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    Home/Original/inverse
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    Inverse View

    It is not the case that Orthogonality in R3 corresponds to orthogonality in physical space when R3 is used to give an argument for H3.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 2 of 2
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    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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