demonstrated that KS arguments require complex amplitudes for spin-1 systems, so importing R3 orthogonality into H3 conflates distinct mathematical structures.
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    Reason against 2 of 2
    ?
    • 1.Physical space orthogonality is defined by spatial orientation of measurement apparatus, while H3 orthogonality encodes quantum state incompatibility, a conceptually irreducible distinction.
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    • 2.Bub and Clifton showed that the operational content of quantum orthogonality relations cannot be recovered from classical spatial geometry without additional interpretive assumptions not present in R3.
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    Related

    Bub and Clifton showed that the operational content of quantum orthogonality rel...Kochen-Specker proofs require the full unitary symmetry group of complex Hilbert...Mermin and Peres demonstrated that KS arguments require complex amplitudes for s...Physical space orthogonality is defined by spatial orientation of measurement ap...
    +3 moreShow less
    R3 can be considered in order to give an argument for H3.R3 is a real Hilbert space lacking the complex structure of quantum mechanics, m...The same reasoning that links H3 orthogonality to physical space orthogonality a...

    Similar

    The same reasoning that links H3 orthogonality to physical space ortho...90%The correspondence between mathematical and physical orthogonality is ...86%By choosing an observable O that selects Sx2, Sy2, Sz2 simultaneously,...84%An earlier example was given without any correspondence between mathem...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: kochen-specker
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    However, the choice of a specific O that selects observables Sx2, Sy2, Sz2 at the same time selects three orthogonal rays in physical space, namely by fixing a coordinate system ±x, ±y, ±z (which defines along which orthogonal rays the squared spin components are to be measured) in physical space. So now, by choice of an observable O, there is a direct connection of directions in space with directions in H3: orthogonality in H3 now does correspond to orthogonality in physical space. The same hol
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

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