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    Carmelics

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    Made withinDC&Austin
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    Perspectives
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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The set P_f of freely falling particle paths cannot be used to establish the differential structure of spacetime without circularity

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Weyl's own constructive program shows P_f can be identified via purely topological and affine criteria prior to any smooth atlas.
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    • 2.The characterization of free-fall paths requires only continuity and extremal properties, not a pre-given differential structure.
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    • 3.Ehlers, Pirani, and Schild (1972) demonstrated that projective structure from particle paths logically precedes and grounds the differential manifold.
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    Reason for 2 of 2
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    • 1.Coordinative definitions in the tradition of Reichenbach permit physical structures like P_f to simultaneously constitute and constrain geometric structure without vicious circularity.
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    • 2.The circularity objection conflates epistemic ordering with ontological grounding—P_f can be ontologically prior even if epistemically accessed via provisional coordinates.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.P_f is a subset of P that consists of paths of spherically symmetric, electrically neutral particles
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    • 2.P_f can only be properly characterized after a coordinate system (differential structure) is available
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    • 3.Using P_f to establish differential structure would require differential structure to already be in place
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