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    Physical space orthogonality is defined by spatial orient... — Carmelics
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    Challenges→Orthogonality in R3 corresponds to orthogonality in physical space when R3 is used to give an argument for H3.

    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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    Key Terms

    Conceptually irreducible(used to emphasize a deep philosophical difference)
    Something that cannot be broken down or explained in terms of simpler concepts—it's fundamentally different in kind, not just degree.
    H3(Mathematical framework for spin-1 systems)
    A three-dimensional Hilbert space in which orthogonality can be put in correspondence with orthogonality in physical space via choice of observable.
    Measurement apparatus(used in physics to discuss how we gather information)
    The instruments or tools scientists use to observe and measure things, like a thermometer or a scale.
    Orthogonality(modal metaphysics)
    In this context, the idea that two things are completely independent or unrelated to each other (literally means perpendicular in geometry).
    Physical space

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    (distinguishing real-world behavior from mathematical representation)
    The actual, real three-dimensional world where things physically exist and move around, as opposed to abstract mathematical spaces.
    Quantum state(quantum mechanics)
    A complete mathematical description of everything we can possibly know about a quantum system (like an electron or photon).
    Spatial orientation(used in discussing measurement)
    The direction or angle at which something is positioned—like whether a tool is pointing up, down, or sideways.
    incompatibility(Characterized as an apparently negative notion, which creates a problem for the positive truth-maker proposal.)
    A relation that obtains between two states when it is not possible for them to obtain together.

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    Truth & Knowledge1 linkedModality & Possibility1 linked

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    Orthogonality in R3 corresponds to orthogonality in physical space when R3 is us...

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