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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Selecting Pythagorean-Riemannian space as the metrical space for physical geometry requires justification

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Pythagorean-Riemannian metric structure is uniquely singled out by the requirement that congruence relations remain invariant under infinitesimal parallel transport.
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    • 2.Weyl himself demonstrated that only the Pythagorean metric satisfies the group-theoretic constraints imposed by the nature of physical coincidences and rigid body motion.
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    • 3.A selection principle grounded in invariance conditions constitutes genuine justification, not an arbitrary preference among equivalence classes.
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    Reason for 2 of 2
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    • 1.Helmholtz and Lie showed that the free mobility of rigid bodies, taken as an empirical constraint, uniquely determines Riemannian metric structure among possible spaces.
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    • 2.If physical geometry must accommodate the behavior of actual measuring instruments, Pythagorean-Riemannian space is not arbitrarily chosen but empirically necessitated.
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    • 3.The demand for justification presupposes a symmetry among metrical spaces that the Helmholtz-Lie theorem demonstrably breaks.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Pythagorean-Riemannian space is one among several possible metrical spaces
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    • 2.There is no a priori reason to prefer one equivalence class of homogeneous functions over another without argument
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